THE UPPER MANTLE TRANSITION ZONE BENEATH SOUTHERN CALIFORNIA by NATHAN ALAN SIMMONS, B.S A THESIS IN GEOSCIENCE Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Approved
Accepted
August, 2000
T 3
ACKNOWLEDGMENTS
/^O /31 y(spinel) -> (Mg-wiistite + perovskite)
(1.1)
where the transformations (denoted with arrows) occur at 410, 520 and 660 km, respectively.
These phase boundaries are summarized in Akaogi et al. (1989) and
illustrated in Figure 1.4. On the other hand, studies conclude that the gamet mineralogical system contributes and may even dominate the transformation boundaries in some cases. Vacher et al. (1998) discusses the importance of the non-olivine components in the upper mantle and concludes that significant gamet transformations into ilmenite and perovskite stmctures occur near the same depths as the olivine components. The combined olivine and gamet phase boundaries are explored by Gasparik (1997) and are illustrated in Figure 1.5. Gasparik (1997) discusses the possibility of mineralogical heterogeneity created by separation of the gamet and olivine components during the evolution of the upper mantle. Ringwood (1994) concludes that delamination of subducted slabs may occur creating a "gametite" layer at the base of the upper mantle. This process is illustrated in Figure 1.6. These studies parallel each other as both consider some layering effects in a combined olivine-gamet
mineralogical
system.
However,
olivine
component
transformations are still considered to be the dominant processes in the transition zone. The stability boundaries associated these phase transformation are typically defined by the corresponding Clapeyron slopes.
The Clapeyron slope describes the
temperature and pressure conditions required for a transformation and is simply the derivative of (change in) pressure with respect to temperature:
(^d^dP/dT
(1.2)
where the subscript d represents the approximate transformation depth. Calculated values for the major Clapeyron slopes are listed in Table 1.1. The estimated average Clapeyron slopes are 2.4 and -2.9 MPa/°C for the 410- and 660-km discontinuities (assuming these are phase transformations). These measurements indicated that these two transformations have approximately equal but opposite slopes.
Positive slopes are indicative of
exothermic phase transformations and negative Clapeyron slopes are indicative of endothermic transformations.
A transformation boundary with positive slope would
shallow in colder regions (such as subduction zones) and deepen in warmer regions (zones with thermal upwellings).
Boundaries with negative slopes respond in the
opposite manor to temperature anomalies in the upper mantle.
Combining these
transformations, the transition zone would thicken in cold regions and thin in warmer regions as long as the temperature anomalies are vertically coherent through the transition zone.
Temperature anomalies can therefore be detected by simply determining the
stmcture and/or thickness of the transition zone.
Discontinuity topography can be
compared to temperature anomalies mferred by velocity stmcture to test the hypothesis that these features are phase transformations rather than abmpt chemistry changes.
1.2.2 Convection Implications Implications of the upper mantle transition zone in mantle dynamics are summarized in King (1994) and Davies (1999). The positive Clapeyron slope associated with the 410-km discontinuity is believed to assist mantle convection while the 660-km
discontinuity is believed to inhibit mantle convection. This is best demonstrated by considering the subduction of a lithospheric slab since the subduction process is a major element in Earth-scale convection (Figure 1.7). As a slab approaches a transformation boundary with a positive Clapeyron slope, the negative temperature anomaly associated with the slab creates a local temperature anomaly about the discontinuity. In this situation, the material above the discontinuity is forced to transform into the denser stmcture. The negative buoyancy associated with the denser material causes the material to sink thereby driving convection. On the other hand, a boundary with a negative Clapeyron slope acts to inhibit the slab from penetrating since the negative temperature anomaly causes the surrounding material to revert to the less dense stmcture. The less dense material creates a local buoyant effect that slows the subduction process and therefore the convection process. There is a tradeoff between the subduction slope and Clapeyron slope that determines if the slab is allowed to penetrate or remain at the upper-lower mantle boundary. The same logic can be applied to a plume rising through the transition zone. In this case, an endothermic transformation would inhibit convection while the boundary would shallow with the plume. If the Clapeyron slope for the endothermic reaction is steep enough, convection may be completely hindered in this situation.
1.3 Tectonic History of Southem Califomia The tectonic framework of southem Califomia is representative of a long history of active tectonics generatmg a complex continental margin. Successive subductiondriven arc collisions as well as subduction polarity reversals and oblique transform plate
motions along the westem margin are possible examples of such complex tectonic events that combine to create the present tectonicframeworkof southem Califomia. Although tectonic evolution may not directly contribute to the stmctural components of the upper mantle transition zone, it should be examined since the tectonic contribution is uncertain. Preceding late Jurassic time, several subduction and collision sequences generating terrain captures and possible subduction polarity reversals occurred along the westem margin of North America consuming oceanic plates. Plate tectonic models summarize this process (Moores and Twiss, 1995; Ingersoll, 1998). In late Jurassic time, the Nevadan orogeny occurred as an oceanic arc complex approached and collided with the westem margin of prehistoric North America. After the consumption and/or capture of the arc system components, subduction of the Farallon oceanic plate continued beneath North America in what was previously the backarc region of the deformed magmatic arc (Schweickert and Cowan, 1975). From the latest part of the Jurassic to late Cretaceous, a simple arc-trench system existed along the westem margin as the Farallon plate continued to subduct (Drewes, 1978; Coney, 1980; Ingersoll, 1998). During this period, the magmatic arc progressed inland into North America (Schweickert and Cowan, 1975; Ingersoll, 1979). Rapid subduction of the Farallon plate occurred through Eocene time generating "flat-slab" subduction beneath the North American plate, which is believed to be associated with the Laramide orogeny (Coney, 1976; Dickinson and Snyder, 1978; Bird, 1984, 1988; Engebretson et al., 1985; Cross, 1986; Spencer, 1996). The subsequent increase of the North American plate velocity over the Farallon plate provided progressively younger, therefore more buoyant, oceanic cmst to enter the subduction
zone.
This probably contributed to the hypothesized "flat-slab" subduction process
(Engebretson and Thompson, 1984). Soon after these events, Neogene tectonics took over as the Farallon slab began subducting at a steeper angle.
The East Pacific Rise subsequently approached the
western margin of the North American plate. This process slowed the subduction rate as positively buoyant material near the spreading center approached the subduction zone. The Farallon plate was eventually consumed and the western margin progressively became a dextral transform margin along the San Andreas Fault system (Atwater, 1970). This dominating dextral motion, possibly due to Pacific and North American plate interaction, eventually generated an extensional region consisting of oblique rifts in the Gulf of California and the Salton Trough that currently resembles an active spreading center. Plate circuit reconstmction has shown that the Pacific plate has moved 1165 kilometers northwestward relative to the North American plate in the last 28.3 million years. It has also been shown that the plate velocity vector has become more northerly during this period resulting in a large-scale plate rotation sequence.
Subducting
fragments of the Farallon slab, in conjunction with transform motion, have also generated "slab windows" under the North American plate that lack subducted oceanic material (Atwater and Stock, 1998).
It is presumed that the Farallon plate fragments continued
subducting around the slab-free zone.
Material from the asthenosphere would have
subsequently risen into the gap(s) and caused a convection cell much like that of a spreading center or continental rift zone (Stewart, 1977). These processes created the present day tectonic stmcture of southem Califomia. 8
The westem North American margin has undergone complex tectonic processes for millions of years. It is unclear whether or not these tectonic processes have affected the composition or stmctural components of the upper mantle transition zone beneath southem Califomia. However, the regional tectonic history and tectonic elements should be considered when interpreting features in the transition zone.
1.4 Seismic Data from Permanent Broadband Stations Broadband data from 21 seismic stations were obtained from the Incorporated Research Institutes for Seismology (IRIS) through the Data Management Center (DMC) coordinated by the University of Washington in Seattle. The southem Califomia stations used in this study were previously a subset of the Global Seismographic Network (GSN) data set. The Southem Califomia Seismographic Network (SCSN) is the newly formed network that now includes these stations. Station names and locations are listed in Table 1.2 and a map of these stations is illustrated in Figure 1.8. Some of these stations have provided up to ten years of earthquake recordings making the entire data set very large. To reduce the data volume, only the recordings from earthquakes with a minimum body wave magnitude (Mb > 5.5) were obtained. The data were subsequently limited according to overall quality by visually inspecting each three-component seismogram with various bandpass fdters applied. After this process, we were left with a total of 14,587 three-component seismograms.
Table 1.1 A List of Clapeyron slopesfromLaboratory Measurements. Reference Akaogi etal. (1989) Katsura and Ito (1989) Ito and Takahashi (1989) Ito etal (1990) Chopelas(1991) Akaogi and Ito (1993) Bina and Helffrich (1994)
C410 (MPa/°C) C660 (MPa/°C) 1.5 ±0.5 2.5 ±1.0
2.95 ± 0.05
-2.8 -4.0 ± 2.0 -2.4 ± 0.4 -2.9 ± 0.3 -2.4 ± 0.5
2.4
-2.9
2.8 ±0.1
Mean
10
Table 1.2 List of Seismic Stations Used in this Study. STATION NAME
ABBREVIATION LATITUDE
Barrett Dam Calabasas Columbia College Cottonwood Creek Glamis Goldstone Lake Geothermal Program Office Lake Isabella Jamestown Mammoth Lakes Needles Osito Adit Pasadena Pinyon Flat Observatory Rancho Palos Verdes Santa Barbara San Nicolas Island Superstition Mountain Seven Oaks Dam University of Southern CA Victorville
32.68°N 34.14°N 38.03°N 36.43°N 33.05°N 35.30°N 35.64°N 35.66°N 37.92°N 37.63°N 34.82°N 34.61°N 34.14°N 33.61°N 33.74°N 34.44°N 33.24°N 32.94°N 34.10°N 34.01°N 34.56°N
BAR CALB CMB CWC GLA GSC GPO ISA JAS MLAC NEE OSI PAS PFO RPV SBC SNCC SMTC SVD
use VTV
11
LONGITUDE ELEV(m) 116.67°W 118.62°W 120.38°W 118.08°W 114.82°W 116.80°W 117.66''W 118.47°W 120.42°W 118.83°W 114.59°W 118.72°W 118.17°W 116.45°W 118.40°W 119.71"W 119.52°W 115.72°W 117.09°W 118.28°W 117.32°W
496 276 719 1553 514 954 735 817 425 2134 139 706 257 1245 64 61 227 3 574 17 812
•7 km Peridotite zone
1 Crust L-v Mohorovidc "35 knv
(Upper mantle)
Lithosphere
B
350 km
Upper Mantle
410 km discontinuit)! Transition zone
(Transition zone) ' 660 km discontinuity
750 km
— 1000 km —
(Lower mantle) Perovskite zcme
D*
Lower Mantle
-2750 km
(D") 2889 km
CBL
Core-mantle boundar]
Outer Core Inner core boundary 5154 km-
IrmerCore
Figure 1.1. Components Defining the Upper Mantle Transition Zone. Source: Taken directly from Davies (1999).
12
I
volcano
trench
magma Continental crust
continental crust mantle flow
Mantle flow
Figure 1.2. Overview of Mantle Convection and Tectonic Processes.
13
•8
I"a o
I
o
u
200
400
600
800
1000
Depth (km)
Figure 1.3. Compressional Velocity (dashed lines) Compared to Mineral Velocities. The "ol" stands for olivine and the "Mg-pv" stands for magnesium perovskite. Source: TakenfromAnderson (1989).
14
Temperature (*'C) 0
500
1000
1500
300
400
E 500 Q.
a 600
700
800
J
I
I
I
•
'
'
'
Figure 1.4. Stability Fields for Olivine Component Transformations. Source: Edited from Akaogi et al. (1989).
15
2000
10
15 Pressure (GPo)
Figure 1.5. Transformation Boundaries for a Mixed Olivine/Garnet System. "01" is olivine; "Ga" is gamet; "Bt" is P-spinel; "Sp" is y-spinel; "II" is ilmenite; "Pv" is perovskite; "Mw" is magnesiowustite. Source: Adapted from Gasparik (1997). 16
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Figure 3.8. Conversion Points for Each Phase for the 3105 Total Receiver Functions Used.
56
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Be ,«i 5 3 Xq SMO||Bqs A;inui;uoosip UDf 099 sq; Z UOUBOOJ ;V a puBd ui UAvoqs SB ;u9piA9 OS|B SI 9jn;onj;s X;po|9A puB X;inui;uoosip UDi-099 9q; u99M.;9q UOI;B|9JJO3 ((9^1^110)^ '•— (9uiAip)x) '91) 9dois uojX9dBi3 9Ai;isod B q;iM UOUBUUOJSUBJ; 9SBqd B q;iM ;U9UI99JSB 9uoj;s Ul 9JB S9jn;B9j 9S9qx UDJ $3-03- su9d99p UDj-Qlt? 9q; qoiqM ;B AJBUIOUB X;poi9A-Moi B SMoqs \ UOI;BOO| puB (S9pjp) UDf-Ql^ MO||Bqs B o; spuods9Jjoo (oniq) uoi§9J A;popA-q9iq gq; 9J9qM SMoqs (sj9:5fjBui ^OBjq PHOs) SUOI;B;S omisps j o J9;snp 9SU9P 9q; JB9U X uouBooq sppoui OM; 9q; JO uouBpxioo Q £ 9q; SMoqs (p) uouBqjnviod X;popA 9q; o; 9jn;3ru;s UDi-Qlt^ sq; SuuBduioo dBui y ^ S3~ SuiMO||Bqs Aq (p9J ui UAvoqs) 9jn;B9j (9jn;BJ9dui9; qSiq '90U9q) A;popA-M.oi 9q; o; spuods9j X;inui;uoosip UD{-099 9qx ;s9M-;sB9 9uipu9j; No3>£ 9pn;i;B| ;B 9jn;onj;s X;inui;uoosip U D | - 0 9 9 9q; S9;Bj;suom9p D UOI;O9S (9n|q ui uMoqs mnmpcBui A;popA 9ABM-
p and y-> (perovskite +
magnesiowustite) in the olivine system, then regional temperature variations can be calculated based on published Clapeyron slopes.
5.1 Imaging the Transition Zone 5.1.1 Receiver Function Processing and Stacking For the regional interpretation, 3D images were generated for several combinations of stacking parameters as discussed in Chapter III. We pre-processed receiver functions for Pds, PPds, PcPds and PKPdfds events with a 0.3 Hz Gaussian filter. Stacking parameters must be chosen so that the image will have laterally coherent features over large regions. However, the assumption of lateral continuity within the stacking algorithm destroys signal from vertical stmcture if the search radii are allowed to be too large. In some locations, this is inevitable as there are geographical windows lacking significant amounts of data.
72
Evaluation of several 3D images created with different stacking parameters was necessary to determine the optimal tradeoff between lateral coherency and vertical stmcture resolution for the data set.
The best 3D image was produced using the
following parameters:
Minimum number of contributing stations per node:
6
Minimum number of traces per node:
100
Maximum search radius about a node:
1.0°
Sample increment (node spacing):
0.2°.
With these parameters, some stmctures are still difficuh to interpret. For this reason, other 3D images, created with less stringent constraints, were used in conjunction for interpretation purposes.
By relaxing these constraints, we sacrifice resolution for
coverage. In the most data rich areas, stacking bins were much smaller than implied by the above bounding constraints.
5.1.2 Resolution Issues within the Transition Zone Due to ray path geometries, conversion points at 660 km are distributed more suitably (uniformally and contmuously) for stacking than conversion points near 410 km. Conversion points near the 410 km depth tend to occur in clusters causing lateral weighting problems since our algorithm attempts to use data from a fixed number of stations for each stacked value. These weighting problems make the 410 km region more difficuh to interpret over large areas than the stmctures near the base of the transition zone. 73
Figure 5.1 shows the number of traces required in each node at 410 and 660 km for the stacking parameters listed above. The number of traces used in each cell is more erratic for 410 km (i.e.. Figure 5.1a). Near Los Angeles (LA), -400 receiver fimctions are stacked in a confmed region. Similarly, -350 receiver functions are used in stacks in extreme southem Califomia. Other regions, however, use 90-100 traces. The number of traces used at 660 km is shown in Figure 5.1b. At 660 km, the data coverage is more uniform (100-110 receiver functions per bin) and therefore has fewer lateral weighting problems than stacks at 410 km. The required search radii for the primary stacking constrains are shown in Figure 5.2. At 410 km (Figure 5.2a), the search radii range from 0.3° to the maxunum of 1.0°. The area with the smallest search radii is just southeast of Los Angeles (LA) where 6 stations and 100 receiver fimctions were found within a small region.
In extreme
southem Califomia, however, the search radii increase dramatically at 410 km. At 660 km (Figure 5.2b), the search radii are distributed more appropriately. The search radii are -0.4° throughout most of the region including extreme southem Califomia.
5.2 Image Interpretation of the Transition Zone 5.2.1 3D Image Cross Sections An east-west cross section through the 3D image is shown in Figure 5.3. The 410 km discontinuity exhibits a depression of-15 km centered at 116.5°W (-116.5). This is expected given the negative velocity perturbation (displayed in Figure 5.3b) and the exothermic transformation in the olivine system (a-> p stmctures). Stmctures near the base of the transition zone are more complex. The gamet system transformation (-710 74
km) appears in this cross section (gt) and interacts with the olivine discontinuity (-660 km) to some degree. Also, since the search radii are relatively large in this region (-0.9°), smearing of amplitudes from east to west destroy the apparent stmcture near 118°W as indicated by the arrows in Figure 5.3a.
This interpretation is in strong
agreement with the velocity perturbation model shovm m Figure 5.3b. A cross section at 33° (Figure 5.4) shows small-scale stmctures in a region with a complex velocity setting.
The 410-km discontinuity shallows ~15km near 118°W
(Figure 5.4a). Inspection of the velocity model (Figure 5.4b) reveals this zone to be seismically fast suggesting low temperatures. The 660-km discontinuity exhibits more low-wavelength stmctures as would be expected given the sampling distribution at this depth. There appears to be a small-scale stmctural high on this discontinuity near 117°W (Figure 5.4a). After observing the velocity model (Figure 5.4b), it seems likely that this stmcture may be a small-scale (-120 km) feature and that its vertical extent may be sharp and dramatic. A crossing section at 117.2°W supports the existence of this smallscale stmcture (Figure 5.5). The arrow demonstrates that the discontinuity shallows from south to north creating an apex near 33°N. Another important visible feature observed in Figure 5.4 is the separation of the 660-km discontinuity and the gamet transformation (gt). The arrow near 115°W in Figure 5.4b labels this separation within a seismically slow zone. This anticorrelation effect is what is expected given the mbced olivine/gamet system in a warm region as discussed in Chapter IV. Figure 5.6 shows an east-west cross section at 34.2° crossing the center of the high-velocity zone at 410 km. The 410-km discontinuity shallows -30 km near 118.5°W 75
where the velocity perturbation is +0.5% (Figure 5.6b).
This feature is not readily
apparent in the cross section smce the stmcture is not completely represented due to smearing. However, a north-south cross section at 118°W (Figure 5.7) supports the interpretation. In this portion of the 3D image, the feature is readily apparent in the figure.
Near 660 km, a low velocity stmcture exists (Figure 5.6b).
The 660-km
discontinuity depth shallows as expected in a low-velocity (high-temperature) zone. This feature is imaged easily due to the sampling and the size of the velocity stmcture. This cross section demonstrates that the 410- and 660-km discontinuities will not always be anticorrelated. The high-velocity zone near 410 km is adequately imaged in an east-west cross section at 35°N (Figure 5.8). The feature is detectable as a resuh of the relatively small search radii (-0.4°) used (Figure 5.8a). The shape and extent of the high-velocity zone in this region can be seen in Figure 5.8b. The shape of the interpreted stmcture matches the shape of anomalies in the velocity model stmcture accordingly (centered at 118°W).
5.2.2 Horizon Mapping and Velocity Model Comparison The depths to the 410- and 660-km discontinuities are completely mapped for southem Cahfomia in Figures 5.9 and 5.11 respectively. Both discontinuities exhibit a shallow trend near Los Angeles extending to the northem portion of Baja, Califomia. In this region, the discontinuities are correlated due to the velocity perturbation gradient that exists within the transition zone. The 410-km discontinuity deepens dramatically from the Mojave Desert extending into Arizona. However, this region does not have very good coverage at 410 76
km. Another deep trend extends from Arizona through the Salton Trough region. The stmctural trends at 410 km also match the velocity stmcture well (Figure 5.10). Other than the stmcture beneath Los Angeles, a stmctural high exists on the 660km discontinuity offshore from Califomia (south of Los Angeles, Figure 5.11). Also, a stmctural low exists just east of this feature near the Gulf of Califomia.
Another
prominent feature is a stmctural low east of the stmctural high beneath Los Angeles. These stmctural trends match the Dueker (personal communication) velocity perturbation model, especially beneath the Los Angeles region (Figure 5.12). 5.3 Temperature Calculations Using published results for the Clapeyron slopes for the olivine transformations, we calculated expected thermal anomalies associated with the interpreted stmctures at 410 and 660 km depths. See Chapter I for the range of results for the Clapeyron slopes. Since we observe -40 km of vertical stmcture on the discontinuities, we chose to use the upper end of the range of Clapeyron slopes (Q. We have used the slope determined from Bina and Helffrich (1994) for the 410-km:
^410 = 2.9 MPa/°C.
(5.1)
For the 660-km, we chose the upper-end value determined by Mao et al. (1991):
^660 =-2.9 MPa/°C.
(5.2)
77
Using the defmition of Clapeyron slope and the following formulation from Turcotte and Schubert (1982), the temperature anomaly can be determined:
5P = p g 6 z .
(5.3)
Solving for temperature anomaly gives:
6T = p g 5 z / ; .
(5.4)
Using this solution, a 20 km stmcture would give a -236°C temperature anomaly. Also, using an equation from Anderson (1989), we calculated the temperature variations from the velocity model:
5T = 6 Vp / (4.1 ± 1.1 X 10-^ km/sec/°C).
(5.5)
Comparison of the stmcture- and velocity-derived temperature variations is illustrated in Figure 5.13. The calculated temperature distribution range for the observed stmctures is higher than that of the velocity-derived temperatures. This could obviously be an effect of the uncertainty of the Clapeyron slopes or the velocity conversion factor. On the other hand, it should be expected that temperature ranges from the observed stmctures would be greater due to the increased resolution. The smoothmg of the velocity perturbation model could diminish significant velocity contrasts. Observed stmctures are identified in the distribution plots (Figure 5.13).
78
5.4 Conclusions from Regional Observations The 410- and 660-km discontinuities are interpretable over most of the study area in southem Califomia. The stmctural/velocity relationship seen in these images generally match what would be expected from phase transformation boundaries in the olivine system. Temperature anomaly distribution inferred from the topography of these two discontinuities is comparable to the distribution calculated from an independent velocity model.
This provides evidence that the interpreted discontinuity topography can be
achieved with the inferred temperature anomalies. It is obvious from the above discussion that small-scale temperature anomalies (inferred from the velocity model) are not vertically coherent across the transition zone of southem Califomia. Small-scale estimates of transition zone thickness beneath southem Califomia would, therefore, be meaningless with regard to estimates of mantle temperature. Other regional scale studies have found that thermal anomalies estimated from transition zone thickness on a regional scale do agree with relationships expected based on regional tectonics. As a resuh, we suggest that there may exist localized thermal anomalies within the transition zone that are not related to continental scale tectonics. Altemately, we must consider that thermal anomalies based on estimates of transition zone thickness alone, must be scmtinized when we consider regional or global mterpretations.
79
350
300 37.5
250
-200 35.0
32 5 h
30.0 N 120.0 W
117.5'W
115.0'W
112.5 W
150
37.5
- 100
35 0
;^
m 50 32.5 N
30.0 N 120.0'W
117.5'W
115.0 W
112.5 W
Figure 5.1. Number of Traces Per Cell for the Stacked Image at 410 km (a) and 660 km (b). 80
|1.2
a
1 1
09
08
07
06 32.5 ^
05
0.4
30.0' N
10.3 i1.2
ri.i
l0.9
10.8
|0.7
0.6 32.5>
0.5
0.4
30.0
120.0 W
115.0°W
117.5 W
1125 W
l03
Figure 5.2. Search Radii at 410 km (a) and 660 km (b) Used for the Stackmg Constraints.
81
-08
106
05
-122
-121
-120
-119
-118
-117 -116 Longitude
-115
-114
-113
-112
100
200
300
400Q. V •a
--0.1
500
600'¥
700 i
800
122
-121
laMmiMMMiBKsaBiseisaJJ saaw!taMtHi^^.KA^mmmmm -120 -119 -118 -117 -116 -115 -114 -113 Longitude
-112
-0 5
Figure 5.3. East-west Cross Section at 32° with the Search Radii and the Velocity Perturbation (%) in the Backgrounds (a and b respectively).
82
'08
700 -. -122
-121
-120
-119
-118
-117 -116 Longitude
-115
-114
-113
-112
10.2 0.1
-0.1 1-0.2 -0 3
Figure 5.4. East-west Cross Section at 33° with the Search Radii and Velocity Perturbation (%) in the Backgrounds (a and b respectively).
83
i0.5
0.4 0.3
lo2
I0.I
[0 f-0.1 ).2
1-0.3 1-0.4 -0.5
Figure 5.5. A Partial North-south Cross Section at 117° with Velocity Perturbation (%) m the Background Demonstrating the Small-scale Stmcture Near 33°.
84
a
-0.8
0.7
l0 6
05
04
-122
-121
-120
-119
-118
-117 -116 ongitude
-115
-114
-113
-112
...-- 0 4
0.2 0.1
-0.1 -0.2
-122
-121
-120
-119
-118
-117 -116 Longitude
-115
-114
-113
-112
Figure 5.6. East-west Cross Section at 34.2° with the Search Radii and Velocity Perturbation (%) m the Backgrounds (a and b respectively).
85
200 r
250 0.3 300 0.2 350
0.1
E 400
-0
Q. T3
-0 1
450
500 -0.3 550
600
-0.4
34 Latitude
-0.5
Figure 5.7. A Partial North-south Cross Section at 118° with Velocity Perturbation (%) in the Background Demonstrating the Small-scale Stmcture Near 34.2°.
86
a
0.8
|0 7
l06
05
-122
-121
-120
-119
-118
-117 -116 Longitude
-115
-114
-113
-112
^0.5
0.2 0.1
1-0.2 -0.3 1-0.4
-122
-121
-120
-119
-118
-117 -116 Longitude
-115
-114
-113
-112
Figure 5.8. East-west Cross Section at 35° with the Search Radii and Velocity Perturbation (%) in the Backgrounds (a and b respectively).
87
-405
-410
37.5 -415
-420 35.0 >J -425
^-430 32.5 M
•435
30.0 N 120.0 W
115.0 W
117.5 W
112.5 W
1-440
Figure 5.9. Interpreted Depths to the 410-km Discontinuity for Southem Califomia. Red corresponds to a deeper discontinuity and assumed higher temperatures based on the hypothesis that olivine mmerals dominate this region. 88
40.0^
+: 20 km deeper than mean o: 20 km shallower than mean size proportional to magnitude 37.5
35.0
32.5^
30.0 Ni
120.0 W
117.5 W
115.0 W
112.5 W
-0.5
Figure 5.10. P-wave Velocity Perturbation (%) at 410 km Based on the Dueker Model. Symbols represent the interpreted discontinuity depths with the mean removed.
89
40.^
-650
-655
37.5
-660
-665
35.0
--670
-675
32.5 f^
•680
-685
30.0' N 120.0 W
117.5°W
115.0M/V
112.5 W
-690
Figure 5.11. Interpreted Depths to the 660-km Discontinuity for Southem Califomia. The colors are reversed from Figure 5.9 based on the assumption that this discontinuity is anticorrelated to the 410-km discontinuity. 90
,0.5
40.'i-^
I
0.4
10.3 [I
37.5
0.2
10.1 35.0
10 -0.1
1-0.2 32.5^
-0.3 -0.4 30.0 N 120.0 W
117.5 W
115.0 W
112.5 W
1-0.5
Figure 5.12. P-wave Velocity Perturbation (%) at 660 km Based on the Dueker Model. Symbols represent the interpreted discontinuity depths with the mean removed.
91
temperature distribution at 410 km
as
120 100 S 80 u
i 60
"in i
ZJ
r 1 ] r-
20 h n„n. .r-irini-ir -500
_.
n nnn^nnrf] Dc^
0 Temperature (C)
500
temperature distribution at 660 km
Temperature (C)
Figure 5.13. Temperature Distribution Comparison for the Interpreted Discontinuity Depths (bars) and the Dueker Velocity Model (black lines).
92
CHAPTER VI THERMAL CONTROL OF UPPER MANTLE DISCONTINUITIES
Many seismic studies conclude that large velocity discontinuities exist near 410 and 660 km depths. Mmeral physics (see Chapter I) mdicates that this is a transitional region between upper and lower mantle properties.
Determining the nature of this
transition zone is important to understand Earth-scale thermal convection. These velocity increases have been attributed to both pressure-induced phase transformations and chemical stratification.
Earth-scale convection processes depend heavily on the tme
mechanism behind the observed seismic discontinuities.
Detailed imaging of the
transition zone beneath southem Califomia gives strong evidence that these discontinuities are attributable to thermally controlled, pressure-induced phase transformations.
Interpretation of these images has resulted in a clear statistical
correlation between short wavelength variations in discontinuity depth and velocity. A linear relationship between velocity perturbation and discontinuity depth variations has been found and the slope of this line provides a useful constraint on the properties of the upper mantle transition zone discontinuities.
6.1 The Behavior of Upper Mantle Discontinuities Determining the mechanism(s) behind the observed seismic discontinuities at 410 and 660 km is important to develop an understanding of Earth-scale convection processes. If chemical layering in the transition zone causes these velocity increases, thermal convection would be layered as well. This type of convection would not be a 93
necessity if the transition zone discontinuities were caused by pressure-induced phase transformations (see Davies (1999) for an overview). If the upper mantle discontmuities were attributable only to iso-chemical phase changes, we would expect depth variations m these features to correlate (or be anti-correlated) with velocity (also believed to be thermally controlled).
In this paper we measured the topography on these imaged
discontinuities beneath southem Califomia and compared the result to the velocity stmcture in the transition zone. Using this detailed three-dimensional (3D) unage of the transition zone, we find strong evidence for a linear relationship between depths to these discontinuities and velocity stmcture.
The slopes of the depth versus velocity lines
provide constraints on modeled values for the Clapeyron slopes of the observed phase transformation boimdaries and the thermal relationship between mantle velocity and temperature. The 410-km discontinuity has been attributed to an exothermic pressure-induced phase transformation in the olivine system where (Mg,Fe)2Si04 (olivine) transforms from the a to p mineral stmctures (Ringwood, 1975; Bina and Helffrich, 1994). The pressure required for this transformation to occur increases as temperature increases causing the boundary to deepen (and vice versa). The 660-km discontinuity has been attributed to an endothermic dissociation of y-olivme into perovskite and magnesiowustite (Ringwood, 1975; Bina and Helffrich, 1994; Ito et al., 1990). This endothermic transformation occurs at shallower depths as temperature increases and vice versa for a temperature decrease. Chemical stratification can also be the cause of seismic discontinuities in the transition zone (Ringwood, 1994; Gasparik, 1997). The evolution of the upper mantle transition zone has been explored and has resulted in chemical stratification induced by subduction 94
processes as a possible interpretation.
Subducted slabs may stagnate creating a
transformation boundary at 410 km within the gamet mineralogical system. If subducted material reaches the base of the transition zone, layering may occur as the material attains neutral buoyancy and accumulates near 660 km (Ringwood, 1994; Gasparik, 1997). This would produce a significant seismic discontinuity near the base of the transition zone. Chemically stratified layers would not necessarily respond to temperature anomalies in the transition zone.
However, phase transformation boundaries are temperature and
pressure dependant and shallow or deepen when temperature anomalies are present. The focus of much recent seismic work is measuring variations in the depths to these features with respect to thermal anomalies inferred from seismic velocity variations (Revenaugh and Jordan, 1991; Shearer and Masters, 1992; Vidale and Benz, 1992; Dueker and Sheehan, 1997; Gurrola and Minster, 1998; Tajima and Grand, 1998; Thirot et al., 1998). Because of vertically coherent negative thermal anomalies associated with subducted slabs, results from subduction zones typically support the expected velocitydepth relationships for olivine phase change models. Study of discontinuity responses to plumes also supports the phase change hypothesis for the transition zone. For example recent work mdicates that the transition zone thins by -20 km beneath the Iceland plume (Shen et al., 1998). Studies of the long wavelength stmcture within the transition zone are ambiguous and frequently resuh in thickness estimates near the global average. Recent work indicates an average transition zone thickness of 241 km beneath the East Pacific Rise (e.g., Lee and Grand, 1996), which is very near the global average of 244 km (Shearer, 1991). We also find a mean transition zone thickness of 241 km beneath central and southem Califomia, which is also very near the global average. Over short 95
wavelengths, however, there is significant topography on these discontinuities; and in this study, we considered each discontinuity independently rather than focusing on thickness. Only in recent years have data sets become rich enough to allow mdependent investigation of short-wavelength depth variations of the two major transition zone discontinuities usmg data with greater frequency content (we low pass filter at 3 seconds).
6.2 Evaluation of 410- and 660-km Discontinuity Topography The time-domain receiver functions are converted to the depth domain using ray tracing algorithms (e.g., Buland and Chapman, 1983) and a combmed 1D/3D velocity model for each given ray path geometry. This combined model is based on the iasp91 (Kennett and Engdahl, 1991) standard spherical Earth model to approximate incoming ray paths and the NA95 (Van der lee and Nolet, 1997) local 3D velocity model of North America to correct for regional velocity stmcture. After location of the compressionalto-shear wave conversion points at sampled depth intervals, receiver function amplitudes are biimed based on the abundance of sampling about a geographical nodal pomt (Dueker and Sheehan, 1997, 1998; Owens et al., 2000; Sunmons and Gurrola, 2000). The best sampling of the transition zone occurs beneath the Los Angeles (location X, Figure 6.2d) region.
Detailed velocity stmcture is complex in this region as
determined by P-wave travel time residual inversion as the backgrounds in Figure 6.2d-e demonstrate. Near 410 km depth beneath location X, a seismically fast zone exists ( - 1 % compressional velocity). Near this particular negative temperature anomaly, the 410-km shallows by -25-30 km over a lateral range of-125 km (Figure 6.2a-b). This stmcture
96
demonstrates that the 410-km discontinuity responds abmptiy to small temperature anomalies (< 200°C) over short wavelengths m a manner that is consistent with a pressure-mduced phase transformation with a positive Clapeyron slope. This result is consistent with the hypothesized exothermic phase transformation of olivme (a —• p) near 410 km. In the same geographical region -660 km beneath southem Califomia, the P-wave travel tune residual model mdicates that a seismically slow region exists (Figure 6.2e, location Z). This 1% velocity anomaly corresponds to a temperature anomaly of-150200°C (ref. 20). Near 660 km, complications in discontinuity stmcture exist as multiple phase transformations occur in a mixed olivine/gamet mineralogical system (Revenaugh and Jordan, 1991; Dueker and Sheehan, 1998; Simmons and Gurrola, 2000). However in regions with positive temperature anomalies, exothermic gamet transformations are separable from the discontinuity generated by the dissociation of olivine (y stmcture —• perovskite + magnesiowiistite).
As seen in Figure 6.2c, the 660 km discontinuity
shallows in high-temperature regions.
Since the olivine dissociation has a negative
Clapeyron slope, a positive temperature anomaly would cause the transformation to occur at shallower depths, which is exactly what occurs beneath southem Califomia. Evaluation of 3D discontinuity stmcture (Figure 6.2d,e) reveals a strong correlation between 3D variations in discontinuity depth and velocity anomalies in regions with very dense data coverage. Correlation of shallow stmcture on the 410-km and positive velocity anomalies is evident near location X (Figure 6.2d). The shallow 410-km is centered about Los Angeles offsetting the velocity anomaly (X) to some degree but remams strongly correlated. The other most significant feature at 410 km is a 97
deepened discontinuity beneath location Y (northeast of LA) where a negative velocity anomaly exists. This response is consistent with a phase transformation at 410 km with a positive Clapeyron slope as the discontinuity shallows in cold regions while it deepens in hot regions. The high temperature region at 660 km depth causes the associated discontinuity to become -25 km shallower (Figure 6.2e, location Z). The small negative temperature anomalies to the east and southeast of location Z can also be associated with a deepening 660-km. These features are consistent with a pressure-induced phase transformation with a negative Clapeyron slope as the 660-km discontinuity responds oppositely to the 410km discontinuity when the local velocity anomalies are considered at each depth interval. 6.3 Velocity-Topography Relationship Since velocity stmcture beneath this region is not vertically coherent through the entire transition zone, it is important to consider how the discontinuity stmctures respond to the velocity perturbations about each depth interval. By extracting the discontinuity depths and associated velocity perturbations at each geographical node, it becomes apparent that these discontinuities are anti-correlated and each has a Imear relationship with velocity and, therefore, with temperature (Figure 6.3). Considering possible error in discontmuity depth and velocity perturbation, we computed error ellipses for the 95 and 99% confidence intervals. The slopes (M) were determined by a bootstrap re-sampling each data set 1000 times in order to remove any possible bias. This re-sampling has yielded -34.4 ± 4.0 and 29.3 ± 2.8 km/dVp for the 410-and 660-km, respectively (where dVp is percent compressional velocity perturbation at each depth). Using published
98
values of velocity, density, temperature conversion and gravitational force at depth, we obtam estimates of Clapeyron slopes at each depth of 4.0 ± 0.5 and -3.5 ± 0.3 MPaK"^ respectively (Anderson, 1989; Kennett et al., 1995). These Clapeyron slopes are sunple estimates as the M-slopes (slope of the depth versus velocity trend) are the primary observational constraints that may be used for future work to better determine the properties of the transition zone discontinuities. It is important to point out the velocity model used here is damped and the resulting model is non-unique. The velocity models found for most damping factors have resulted in similar pattems of velocity with variable amplitudes. In our computations we used a velocity model representative of the mid ranged values and we arrived at Clapeyron slopes near the upper limits of the laboratory measurements.
It is also
important to point out that the magnitude of the slope of the depth verses velocity curve for the 410- and 660-km discontinuities are similar in value (differing by about 15 %). Our results therefore favor experimental measurements with similar magnitudes for the Clapeyron slopes of these two discontinuities.
99
source
Pds
PPds
PKPdfds
Figure 6.1. Ray Paths for Seismic phases Used to Create Receiver Functions. Approximately 50% of the total receiver fimctions are calculated from Pds arrivals (where d represents a P to S conversion depth). PcPds and PPds arrivals provide -45% of the total number of recordings and PKPdfds arrivals account for -5%. Combined, these phases densely sample the study area providing excellent resolution. 100
101
"sS.
Figure 6.2. Cross Sections of the 3D Image (a-c) and Maps (d and e) Comparing Discontinuity Depths (white line on the cross sections and circles or pluses on the maps) to Velocity Perturbation (color background). These velocity perturbations are found using a conservative (mid-range) damping parameter. It is therefore possible that these velocity anomalies will differ from other models by as much as a factor of two. Sections a and b demonstrate the 410-km discontinuity stmcture at latitudes 33 and 35°N trending east-west. The 410-km abmptiy shallows in the center of the sections near the highvelocity region (~ 1% P-wave velocity maximum shown in blue). Section c demonstrates the 660-km discontinuity stmcture at latitude 34.2°N trending east-west. The 660-km discontinuity responds to the low-velocity (hence, high temperature) feature (shown in red) by shallowing -25 km. A map comparing the 410-km stmcture to the velocity perturbation (d) shows the 3D correlation of the two models. Location X near the dense cluster of seismic stations (solid black markers) shows where the high-velocity region (blue) corresponds to a shallow 410-km (circles) and location Y shows a low-velocity anomaly at which the 410-km deepens -20-25 km. These features are in strong agreement with a phase transformation with a positive Clapeyron slope (i.e., a(olivine) —> P(olivine)). Correlation between the 660-km discontinuity and velocity stmcture is also evident as shown in panel e. At location Z the 660 km discontinuity shallows by -25 km as would be expected in a low-velocity region (inferring a high temperature anomaly; shown in red). The 660-km discontinuity deepens in areas just east and southeast of this anomaly correlating well with a rise in velocity (in blue), which is consistent with a negative Clapeyron slope and can be attributed to the dissociation of the olivine component of the upper mantle.
40.0'ft +>20 km +10 to 20 km
+ 0 to 10 km I O-10 to 0 km O-20 t o -10 km o.•"".•' i
25
200
400
600
800
1000
iteration
104
20^
200
400 600 iteration
800
1(
REFERENCES
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Owens, T.J. "Determination of cmstal and upper mantle stmcture from analysis of broadband teleseismic P-waveforms." Ph.D. Dissertation, University of Utah, Salt Lake City, Utah, 1984. Owens, T.J., Zandt, G. & Taylor, S.R. "Seismic evidence for an ancient rift beneath the Cumberland Plateau, Tennessee: a detailed analysis of broadband teleseismic P waveforms." J. Geophys. Res., 89 (1984), 7783-7795. Owens, T.J., Taylor, S.R. & Zandt, G. "Cmstal stmcture at regional seismic test network stations determined from inversion of broadband teleseismic P waveforms."' Bull. Seism. Soc. Am., 77 (1987), 631-662. Owens, T.J. and Crosson, R.S. "Shallow stmcture effects on broadband teleseismic P waveforms." Bull. Seism. Soc. Am., 78 (1988), 96-108. Owens, T.J., Crosson, R.S. & Hendrickson, M.A. "Constraints on the subduction geometry beneath westem Washington from broadband teleseismic waveform modeling." Bull. Seism. Soc. Am., 78 (1988), 1319-1334. Owens, T. J., Nyblade, A. A., Gurrola, H. & Langston, C A. "410 and 660 km discontinuity stmcture beneath Tanzania, East Africa." Geophys. Res. Lett. 27 (2000), 210-215. Paulssen, H. "Evidence for a sharp 670 km discontinuity as inferred from P-to-S converted waves." J. Geophys. Res., 93 (1988), 10489-10500. Revenaugh, J. and Jordan, T. H. "Mantle layering from ScS reverberations: 2. The transition zone." J. Geophys. Res. 96(1991), 19763-19780. Ringwood, A. E. in Advances in Earth Sciences (ed. Hurley, P. M.). Cambridge: MIT Press, 1966,287-356. Ringwood, A.E. in Composition and Petrology of the Earth's Mantle. New York: McGraw-Hill, 1975. Ringwood, A. E. "Role of the transition zone and 660 km discontinuity in mantle dynamics." Phys. Earth Planet. Inter. 86 (1994), 5-24. Schweickert, R.A. and Cowan, D.S. "Early Mesozoic tectonic evolution of the westem Sierra Nevada, Califomia." Geol. Soc. America Bull., 86 (1975), 1329-1336. Shearer, P.M. "Seismic imaging of upper-mantle stmcture with new evidence for a 520km discontinuity." Nature, 344 (1990), 121-126.
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Shearer, P.M. "Constraints on upper mantle discontinuities from observations of longperiod reflected and converted phases." J. Geophys. Res. 96 (1991), 18147-18182. Shearer, P.M. and Masters, T.G. "Global mapping of topography on the 660-km discontinuity." Nattire 355 (1992), 791-796. Shearer, P. M. and Flanagan, M. P. "Seismic velocity and density jumps across the 410and 660-kilometer discontinuities." Science, 285 (1999), 1545-1548. Shen, Y., Solomon, S.C, Bjamason, I.T. & Wolfe, CJ. "Seismic evidence for a lowermantle origin of the Iceland plume." Nature, 395 (1998), 62-65. Simmons, N.A. and Gurrola, H. "Multiple seismic discontinuities near the base of the transition zone in the Earth's mantle." Nature, 405 (2000), 459-462. Spencer, J.E. "Uplift of the Colorado Plateau due to lithosphere attenuation during Laramide low-angle subduction." Jour. Geophys. Res., 101 (1996), 13595-13609. Stewart, John H. "Basin-range stmcture in westem North America: A review." Geol. Soc. America Mem., 152 (1977), 1-31. Stixtmde, L. "Stmcture and sharpness of phase transitions and mantle discontinuities." J. Geophys. Res. 102 (1997), 14835-14852. Tajima, F. and Grand, S.P. "Variation of transition zone high-velocity anomalies and depression of 660 km discontinuity associated with subduction zones from the southern Kuriles to Izu-Bonin and Ryukyu." J. Geophys. Res. 103(1998), 1501515036. Thirot, J., Montagner, J. & Vinnik, L. "Upper-mantle seismic discontinuities in a subduction zone (Japan) investigated from P to S converted waves." Phys. Earth Planet. Inter. 108 (1998), 61-80. Tull, J.E. Seismic Analysis Code: User's Manual. Livermore, CA: Lawrence Livermore National Laboratory, 1989. Turcotte, D.L. and Schubert, G. Geodynamics Applications of Continuum Physics to Geological Problems. New York: John Wiley and Sons, 1982. Weidner, D. J. and Wang, Y. "Chemical- and Clapeyron-induced buoyancy at the 660 km discontinuity." J. Geophys. Res. 103 (1998), 7431-7441. Vacher, P., Mocquet, A. & Sotin, C "Computation of seismic profiles from mineral physics: the importance of the non-olivine components for explaining the 660 km depth discontinuity." Phys. Earth Planet. Inter. 106 (1998), 275-298. 110
Van der lee, S. and Nolet, G. "Upper mantle S-velocity structure of North America." I Geophvs. Res. 102 (1997), 22815-22838. Vidale, J.E. and Benz, H.M. "Upper-mantle seismic discontinuities and the thermal stmcture of subduction zones." Nattire 356 (1992), 678-683. Vinnik, L.P. "Detection of waves converted from P-to-SV in the mantle." Phvs. Earth Planet, hiter.. 15 (1977), 294-303. Yusa, H., Akaogi, M. & Ito, E. "Colorimetric study of MgSiOs gamet and pyroxene: Heat capacities, transition enthalpies, and equilibrium phase relations in MgSiOs at high pressures and temperatures." J. Geophys. Res. 98 (1993), 6453-6460.
Ill
APPENDIX A THE MATTIMES TOOLBOX USER'S MANUAL
112
MatTimes.A MATLAB-based seismic travel time calculation and visualization toolbox User's Manual for Version 1.0
A development of: The Department of Geosciences at Texas Tech University
Nathan A. Simmons,
[email protected] Harold Gurrola, v4har(a)ttacs.ttu.edu
113
TABLE OF CONTENTS SECTION I. OVERVIEW AND GETTING STARTED
116
II. DATA STRUCTURES
119
2.1 Stmctured Arrays in MATLAB and MatTimes Data Files
119
2.1.1 MatTimes Tool: MKDATAFILE 2.2 Seismic Analysis Code (SAC) Files 2.2.1 MatTimes Tool: SACTOOL III. VELOCITY MODELS
120 123 123 127
3.1 Model Input and Available Models
127
3.1.1 MatTimes Tool: MKMODEL
127
3.1.2 Limitations
130
IV. PHASE DESIGN
132
4.1 MatTimes Tool: MKPHASE 4.1.1 Example Designs 4.2 MatTimes Tool: PHASETOOL V. CALCULATESFG TRAVEL TIMES
132 138 144 146
5.1 MatTimes Tool: TIMETOOL
146
5.1.1 Vector Input
147
5.1.2 Data File Input
149
VI. CALCULATING RAY PATHS
152
6.1 MatTimes Tool: ARCTOOL 114
152
6.1.1 Vector Input
153
6.1.2 Curve File Input
153
6.1.3 Data File Input
154
6.2 MatTimes Tool: PPTOOL
156
6.2.1 Vector Input
157
6.2.2 Curve File Input
157
6.2.3 Data File Input
159
6.3 MatTimes Tool: TRACETOOL
160
6.3.1 Vector Input
161
6.3.2 Curve File Input
162
6.3.3 Data File Input
163
VII. PLOTTING AND Mapping
165
7.1 MatTimes Tool: PL0T3C0MP
165
7.2 MatTimes Tool: CURVEPLOT
167
7.3 MatTimes Tool: PLOTPHASE
169
7.4 MatTimes Tool: MAPPHASE
171
7.5 MatTimes Tool: MOVIEMAP
176
VIII. OTHER UTILITIES
177
8.1 MatTimes Tool: MKEARTH
177
8.2 MatTimes Tool: TURNTOOL
177
8.3 MatTimes Tool: VPLOT
178
8.4 MatTimes Tool: CUTDATA
179
8.5 MatTimes Tool: SEC2DHMS
180
115
SECTION I OVERVIEW AND GETTING STARTED
MatTimes is a seismic travel time calculator and ray path imaging toolbox for MATLAB users designed for seismic research and teaching. This toolbox contains flexible algorithms for importation of Seismic Analysis Code (SAC) data files, as well as, seismic phase design, phase implementation and ray path visualization within the MATLAB environment (Tull, 1989). Travel times and ray paths for real events are quickly obtained using the T(p) methods designed by Buland and Chapman, 1983. Any spherically symmetric Earth velocity model can be used in the calculations, including a combination of separate ID velocity models for each end of a given ray path. The use of depth variables in phase design allows for instantaneous travel time calculations for a suite of phases such as Pds and PKKPds where r4
Tie Phase(s) with Existing Velocity Model(s)
Event Information
Data File
SAC File or Workspace File
Workspace
Send to Workspace \
Calculate Travel Times Save to Data File and/or curve file
I
Calculate Arc Distances
Plot Arc Path
Map Ray Path
Calculate Ray Paths Make Movie of Mapped Ray Path
Figure 1.1. Marr/me^ flowchart.
Some relatively new seismic software packages have been created and may be excellent packages to use in conjunction with this package. For instance, The TauP Toolkit may be more appropriate for some users as it is written in the Java language and contains phase parsing algorithms that do not require user phase design (Crotwell et al.. 117
1999). In some cases, this flexibility may slow down calculations; however, this may not be of much concern to some seismologists. Another recent de\elopment in this field is a MATLAB-based package developed at Sandia National Laboratories called MatSeis (Harris and Young, 1996) that has signal processing and data manipulation algorithms executed from within a Graphical User Interface. To get started, simply change into the "MatTimes"' directory from the MATLAB workspace and type "setup". A GUI will appear called the "MatTimes Guide". This guide will direct the user to the functions of interest. To use this guide in the future, simply type "mattimes" in the workspace.
118
SECTION II DATA STRUCTURES
Seismic data files typically have multiple parameters associated with them. Event, station and data stream indicators are necessary values associated with a seismic event that must be stored and connected to the recorded data at all times if possible. Also, calculated travel times and ray paths are values that should also be linked to a particular stream of seismic data for organizational purposes. MatTimes organizes seismic information in the form of MATLAB structured arrays. Stmctured arrays contain field values permitting a multitude of information to be stored within a single variable, and within a single data file.
2.1 Stmctured Arrays in MATLAB and MatTimes Data Files Structured arrays in MATLAB can be examined by typing: help stmct
in the MATLAB workspace. This command will design a structured variable by creating fields and assigning values to those fields. For example, a simple variable named example with fields/7 andy2 can be created with the following command:
example=stmctCfl ',0,'f2', 1)
where the fields are set to 0 and 1 respectively. The output is as follows:
119
example = fl:0 f2:l.
The values of the fields can be extracted to the workspace by the following:
fl=example.fl
where/7 is in the workspace as well as the variable example. It should also be noted that stmctured variable can be multi-dimensional. For instance, example can be a vector:
example(2).fl=2; example(2).f2=3;
The dot (.) function is an altemative way to set stmctured array fields. The variable example is now a 1 X 2 stmctured array. This form of organization is advantageous when considering seismic data with multiple channels. MatTimes has tools to import and create data files in this structured format. These files can be used in conjunction with most functions within this package of software. However, MatTimes does not require the user to use these formats. All functions can be used without any real data in the typical functional sense in the MATLAB workspace.
2.1.1 MatTimes Tool: MKDATAFILE MKDATAFILE.M is a function that creates a structured data file for use in the MATLAB workspace and MatTimes functions. The command:
mkdatafile(FILENAME)
120
creates a structured variable named data in a file named FILENAME_mt.mat. FILENAME is a string argument naming the plain MATLAB file (.mat) with particular variables that will be combined into a new stmctured file within a single variable. The fields, in the file stmcture below, are filled with the variables of the same name within FILENAME.mat: data= name: import: evtime: begintime: streamtime: station_lat: station_lon: station_elevation: borehoie_depth: compass_az: compass_inc: event_lat: event_lon: event_depth: magnitude: arc_distance: azimuth: backazimuth: gcarc: dt: data:
' exainpie_mt .mat' '21-Mar-2000 17:42:05' [1994 346 7 41 55.4000] [1994 346 7 51 45.1280] 360.2000 34.1483 -118.1717 0.2950 0 90 90 -17.4770 -69.5980 14 8 6.3000 7.6886e+003 318.2648 129.9962 69.0880 0.2000 [1x1802 double]
Exceptions to this mle are that import does not have to be in FILENAME and azimuth must be called az to avoid conflicts with a function in the MATLAB Mapping Toolbox. Here is an example of a data file creation in the workspace: clear name='event0920e'; evtime=[1994 34 6 7 41 55.4];%actuai event time %[Year Julian Hour Minute Second] begintime=[1994 346 7 51 45.128];%starting time %of data stream streamtime=360.2;%stream length in sec station_lat=34.1483;
121
station_lon=-118.1717; station_elevation=0.295; %surface in km borehoie_depth=0;%depth of instrument in km compass_az=90; %orientation (east here) compass_inc=90; %vert. orientation (0 is up) event_iat=[-17.4770];%event info event_lon=[-69.5980]; event_depth=148; %km magnitude=6.3; arc_distance=7688.6; %surface in km az=318.2648;%take-off from source backazimuth=129.9962;%arrival azimuth gcarc=69.088;%arc degrees dt=0.2; %sample increment data=sin([1:1802]/lOO);%bogus data save example.mat %create MatTimes file: mkdatafile{'example') %view contents: load example_mt %plot data plot(0:data.dt:data.streamtime,data.data).
The command: mkdatafile(FILEl ,FILE2,FILE3,NAME) will create a three-component data file with the information in the first three inputs. The output file name is NAME. The original data format is a major issue and must be addressed on a case-by-case basis. This means that the user may be required to create an algorithm to generate such files. However, Seismic Analysis Code (SAC) files can be easily imported into the workspace and placed into the preceding format very efficiently.
122
2.2 Seismic Analysis Code (SAC) Files Typically, seismic data files can be obtained in SAC format. For instance, the Incorporated Research Institutes for Seismology (IRIS) data management center (DMC) provides data files in this format. For this reason, tools were developed to import this particular data type.
2.2.1 MatTimes looV. SACTOOL SACTOOL is a fimction that imports SAC format files into MATLAB as a ".mat" file for use in the MATLAB workspace. This is a flexible function that will generate a stmctured array data file in the same format as MKDATAFILE as previously mentioned. Fields in SAC files are imported in a bit-wise fashion by READSAC and reorganized into the appropriate structured fields. Single files can be imported, but SACTOOL has the ability to import multiple files into a single structured array file with a single variable named data.
This function is designed to create multi-channel files within a single
variable. This is a convenient way to carry around all information for a single event rather than having perhaps three separate files for the north, east and vertical components. This stmcture, however, is left as an option. The command: sactool(FILENAME,DIRECTORY)
will import a single SAC formatted file named FILENAME from the directory, DIRECTORY, into the current directory. If DIRECTORY is left off, it is assumed that the SAC file exists in the current directory. The filename of the imported file will be the
123
same as FILENAME with the exception that it will have a .mat extension. FILENAME and DIRECTORY are string arguments such as:
sactool('event0920z','C:/seismic/data/')
where the directory name ends with a forward slash (/). SACTOOL can also be executed as follows:
sactool(LIST,DIRECTORY) where LIST is a string argument of a variable name listing several SAC files in DIRECTORY. LIST is a stmctured array generated using MATLAB's DIR command. For example, a list can be created with the following:
LIST=dir(FILES) where FILES is a string with a wildcard (*). LIST will be a single column of file names within a stmctured array with the fieldname name. Another extremely useful execution of SACTOOL combines multi-components into a single variable and file. The command: sactool(LIST3,DIRECTORY,NAMES)
will load in three or more SAC files per output file as listed in LIST3. The variable in each file created will be called data while with the other executions, data will have multiple dimensions. Each file in the corresponding row of LIST3 will be placed in data
124
in the filename in the corresponding row of NAMES which is another stmctured array. Full examples of all execution forms and input variable creation are below. In order to use MatTimes utilities successfully with the imported data files, some important steps must be taken to assure absolute compatibility. SAC fields User5. User6, User? and User8 must contain actual event information in order to determine absolute travel time markers. In particular. User5 must be set to the Julian Day of the event. User6 must be the event hour, User? should be the event minute and User8 should be the event seconds with decimals. The values in these fields will be combined into the field evtime in the imported data. The data stream time should also be set to the real time of the first sample in the imported data stream prior to importation so that begintime in data will be understood by the MatTimes utilities.
Examples: 1) Import a z-component data file: sactool(FILENAME) 2) Import all three components for the same event, 0920: DIRECTORY=['C:/MatTimes/Data/']; LIST=dir([DIRECTORY'event0920*']); sactool(LIST,DIRECTORY) 3) Load in three components for a multi component file creation: LIST3=[dir('ev*e') dirCev*n') dirCev*z')]; DIRECTORY=[]; NAMES.name='event0920'; sactool(LIST3,DIRECTORY,NAMES); 4) If LIST3 is long, it is not convenient to type in all output names, so make names for each event triplet: LIST3=[dirCev*e') dirCev*n') dirCev*z')]; [a,b]=size(LIST3); 125
for i=l:a lname=length(LIST3(i).name); NAMES(i).name=LIST3(i).name(l:lname-l) end
126
SECTION III VELOCITY MODELS
Utilization of seismic velocity models is a complex issue that MatTimes attempts to deal with effectively. This package is designed to use one-dimensional (ID) spherically symmetric Earth velocity models for travel time calculations and ray path geometry determination. MatTimes is designed under the premise that the user can decide on a velocity model to use for a given problem. Also, it is often useful to have two separate velocity models in a single travel time calculation where a basic ID model is used near the earthquake source region and a separate ID model is used near the receiver region (seismometer) for local velocity corrections. This flexibility has required extensive algorithms to be developed.
3.1 Model Input and Available Models Inputting user-defined velocity models is not a very simple procedure; however, this package attempts to make this process as straight forward as possible. It is likely that most users will not need to input a model as MatTimes has two popular pre-created velocity models available: IASP91 (Kennett and Engdahl, 1991) and PREM (Dziewonski and Anderson, 1981). It is likely that in the near future, more reference velocity models will be included.
3.1.1 MatTimes Tool: MKMODEL If the user needs to create a new velocity model, a tool exists to do so. MKMODEL creates a MatTimes velocity model for use with all functions in the package. The input into this program can be variables in the workspace or values in a tab-delimited 127
text file. MKMODEL re-samples the input model by linear interpolation; therefore it is assumed that the input model is sufficiently sampled to do so without losing considerable precision. The model is sampled in radius using the following equation:
2
r r._, = r, - \ j ^ + -^-^^dr
1
'•/-•
,
7=2,3,.../7
J
where r^ is the radius of Earth and dr is a depth increment. Our experiments have concluded that this sampling method is effective in that precision in travel time calculations is not lost and that the subsequent functions can evaluate travel times from the sampled model efficiently. The command:
mkmodel([],TXTMODEL,DR)
generates a MatTimes velocity model from values entered in a tab-delimited text model called TXTMODEL. The sampling increment DR should be on the order of 0.1 to 2 km depending on the desired trade-off between precision and efficiency. TXTMODEL is a string argument naming a text file in the current directory. A tab-delimited text file contains three columns where the first column is radius in km (starting with Earth's radius), the second and third columns are compress ional and shear velocities in km/s respectively.
Major Earth components are separated by (-1) in each column at the
interfaces. The first (-1) is placed at the Moho discontinuity, the second separates the upper and lower mantle, the third separates the lower mantle from the outer core and the
128
fourth is at the outer/inner core boundary. This t}'pe of model could be place in a spreadsheet like the following shortened example of IASP91 below: 5.8 5.8 6.5 6.5 -1
336
6336 6251 6251 6161 6161 5961 5961 5711
8.04 8.05 8.05
4.47
8.3 8.3
4.518 4.522 4.87 5.07
-1
-1
5.6 -1
5711 5611 5611 3631 3631 3482
10.79 11.0558 11.0558 13.6564 13.6564 13.6908
5.95 6.2095 6.2095 7,2645 7.2645 7.3015
-1
-1
3482 1217.1
8.0087 10.2578
6371 6351 6351 6336
-1
9.03 9.36 10.2
3.36 3.75 3.75
-1 45 4.5
-1
-1
-1 0 0 -1
1217.1
11.0914 11.2399 11.2409
3.4385 3.5637 3.5645
100 0
This model is not representative of the tme model since it has been heavily decimated. Notice the (-1) at the major interfaces and that the largest radius is the radius of the Earth and the smallest radius is the center of the Earth. Since shear waves cannot, in theory, travel in the outer core, these velocities are set to zero rather than infinity or not-anumber. The command:
mkmodel(MODEL,OUTPUT_NAME,DR)
will generate a MatTimes model from within the MATLAB workspace in the same way as the previous method. MODEL should be a matrix containing the same information as the text file including (-1) at all interfaces.
129
OUTPUT_NAME is a string argument
naming the output velocity model to be placed in the "Models" directory. DR is the same as above. A special execution type uses a reference model and a partial model to simply perturb the existing reference model. This method is designed specifically to make local velocity corrections near the receiver.
Therefore, the partial model should contain
velocity for shallow stmcture only. The calling form for this execution is:
mkmodel(MODEL,OUTPUT_NAME,[],REFMODEL).
MODEL is the partial velocity model that exists in the workspace. This variable should contain three columns similar to the text file format, however, there should be no (-1) values as the model will be interpolated to the same depths as the REFMODEL. Although the new model may have different Moho depths and other dissimilarities, travel time calculations will not be affected.
Examples: mkmodel([],'iasp91.txt',l) creates a model from text file mkmodel(vmodel,'iasp9r,l) creates a model from the workspace mkmodel(vmodel,'iasp91_2',[],'iasp9r) perturbation of iasp91
3.1.2 Limitations The velocity model creation for MatTimes has some limitations, most of which are probably unknown. One limitation is that shallow low-velocity zones case major problems in the travel time calculation algorithms. For this reason, the model design 130
ignores the possible existence of no-tum zones above the outer core boundary. This means that the ray parameter must be a monotonically decreasing value with depth until the outer core is reached (the outer core boundary is a non-monotonic boundary with a significant no-tum zone in all known velocity models often called the shadow zone).
131
SECTION IV PHASE DESIGN Designing seismic phases is one of the most important processes achieved in the MatTimes environment. Phases are treated as piecewise wave front segments that can be used with any velocity model that exists in the environment. Although the logic behind phase design may be somewhat complicated, the benefits are tremendous. After phase design and velocity model association with the phase, travel times can be calculated for any source depth, any receiver elevation and any total arc distance as long as the phase exists. The efficient storage and calculations of phase segments allows for rapid travel time and ray path calculation within the MATLAB scripting environment. Also, an important function of MatTimes phase design is the ability to create a phase that is actually a suite of phases such as Pds that can be calculated simultaneously without embedded loops. There is no doubt that there are limitations in phase design, however, all major seismic phases as well as a multitude of obscure phases can be created without complications.
4.1 MatTimes Tool: MKPHASE MKPHASE is the primary tool used in phase design. This is a Graphical User Interface (GUI) that allows the user to create a specified phase in an organized manner. Figure 4.1 is an illustration of this GUI. To see a list of phases in your workspace, type "phases" at any time.
132
Partial Ray* IntegraJs
I
Figure 4.1. The MKPHASE Graphical User Interface (GUI).
The first issue in phase creation is naming conventions. The user has complete control over phase naming since a naming box in the GUI is available for input. However, some considerations must be examined prior to naming. Firstly, if the proposed phase name is being used, you may not want to replace the phase. A "List" button is found just above the naming box that will list the current phases in the workspace. Secondly, if the phase will have a depth variable, a "d" should be within the phase name (i.e., Pds). It is not absolutely necessary to conform to this naming convention, however it is suggested as some functions do interpret the "d" to be a variable depth. An example where this could be a problem is the phase PKPdf v/htTQ d would not be a depth variable. This problem could be avoided by naming this phase PKIKP or PKPic where ic represents the inner core since this branch of the PKP group travels into the inner core. Lastly, the PC environment is not case sensitive, so PKiKP and PKIKP are indistinguishable. A good way to avoid this problem is to replace "i" with "r" meaning reflection. 133
The second major item in column one of the MKPHASE GUI is the "Variable Depth Range" box. This input box is provided so that the user can define the span of variable depths that could be used in the phase. For example, the phase Pds would have to have d defined within this box. Most likely, the user would primarily want this phase to calculate P410s and P660s. If these were the only phases needed in this variable phase, then the input in the box could be:
[410 660];
where both discontinuity phases as well as all in between (such as P520s) could be calculated. However, in between S-wave conversions would not calculated with much accuracy. The best input into the "Variable Depth Range" box would be like the following:
[0:10:800];
where all Pds phases between POs (P) and P800s where an S-wave conversion at 800 km could be calculated. The increment (in this case, 10) defines the interval at which all stored vectors will be calculated. The lower this value, the more accurately the travel times and ray paths are calculated. Obviously, the user must decide on the tradeoff between accuracy and storage space for these types of phases. The next major item, and perhaps the most complicated, is input of the deepest incidence. In order to use these phases in MatTimes, the wave type and depth of the deepest portion of the wave front must be known in order to determine possible ray parameters for the designed phase. Check boxes are provided to enter the wave type. 134
The choices are: a) P, b) 5 or c) P andS. For example, the refraction phase P would ha\ e a deepest incidence reaching the tuming point as a compressional wave. Similarly, S would have shear wave reaching the tuming point, so S would be chosen in this case. A unique situation is where both P and S reach the deepest point in the entire wave front. Examples of this situation would be PcS or ScP. These phases would have both P and S waves reaching the outer core. MatTimes also needs to know whether the deepest wave front incidence is a reflection or refraction and the location (in depth) of this incidence. Buttons named "Refraction" and "Reflection" near the bottom of the GUI must be depressed to set this option. Also, immediately beneath each of these boxes, there are pop-down menus used for deepest incidence depth determination. The choices for refraction are: • • • •
cmst upper mantle lower mantle outer core
• inner core. By choosing one of these options, you can instmct MKPHASE the range in which the deepest segment of a wave front will tuming. For example, the phase P would be tuming in the lower mantle, whereas PKKP will tum in the outer core. Similar to refraction, the reflection depth can be chosen as one of the following: • • • •
moho lower mantle outer core inner core.
135
By choosing a reflection depth, MKPHASE can determine that the hypothetical tuming depth would be beneath the chosen depth limiting the possible ray parameters for the phase. The next issue in phase design is the selection of the velocity model. Depressing the "Choose a Velocity Model" button and selecting an available velocity model from the list box do this. The selected velocity model is plotted on the GUI for evaluation. If no model is chosen, IASP91 is used. This stage of phase design is not of particular importance as the model is primarily used for plotting and travel time curve calculation for visualization purposes after completion of the phase. Upon completion, any velocity model can be linked with the phase. The last column of the MKPHASE GUI is where the actual partial ray path segments of the phase are created. A "segment" is a vector consisting of: 1) A beginning depth; 2) A wave type; and 3) An ending depth. For example, the first segment of Pds would be: Source P Tum where "Source" denotes that ray path begins at the source depth. This value should not be entered as a number since typing "Source" will make this depth a variable depending on actual source depth. The "P" denotes that this segment wave type is a compressional wave. The input "Tum" is a variable depth that denotes that the wave segment will reach its tuming point. Adding the second segment of Pds adds two more values to this stream: Source 136
p Tum P Variable where "P" is the same as above and "Variable" denotes that the wave segment will reach a variable depth (as given in "Variable Depth Range") as a P-wave. Here is the completed wave segment group: Source P Tum P Variable S Receiver where "S" denotes that the last branch is a shear wave and "Receiver" denotes that the final wave front segment reaches the seismometer at its particular elevation. This means that this segment group contains four variables: 1) 2) 3) 4)
Source Tum Variable Receiver.
Table 4.1 lists the possible qualifiers for the "Partial Ray Integrals" box.
P-wave S-wave
turning variable source point depths depth
inner core
outer core
lower mantle
upper mantle
moho
p
s
Turn Tum
Depths
Source
lnner_Core
Outer_Core
Lower_Mantle
Upper_Marrtle
Moho
p
s
tum
depths
source
Inner Core
Outer Core
Lower Mantle
Upper Mantle
MH
T
D
S
inner_core
outer_core
lower_mantle
uppef_mantle
M
t
d Variable variable
s
inner core
outer core
lower mantle
upper mantle
mh
0
IC
oc
LM
UM
m
ic
oc
Im
urn
Table 4.1, List of possible qualifiers in the "Partial Ray Integrals" box.
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The final steps are to depress the "Apply" and "Done" buttons beneath in the phase segments input box. The "Apply" button will save the phase information and link this information with the velocity model. The ray paths will be drawn on an Earth model for the maximum, minimum and median values of the ray parameter range for the designed phase. This is good check to see if phase was designed as desired. The "Done" button will complete the design and plot a travel time curve for the phase.
4.1.1 Example Designs The first example demonstrates the possible inputs for Pds. Figures 4.2, 4.3 and 4,4 illustrate inputs, an example ray path and the associated travel time curve, respectively. The second example demonstrates the possible inputs for PKKP. Figures 4.5, 4.6 and 4.7 illustrate inputs, example ray paths and the associated travel time curve, respectively. Notice that the tuming depth is constrained to the outer core and how MKPHASE does not really interpret the first and last \'alues assigned in the "Partial Ray Integrals" box as it is always assumed that the source depth is variable as well as the seismometer elevation.
138
Help Choose a Velocity Model pPropossd PhBsa . N o m e : ,,-
6000
Source P Turn P
5000
Variable
Pdj
S Receiver
V a r i a b l e Depth Range
I
Partial R a y IntegraJs
|0:2aeoo]
4000
Deepest Incidence
E (A
F
P
r
S
r
PandS
Rehadion I lower, mantle
2000
d 1000 -
Reflection
I [enlet reflection deplh)
i 3000 re
Apply ^
I velocity (km/s)
Figure 4.2. Example inputs in MKPHASE for Pds. P660S, Iasp91, source: 33 k m
gcarc: 60 deg, rayp: 384 sec/rad
Figure 4.3. Example ray path calculation for a P660s and an event occurring at 33 km depth with a 60° great circle arc distance.
139
P660s, Iasp91, source: 33 km
10
20
30
40
50 60 arc distance (degrees)
70
80
90
100
Figure 4.4. Travel time curve for P660s as designed by MKPHASE. The source depth was chosen to be the same as in Figure 4.3.
Help Choo«e « Velocity Hodei PropoBsd Phase Name:
6000
0 P Turn P Outer Care P Turn P 0
PKKP
5000 Variable Depth Range
r
4000 Deepest Incidence
Parlia] Ray Integrals
E
17 P ns r p « i s 120°° ;;iii:::::;r:;T:;:;":ii::::r:-:
Refiadion [outer coie::
(D
2000
"3
\
^
:
1000 Refleclian I (enter teflecboo deplh]
I \
Apply 2j
0
5 10 velocity (km/s)
Figure 4.5. MKPHASE inputs for PKKP.
140
PKKP, Iasp91, source: 0 km
Mil
Figure 4.6. Ray paths for the designed phase PKKPab and PKKPbc. Ray path (1) is traced using the lowest ray parameter, ray path (2) is traced using the median ray parameter and ray path (3) is traced using the maximum ray parameter for this phase. PKKP, Iasp91, source: 0 km
1880
1860
1840-
1820 •y
•o c o
a 1800 a E
1780
1760
1740
1720
70
80
90
100 arc distance (degrees)
110
120
130
Figure 4.7. PKKP travel time curve displaying non-monotonic properties.
141
The next example demonstrates a reflected phase: PcS. Figures 4.8, 4.9 and 4.10 illustrate the constmction of this phase, example ray paths and the travel time curve respectively.
Help Choo«e 9 Vekxaty Hodd | Proposed Phase Name:
Partial Ray Integrals 0 P oc s 0
PcS Varfable Depth Range
Deepest Incidence r
P
r
S
F
P«tdS
Refiadion [(enter tuirwig branch)
^
Reflection I outer core
Apply
zl
Done 0
5 10 velocity (km/s)
Figure 4.8. MKPHASE inputs for PcS.
142
J
PcS, iasp91, source: 0 km
Figure 4.9. Ray paths for PcS. Ray paths 1-3 are the minimum, maximum and median ray parameters, respectively. PcS, Iasp91, source: 0 km 920 r 900-
880 860 _840 in •D
C O
o 820
IS, a
E = 800 780 760 740 720
10
20
30 40 arc distance (degrees)
Figure 4.10. Travel time curve for PcS.
143
50
60
70
4.2 MatTimes Tool: PHASETOOL PHASETOOL is an important MatTimes function that creates a library file linking a phase with a velocity model. By executing PHASETOOL, a file is generated and saved in the "Libfiles" directory. This library file is called upon by many functions in MatTimes. The phase designed in MKPHASE is interpreted in this function and compact vector information is stored within a stmctured array. The calculation time required by this function is noticeable, however, it only has to be executed once for a given phase/model pair. The command:
phasetool(PHASE,MODEL) generates a library file that links PHASE with MODEL. PHASE is a string argument naming a phase generated in MKPHASE (i.e., 'Pds'). MODEL is a string argument naming a velocity model file (i.e., 'iasp9r). The created library file will be save in "Libfiles" and will be named PHASE_MODEL_lib.mat (i.e., Pds_iasp91_lib.mat). It is apparent from this execution method that any phase can be linked to any velocity model after execution of MKPHASE. A phase can also be linked to two velocity models simultaneously, which creates a "two-ended" model where one velocity model is associated with the source region and the other is associated with the receiver region. This is important for making local velocity corrections on travel times and ray paths. The command:
phasetool(PHASE,MODEL,RMODEL)
144
creates a two-ended velocity model library file. In this execution method, the third argument (RMODEL) is a string argument naming a local ID velocity model. The saved library file is named PHASEMODEL-RMODELJib.mat where "~" denotes a twoended model as will be recognized by other functions in MatTimes.
Examples: 1) Link PKKP with the velocity model IASP91: phasetool('PKKP','iasp91'); 2) Link PT^:^ with the velocity model PREM: phasetool('PKKP','prem'); 3) Create a library file for Pds with IASP91 and a pre-created slower version of IASP91: phasetool('Pds','iasp9r,'slowiasp9r);
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SECTION V CALCULATING TRAVEL TIMES
Calculation of travel times in MatTimes is the primary focus of the algorithms and logic. Therefore, calculating travel times is done very efficiently within the workspace. Single travel times or a suite of travel times for a phase with a variable depth range, can be calculated for a ray path beginning at any source depth and ending at a seismometer at any elevation. Also, if multiple times exist, all possible times for that phase are calculated simultaneously. Flexibility has been maintained in the algorithms as several options for input exist.
5.1 MatTimes Tool: TIMETOOL TIMETOOL is the primary tool used in calculating travel times in MatTimes. Many useful input and output forms exist for this function, however, efficiency has maintained by using existing MATLAB functions and matrix algebra logic. Calculated information is always available in the workspace and is saved to a file in the "Curves" directory (called a "curve" file) by default. The curve file contains basic I/O data used and calculated during execution. The file contains three variables: curves, input and output. These variables are stmctured arrays with the fields listed in the following example of o. Pds curve file contents:
curves times: [60x1 double] tau: [60x1 double] ranges: [60x1 double]
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input phase: depths: 660 model: event: [60 33] receiver: 0 output = time: 672.1876 raypar: 383.7647
The variable curves contains travel time curve(s) and T(p) vector(s). The variables input and output are simply the input and output to and from TIMETOOL respectively. The field values will become obvious as the execution methods of TIMETOOL are explained. Output of this file makes the execution of other functions simple and also retains calculated information that may be needed at a later time. For example, the travel time curve can be simply plotted with the following command after loading the curve file:
plot(curves.ranges,curves.times)
however, a command named CURVEPLOT is used for this purpose.
5.1.1 Vector Input The command:
[time,rayp]=timetool(PH,D,MODEL,E,R,NAME)
will compute travel time(s) (seconds) and ray parameters(s) (sec/radian) for the desired phase and model pair. PH is a string argument naming an existing phase (i.e., 'Pds') and 147
D is the depth variable value(s) (i.e., [410 660]). If the phase does not have a variable depth associated with it, the input should simply be and empty vector surrounded with brackets ([]). MODEL is a string argument naming the velocity model used in the calculation (i.e., 'iasp9r). MODEL could also be a two-ended model denoted with "~" (i.e., 'iasp91~slowiasp9r). E and R are the event and receiver information respectively. There are two possible ways to enter E and R. One choice is to provide TIMETOOL with the arc distance and source depth within E and the receiver elevation within R such as the following:
E=[60 33]: R=[0]; where the first value of E is the arc distance in arc degrees and the second value is the source depth in kilometers. R, in this case is simply the seismometer elevation from the Earth's surface in kilometers. The second choice of input is to provide TIMETOOL with the actual coordinates of the event and receiver such as the following:
E=[52-112 200]; R=[30-112 0.9];
where the first two values of each are the latitude and longitudes of the earthquake and seismometer respectively. In this case, TIMETOOL relies upon utilities in the Mapping Toolbox to determine great circle arc distance based on geodetic data provide by NASA and JPL. The MatTimes fimction TRACETOOL is used for this problem. TRACETOOL is outlined the RAY PATHS portion of this manual. In this type of execution, the I/O is saved to the curve file named NAME_curves.mat where NAME is an input. If NAME is 148
left out of the argument list, the name P_MODEL_curves.mat is assumed where P and MODEL are input strings. Therefore, any time that TIMETOOL is ran without a curve file name, this file is replaced.
5.1.2 Data File Input Another execution form of TIMETOOL allows for the input of a MatTimes data file as created with MKDATAFILE or SACTOOL. This execution method is useful as the event and receiver information can be extracted and calculated values can be saved to the data file as new fields in the structured array. These values can be used as markers within the data stream. The command:
[time,rayp]=timetool(PH,D,MODEL,DATAFILE,NAME)
where DATAFILE is a string argument naming the saved data (i.e., 'event0920z'). This command will save the travel time and ray parameter values to the stmctured array in DATAFILE as fields: PH_MODEL_dpth, PHMODELjime and PH_MODEL_rayp where PH and MODEL are the input strings. The "_dpth" extension refers to the input variable depth vector. The "time" and "_rayp" refer to the calculated travel time(s) and ray parameters(s) respectively. If NAME is an input, a curve file is generated as well.
Examples: 1) Calculate travel time and ray parameter for i' at 35° arc distance for the IASP91 velocity model and surface focus: [time,raypar]=timetool('P',[],'iasp91',[35 0],[0]) 2) Calculate travel time and ray parameter for P at 35° arc distance for the a two-ended velocity model and surface focus: 149
[time,raypar]=timetool('P', [] ,'iasp91 ~slowiasp91', [3 5 0], [0]) 3) Calculate travel time and ray parameter for P at 35° arc distance for the IASP91 velocity model and surface focus and save to a curve file with the preferred name "tempcurve": [time,raypar]=timetool('P',[],'iasp91',[35 0],[0],'tempcurve') 4) Calculate travel times and ray parameters for P220s, P410s and P660s from two particular locations: E=[35-112 35]; R=[2-110 0.5]; [time,raypar]=timetool('Pds',[220 410 660],'iasp91',E,R) 5) Calculate travel times and ray parameters for PKKP at 110° which has two possible values: [time,raypar]=timetool('PKKP',[],'iasp91',[l 10 0],0) gives: time = [1786.2 1773.9]; raypar=[253.79 184.51]; 6) Calculate travel times and ray parameters for P220s, P410s and P660s for the event/receiver pair within a data file imported with SACTOOL: sactoolCevent0920z'); [time,raypar]=timetool('Pds',[220 410 660],'iasp91'.'event0920z.mat') Load in the data file, and look at its contents: load('event0920z') data = name:'c:/programs/mattimes/data/event0920z.mat' import: '23-Mar-2000 16:52:03' evtime: [1994 346 7 41 55.4000] begintime: [1994 346 7 51 45.1290] streamtime: 360.2000 stationjat: 34.1483 stationjon:-118.1717 station_elevation: 0.2950 150
borehole_depth: 0 compass_az: 0 compass_inc: 0 eventjat: -17.4770 eventjon: -69.5980 event_depth: 148 magnitude: 6.3000 arc_distance: 7.6886e+003 azimuth: 318.2648 backazimuth: 129.9962 gcarc: 69.0880 SACTO: 60.1355 SACTl: 593.9830 SACT2: 214.4268 SACT3: 863.8177 SACT4: 85.2001 SACT5: 646.5028 SACT6: 645.4480 dt: 0.2000 data: [1x1802 double] event: [-17.4770 -69.5980 148] receiver: [34.1483 -118.1717 0.2950] Pdsjasp91_dpth: [3x1 double] Pdsjasp91 time: [3x1 double] Pds iasp91 rayp: [3x1 double]
151
SECTION VI CALCULATING RAY PATHS
Ray path locations can be determined in MatTimes using pre-computed partial ray path integrals in the library files created by PHASETOOL. All ray paths are determined in an incremental sense based on the desired velocity model sampling. Entire ray paths can be determined with a simple function execution. Also, certain ray path segments can be determined as are defined by MKPHASE. Tools are available to find incremental arc distances and real world coordinates using the Mapping Toolbox.
6.1 MatTimes Tool: ARCTOOL ARCTOOL is a flexible function that calculates incremental arc distances and times for a given seismic event and phase. Values are determined from files in the "Tau" directory that are generated by MKTAU and MKTAUb which are sub-functions of MKMODEL. In these files, vector information for the velocity model is compactly stored. The I/O operations of this function are similar to TIMETOOL. The values can be stored in a curve file or data file, depending on the input. Also, particular segments of a phase can be determined as well as a vector describing the wave type at each point. This function does not determine real coordinates, just incremental arc distances in degrees along the Earth's surface. Plotting and mapping functions require this tool in conjunction with TRACETOOL visualize ray paths.
152
6.1.1 Vector Input The command:
[x,z,t,w]=arctool(MODEL,RP.PH,SD,V,SEG)
determines the incremental arc distances (x), depths (z), times (t) and wavetype (w) for the ray path defined by the velocity model (MODEL), ray parameter (RP, in sec/rad), phase (PH), source depth (SD), depth variable (V) and the segment number for the phase (SEG). MODEL and PH are string arguments naming an existing velocity model (i.e., 'iasp9r) and an existing phase (i.e.,'PKKP'). respectively. SEG, if chosen as input, is the segment number of the desired phase. For example, the last segment of Pds is the 3^^ since the first consists of a ray path from the source to the tuming point, the second is from the tuming point to the variable depth and the third is the S-wave from the variable depth to the seismometer. If this value is left off, all segments are assumed. If the phase does not have variable depths associated with it, V should be set as an empt} vector ([]).
6.1.2 Curve File Input A convenient way to execute ARCTOOL is to use a curve file generated by TIMETOOL. In this case, the ray parameter in the output variable is used as well all values in the input variable. This makes execution very simple. The determined \ alues are saved to the input curve file for later retrieval. However, the values are alwa\ s generated within the MATLAB workspace. The command:
[x,z,t,w]=arctool(CURVEFILE,SEG)
153
will calculate incremental values for the ray path using the values stored in CURVEFILE as input. SEG is the same as the vector input and CURVEFILE is a string argument naming a curve file generated by TIMETOOL (i.e., 'Pdsjasp9r). In this case, new fields are set the curve file variable output. Here is an example of a curve file contents after this type of execution:
curves = imes: [60x1 double] tau: [60x1 double] ranges: [60x1 double] input = phase : depths: model: event: receiver:
' Pel:- ' 660 ' asr [60 33] 0
output = time: 672.1876 raypar: 383.7647 x: [150x1 double] z: [150x1 double] t: [150x1 double] wave: [150x1 double]
where the fields x, z, t and "wave" are now within the stmctured variable output.
6.1.3 Data File Input Another convenient way to execute ARCTOOL, is by using a data file created by MKDATAFILE or SACTOOL as input. This type of input is similar to a curve file input except that the values are saved out to the data file as new fields in the stmctured array 154
data which can be a single or multiple component data stmcture as discussed in the DATA STRUCTURES section of this manual. This type of I/O manipulafion is extremely useful when computing ray path geometries for many seismic events as the output is linked directly with the data file. The command:
[x,z,t,w]=arctool(DATAFILE,PH,MODEL,SEG)
will determine incremental values and store them within DATAFILE. All input with the exception of DATAFILE are the previous execution methods. DATAFILE is a string argument naming a data file created by MKDATAFILE or SACTOOL (i.e., 'event0920z.mat'). The fieldnames added are easily identifiable in data with the nomenclature: PHASE_MODEL_arcx, PHASE_MODEL_arcz, PHASE_MODEL_arct and PHASEMODELarcw. The letter appended to arc corresponds to the workspace output variable. This type of naming is useful when calculations are needed for more than one velocity model and for a combination of phases. Also, the user always knows what the values in the field represent. There is no known limitation of the number of fields that can be added to the stmctured array.
Examples: 1) Calculate the progressive arc distances and times for SKKS having a ray parameter of 240 sec/rad and a source depth of 35 km: [x,z,t,w]=arctool('iasp91',240,'SKKS',35,[]); 2) Calculate the progressive arc distances and times for SKKS and a twoended velocity model having a ray parameter of 240 sec/rad and a source depth of 35 km: [x,z,t,w]=arctool('iasp91~slowiasp91',240,'SKKS',35,[]); 155
3) Calculate the progressive arc distances and times for P410s having a ray parameter of 350 sec/rad and a source depth of 35 km: [x,z,t,w]=arctool('iasp91',350,'Pds',35,410); 4) Calculate the progressive arc distances and times for P having a ray parameter and source depth as defined in a curve file: arctool('PJasp91'); 5) Calculate the progressive arc distances and times for P having a ray parameter and source depth as defined in a data file imported from SAC: sactool('event0920z'); timetool('P',[],'iasp91','event0920z.mat'); arctool('event0920z.mat','P','iasp91'); Load in the data file and examine the new fields in the variable data: load('event0920z') data(l) You should see the following fields appended to the bottom of the stmctured array: P iasp91_arcx: [148x1 PJasp91_arcz: [148x1 PJasp91_arct: [148x1 PJasp91_arcw: [148x1 PJasp91_arcs: [1 2]
double] double] double] double]
6.2 MatTimes Tool: PPTOOL In some cases, only the back projection of ray paths from a seismic station is needed. For this reason, the tool PPTOOL was developed. PPTOOL is similar to ARCTOOL in that the I/O character is the same. If a curve file is used as input, the calculated points (in arc degrees) are save to the curve file. On the other hand, a data file can be used as input with similar results. This function is the same as ARCTOOL when 156
only the last segment of a phase is determined. However, PPTOOL is more compact, hence faster, and output values are in terms of progressive arc distances from the seismometer. If a two-ended model is input (i.e., 'iasp91~slowiasp9r), the 2"^^ model is assumed to be the model to trace with.
6.2.1 Vector Input No form of a data file is needed for PPTOOL. The command:
[x,z,t]=pptool(PH,MODEL,W,RP,DEPTHS)
will find piercing points away from the seismic station for the wave type (W, 'p' or 's') and the ray parameter (RP, in sec/rad). PH is a string argument naming an existing phase (i.e., 'P') and MODEL is a string argument naming an existing velocity model (i.e., 'iasp91'). DEPTHS are the depths to sample (i.e., [0:20:760]). PH is a necessary input in order to check the existence of the input ray parameter. If RP is invalid, x and t will be vectors equal to Not-A-Number (NAN).
6.2.2 Curve File Input A convenient way to execute PPTOOL is to input a curve file as computed by TIMETOOL. This curve file will contain all updated information from the last execution of TIMETOOL with the given model and phase. This means that you do not have to input the variables from the workspace. The command:
[x,z,t]=pptool(CURVEFILE,DEPTHS)
157
will compute piercing point from the station at DEPTHS. In this case, ray parameter and phase information are extracted from CURVEFILE and the wave type of the last segment of the phase is assumed (i.e., for Pds, type 's' is used). New fields will be set to the varaiable output in CURVEFILE. Here are the contents of output after execution of PPTOOL:
output = time: 413.9774 raypar: 493.5571 ppx: [1x39 double] ppt: [1x39 double] ppz: [1x39 double]
where the fields ppx, ppt and ppz are added to the file. The field time still corresponds to total travel time for the phase. This stmctured array can simply be called from subsequent functions for plotting and calculation purposes. If the phase contains a variable depth range and multiple depths were used during the call to TIMETOOL, another useful execution method is used. The command:
[x,z,t]=pptool(CURVEFILE)
without the depths input will assume that the curve file has a variable depth range associated with the phase. In this case, PPTOOL will calculate the piercing point at the variable depth value for the last wave type in the phase segments. The corresponding ray parameter is used. For example, to calculate P410s and P660s conversion points simultaneously, use the following command sequence:
158
timetool('Pds',[410 660],'iasp91',[35 0],[0]); pptool('PdsJasp91'); where an arc distance of 35° and a surface focus were chosen.
6.2.3 Data File Input A MatTimes data file generated by MKDATFILE or SACTOOL can also be input for PPTOOL. This calling method is similar to the curve file input except the needed fields are located within the stmctured array data in the data file. This allows the user to store ray path geometries directly to the data file for later retrieval. The command: [x,z,t]=pptool(FILE,PH,MODEL,DEPTHS)
will compute piercing points for the ray parameter stored in FILE at DEPTHS. FILE is a string argument naming an existing MatTimes data file (i.e., 'event0920z'). The other inputs are the same as those with vector input. The values will be saved to the data file stmctured array data. With data file input, PPTOOL also calls the function TRACETOOL to determine actual latitude and longitude positions. Example fields added to the data file are illustrated below:
Pds iasp91_pptz: [2x1 double] Pdsjasp91_pph: [2x1 double] Pdsjasp91_ppln: [2x1 double] Pdsjasp91_pptx: [2x1 double] Pdsjasp91_pptt: [2x1 double]
159
The field name extensions pptz, pptx and pptt are the piercing point depths, arc distances, and times respectively. The field names with the extensions pplt and ppln are the latitude and longitude locations of the piercing points respectively.
Examples: 1) Calculate piercing points for P at 0 to 660 km for an increment of 20 km with a ray parameter of 300 sec/rad: [x,z,t]=pptoolCP','iasp91','p',300,[0:20:660]); 2) Calculate piercing points for /* at 0 to 660 km for an increment of 20 km with a ray parameter of 300 sec/rad: [x,z,t]=pptool('P','iasp91','p',300,[0:20:660]); 3) Calculate piercing points for all S-waves in the Pds curve file where multiple ray paths were determined: [x,z,t]=pptool('Pds iasp91'); 4) Use a data file imported from SAC as input to calculate piercing points of P41 Os and P660s: sactool('event0920z') timetoolCPds',[410 660],'iasp9r,'event0920z.mat'); pptoolCevent0920z','Pds','iasp91');
6.3 MatTimes Tool: TRACETOOL In conjunction with ARCTOOL or PPTOOL, TRACETOOL will calculate coordinates of a given ray path. This function relies upon the Mapping Toolbox 1.1 and geodetic data obtained from NASA and JPL. These values were obtained from http://ssd.jpl.nasa.gov/phys props earth.html and are listed below:
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semi-minor axis semi-major axis eccentricity
6356.752 km 6378.140 km 0.08183
where the average radius is 6367.446 km. Points are determined by initially finding the azimuth to project the ray path towards. TRACETOOL can also be used as a simple tool to determine azimuth or back azimuth with the input of two points on the surface of the Earth. An arc vector as generated by ARCTOOL or PPTOOL that may have been saved in a curve file or a MatTimes data file determines sample points.
6.3.1 Vector Input TRACETOOL can be called as strictly a workspace function where no files act as input. The command:
[lat,lon,az,gca]=tracetool(E,R,X)
traces out an azimuthal path between the event location (E) and the receiver location (R) based on the progressive arc distances from the event location within the vector X. E is the event location where the first element is latitude a the second element is longitude. R is similar to E except that it is the location of the earthquake epicenter. Note that it would be simple to reverse the input order of E and R is distances from the receiver reside in X. In such a case, the back azimuth would be calculated rather than the azimuth. The outputs Iat and Ion are the latitudes and longitudes, respectively. The outputs az and gca are the azimuth (degrees from north) and great circle arc distance in degrees.
161
6.3.2 Curve File Input A more practical way to execute TRACETOOL would be to use a curve file inifially generated by TIMETOOL and updated with ARCTOOL or PPTOOL. If the curve file has the relevant fields needed (fields set in the aforementioned functions), TRACETOOL will determine the coordinates as sampled in the arc vector that resides in the variable output. The values calculated will be saved in new fields within the curve file. The command:
[lat,lon,az,gca]=tracetool(CF,FLD) calculates the ray path coordinates based on information obtained from the curve file (CF). CF is a string argument naming an existing curve file that must have been input to ARCTOOL or PPTOOL prior to execution. In this case, TRACETOOL needs to know whether the calculations to perform are on the fields with piercing point arc distances or the fields with ray path arc distances (from the source). For this reason, FLD is an input and can be one of two values: 1) 'ppt' or 2) 'arc'. If 'ppt' is chosen, the piercing point locations will be determined. Otherwise, if 'arc' is chosen of FLD is left off, arc distances from ARCTOOL will be used. The input curve file will output to the same name with the following additional fields created within the variable output:
pplat: [129x1 double] pplon: [129x1 double]
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where pplat and pplon are the ray path latitudes and longitudes at each sampled depth in the field z.
6.3.3 Data File Input Another calling form of TRACETOOL is to use a MatTimes data file created by SACTOOL of MKDATAFILE as input. This case is similar to calling a curve file except the values are saved in fields within the data file. The command:
[lat,lon,az,gca]=tracetool(FILE,PH,MODEL,FLD)
will find the ray path coordinates and save them to field in the variable data within the data file FILE. In this case, FILE is a string argument naming a data file. PH and MODEL are string arguments naming the phase and velocity model desired. The values must correspond to existing field names in the data file. This is assured if ARCTOOL or PPTOOL have been executed using the data file and the same phase and velocity model. The new fields saved to the data stmctured array in FILE are named as PH_M0DELj3plt and PH_MODEL_ppln for piercing point input. If the input is data from ARCTOOL, the fields' names are PH_MODEL_arh and PH_MODEL_arln. In both cases, the It stands for latitude and the In stands for longitude.
Examples: 1) Find the surface ray path between two points on the Earth for 1 °, 3° and 5° from the event at 30°N and 114°E: [lat,lon]=tracetool([30 114],[35 112],[1 3 5]); 163
2) Find the ray path coordinates for an entire ray path using values within a curve file: [lat,lon,az,gca]=tracetool('PJasp91'); 3) Find the azimuth and great circle arc between to coordinates: [az,gca]=tracetool([30 114],[35 112]); 4) Find piercing point locations for Pds conversion points from a depth of 0 km to 900 km using a data file as input: timetool('Pds',[0:20;900],'iasp91','event0920z'); pptool('event0920z','Pds','iasp91'); tracetool('event0920z','Pds','iasp91','ppt');
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SECTION VII PLOTTING AND MAPPING
Plotting and mapping are essential processes used in all types of seismic analyses. MATLAB provides many flexible graphical functions that are used by MatTimes to view seismic data, travel time curves and ray paths. The Mapping Toolbox provides functions that are used by MatTimes to visualize ray path traces on the surface of the Earth in the form of maps and animations. Although mapping has not been the highest priority of MatTimes development, publication-quality maps can be produced for interpretation, manuscripts or as teaching tools.
7.1 MatTimes Tool: PL0T3C0MP Although plotting seismic data is very simple within the MATLAB workspace, it is not necessarily simple to plot data embedded within a data file including travel time markers that may exist within the stmctured array. The function PL0T3C0MP allows MatTimes users to plot multi-component (or single component) data files with a single input. The command:
plot3comp(FILE)
will plot all data components and markers in FILE. FILE is a string argument naming a MatTimes data file created by MKDATAFILE or SACTOOL. Figures 7.1 and 7.2 are single and three-channel data plots with markers, respectively.
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F
MlOt P960S
6000
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4000
2000
E
0
-2000
-4000
-6000
_j
50
100
150
200 sees
L_
250
300
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Figure 7.1. A single component plotting example with P, P410s and P660s time markers.
P410S P660S
400
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event09202 AAj\AAw^'^^^-v\,'^'v-A^pv/~w\AAA/\^^ -5000
-10000
50
100
150
200 sees
250
300
350
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Figure 7.2. An example of a three-component data plot created by PL0T3C0MP. Travel time markers were determined with TIMETOOL.
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Examples: 1) Import a single component from SAC and plot the data with a P-wave travel time marker (see Figure 7.1): sactool('event0920z') [time,raypar]=timetool('P',[],'iasp91','event0920z.mat') plot3comp('event0920z') 2) Import and plot three components with P, P410s and P660s markers (see Figure 7.2): LIST3=[dir('event0920e') dir('event0920n') dir('event0920z')]; DIRECTORY=[];NAMES.name='event0920'; sactool(LIST3,DIRECTORY,NAMES); [time,raypar]=timetool('P',[],'iasp91','event0920.mat') [time,raypar]=tinietool('Pds',[410 660],'iasp91','event0920.mat') plot3comp('event0920')
7.2 MatTimes Tool: CURVEPLOT After the execution of TIMETOOL, a curve file is created in the "Curves" directory. In this file, travel times computed for the inputs of the last execution of TIMETOOL are stored in stmctured arrays.
Complete travel time curves for every
possible range for the phase in the curve file. The travel time curve(s) in the data file are times adjusted by the source depth and variable depth(s) used in the last execution of TIMETOOL. The command:
curveplot(CURVE,C)
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will plot the travel time curves within the curve file CURVE with the color specified with C. CURVE is a string argument naming a curve file (i.e., 'PJasp9r) and C is a string with the plotting style (i.e., 'k*'). If the curve file has multiple curves as computed with multiple variable depths, all curves are plotted. Figures 7.3, 7.4 and 7.5 are example curve plots. PP, laspSI, tourci: 0 km
iaoo
1600
1400
-S 1200
E 1000
600
20
40
60
80 100 120 arc distanct (d«gr«as)
140
160
180
Figure 7.3. Example output from curve plot for PP with a source depth of 0 km. Notice the multi-valued nature of the phase at 170° where the phase wraps. Pds, laspSI, sourca: 3S km 900
10
20
30
40
50 60 arc dislanc* (degrats)
70
Figure 7.4. Example curve plot of P, P410s, and P660s calculated with a source depth of 35 km. This is done with two executions of CURVEPLOT.
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PKKP, laspSI, source: 0 km 1
1900
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1
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1
1
1
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1700 50
1
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1
60
70
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1
90
1
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100 110 120 arc distance (degrees)
1
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1
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Figure 7.5. Example curve plot of PKKPab, PKKPbc, PKKPcd and PKKPdf for a surface focus and the IASP91 velocity model.
7.3 MatTimes Tool: PLOTPHASE Simple 2D representations of ray paths are often useful illustrations to describe the geometry of a given phase. A flexible tool, PLOTPHASE, is used for such illustrations. The command:
plotphase(PH,M,RP,SD,V,F,C)
will plot a ray path through a 2D Earth model for the phase (PH) and velocity model (M) using the ray parameter (RP in sec/rad). PH and M are string arguments naming the phase (i.e., 'PKKP') and model (i.e., 'iasp9r). SD is the source depth and V is the variable depth if the phase has this option. F is a flag value that determines the type of 2D Earth to draw. For a value of F equal to 1, the Earth model will be a simple line plot. 169
If F is equal to 2, the Earth model will be a patch object where colors separated major Earth components. For F equal to 3 or 4, the model will be similar to 1 and 2 respectively except that some text will be placed on the plot. C is the style (color and line type) of the ray path to be dravm. A simpler way to call PLOTPHASE is to use a curve file as input. The command:
plotphase(FILE,F,C) will extract the relevant information from FILE to draw the ray path. Using this command after execution of TIMETOOL followed by ARCTOOL is the easiest method to plot ray paths. ARCTOOL must be executed using the curve file as input prior to using this function, as incremental arc distances must be known. Symbols are used to indicate the source and seismometer locations at the two ends of the drawn phase. All plotting is done in polar coordinates. See the MATLAB function POLAR for further guidance. Figures 4.3, 4.6 and 4.9 demonstrate some output from PLOTPHASE. Figure 7.6 demonstrates a ray path plot for PKKKP.
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PKKKP, iasp91, source: 300 km
gcarc: 58 deg, rayp: 120 sec/rad
Figure 7.6. A ray geometry plot of PKKKP using PLOTPHASE. The source depth is 300 km. The numerical values on the 2D model are the model radii for the inner/outer core boundary (1217), the lower mantle boundary (3482), the upper/lower mantle interface (5711) and the Earth radius (6371). This particular plot was created using option 4 for the flag value.
7.4 MatTimes Tool: MAPPHASE MAPPHASE uses tools in the Mapping Toolbox to map out a phase path on the surface of Earth. This type of illustration is especially useful for publication and teaching purposes. MAPPHASE has been made flexible and simple as most options existing in the mapping utilities are used in a compact fashion. The user can define desired map
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preferences for particular needs and MAPPHASE allows input from data files and curve files. The command:
mapphase(MODEL,PH,E,R,V,MAPPREF)
will map out the surface trace of the phase (PH) between the event and receiver (E and R, respectively) locations. With this type of execution, a curve file is created and ARCTOOL is executed using the curve file as input followed by TRACETOOL to find real coordinates. The mapping preferences are stored within MAPPREF which is a string argument naming the file (i.e., 'mymap'). MODEL is a string argument naming the velocity model (i.e., 'iasp9r) and PH is a string argument naming the phase (i.e., 'PKKP'). The input argument V is the variable depth of the phase. If the phase does not have a variable depth associated with it, the argument should be an empt}' vector as always ([]). See TIMETOOL for further explanation of the input arguments. To make a mapping preference file, certain variables must be assigned and saved from the MATLAB workspace. Although variable names in the explanation are upper case, the actual variable names should be lower case (i.e., "PROJECTION" should actually be "projection"). PROJECTION is a string name of one of many possible map projections supplied by The Mapping Toolbox. MTYPE is string describing the type of map to plot. The only opfions are 'lines' and 'topo'. LINEWIDTH and SYMBOLSIZE correspond the sizes of the mapped phase line width and E/R locator symbols respectively. ORIGIN is a vector describing the view of the map. If 0RIGIN=1. the map origin will adjust automatically to include a continuously mapped phase. If ORIGIN=0, no adjustment will be made as the map will be centered about 0 degrees longitude. If 172
ORIGIN is a three-component vector, the origin of the map will be adjusted according!). COLORS is a two-element cell array containing color and line preferences for P and S waves respectively.
MARKER is a two-element cell array providing event and receiver
marker colors and shapes. FACECOLOR is a one-element string of the interior symbol color. The following is a sample preference file created in the workspace:
mtype='topo'; proj ection='vperspec'; linewidth=1.5; symbolsize=8; origin=[15-140 0]; colors={'r' 'r'}; (can also be 'k:', etc.) marker={'r*' 'r^'}; facecolor='y'; save my_map_preferences.mat where the projection name corresponds to available projection types in the Mapping Toolbox. If a curve file has been previously generated, MAPPHASE can use is as input. The command: mapphase(CURVE,MAPPREF)
will create a map from values saved within the curve file CURVE (i.e., 'PKKPJasp9r). If MAPPREF is not an input, a defauh map style is used. To use this type of execution method, ARCTOOL and TRACETOOL must have been previously executed using CURVE as input.
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Another convenient way to execute MAPPHASE is input a MatTimes data file created by MKDATAFILE or SACTOOL. The command:
mapphase(FILE,PH,M,V,MAPPREF) will execute the necessary sequence of functions to map out the desired phase based on information found in FILE. All inputs are the same as above except FILE which is a string argument naming a data file. This is a quick way to visualize a ray path for a real event without executing functions individually. Figures 7.7, 7.8 and 7.9 are example maps created with IVIAPPHASE.
Event: -20,-179,250, Receiver: 35,-118,1, Phase: P660s, Model: IASP91
Figure 7.7. Example map created with IVIAPPHASE for an event in the Tonga region recorded in Califomia. The P660s is mapped in red.
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Event: 30,112,0. Receiver: 50,0,0, Phase: P660s, Model: iASP91
Figure 7.8. Example map created with ]S/IAPPHASE. Event: 30,112,0, Receiver: 50,65,0, Phase: ScP, Model: IASP91
Figure 7.9. A simple map created by MAPPHASE with a ray path for ScP plotted. Notice that the S-wave segment is colored in red and the P-wave is m black.
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7.5 MatTimes Tool: MOVIEMAP Animated maps of phase paths may provide a helpful teaching tool or other presentation device. For this reason, MOVIEMAP has been include with MatTimes. This function will create and play a movie of a spinning globe (or scrolling map) with a mapped phase within the MATLAB workspace. The command:
moviemap(CURVE,INC,N,MAPPREF) will create a play a movie of frames determined by the longitude increment INC. The movie will be played N times, and if N is negative, the movie is played N times in forward and reverse. CURVE is a string argument naming a curve file and MAPPREF is the same as in MAPPHASE.
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SECTION VIII OTHER UTILITIES
There are some extraneous functions that do not necessarily fit under any classification in this manual. There are functions that underlie other functions as well as some utilities that we have found to be useful. This section is dedicated to describing some of these functions that may be of use to the user for individual purposes, however they are of lesser importance.
8.1 MatTimes Tool: MKEARTH MKEARTH is a fimction called by PLOTPHASE to create the Earth patch/line object in polar coordinates. The command: mkearth(MODEL,F)
will create the patch or line object representation of Earth based on the velocity model (MODEL) depth interfaces. The input, F, is a flag value indicating the type of object to be created. See PHASETOOL for further instmctions.
8.2 MatTimes Tool: TURNTOOL TURNTOOL is a function that determines the tuming depth for a particular model and ray parameter. This function can be used to assure that a phase tums in the appropriate region. The command:
[TP,TS]=tumtool(MODEL,RP,SHAD)
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will determine the tuming depth for both P and S waves for the ray parameter (RP, in sec/rad). SHAD is an indicates whether or not the ray path can tum within the outer core shadow zone. If the ray path is allowed to tum in the shadow zone, SHAD should be the ' ,
string y
• '
8.3 MatTimes Tool: VPLOT To quickly look at a velocity model, VPLOT can assist. VPLOT simply calls on the velocity model in the "Models" directory and plots both P and S wave velocities versus radius. The command: vplot(MODEL,COLOR) will plot the velocity model (MODEL) with the line color COLOR.
5 10 velocity (km/s)
Figure 8.1. Example output from VPLOT created with "vplotCiasp91','k')".
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8.4 MatTimes Tool: CUTDATA CUTDATA is a funcfion that will clip data within MatTimes data files about a particular travel time. For instance, if a data file contains the entire wa\eform and onl>' particular part of the data is needed, CUTDATA will update the file to contain only a windowed portion and also update fields in the stmctured array appropriately. The command:
cutdata(L,PH,V,MODEL,W,M)
will cut the data files listed in the stmctured list, L. The list can be generated with a form of the following command: L=dir('event*');
PH and V are the phase and variable depth respectively. MODEL is the velocity model name and W is the wdndow to cut. The first element of W is the pre-phase time in seconds to keep and the second element is the post-phase time in seconds. The input M determines whether the data file will deleted if the appropriate time window does not exist. If M is equal to 0, no files will deleted. If M is equal to 1, the data files within the list will be deleted if the appropriate time window or the phase does not exist for the given event.
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8.5 MatTimes Tool: SEC2DHMS SEC2DHMS will convert seconds into Julian day, hours, minutes and seconds. This function could be needed to create the variable begintime to create a MatTimes data file. The command:
[jd,h,m,s]=sec2dhms(SECS) will convert SECS to Julian day Qd), hour (h), minutes (m) and seconds (s).
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USER'S MANUAL REFERENCES
Buland, R. and Chapman, C.H. "The computafion of seismic travel times." Bull. Seism. Soc. Am. 73 (1983), 1271-1302. Crotwell, H.P., Owens, T.J. & Ritsema, J. "The TauP Toolkit: Flexible seismic travelrime and ray-path ufilities." Seism. Res. Lett. 70 (1999), 154-160. Dziewonski, A.M. and Anderson, D.L. "Preliminary reference earth model." Phys. Earth Planet. Inter. 25 (1981), 297-356. Harris, J.M. and Young, CJ. "MatSeis: A seismic toolbox for MATLAB." 18^ Seismic Research Symposium on Monitoring a Comprehensive Test Ban Treaty, Phillips Laboratory (1996). Kennett, B.L.N, and Engdahl, E.R. "Travel times for global earthquake location and phase identification." Geophys. J. Int, 105 (1991), 429-465. Tull, J.E. Seismic Analysis Code: User's Manual. Livermore, CA: Lawrence Livermore National Laboratory, 1989.
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APPENDIX B MATTIMES SOURCE CODE
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Location:/MatTimes/Graphics/curveplot.m ftinctioncurveplot(pliase,model,source_depth,d,color) %MatTinies Tool: %
%CURVEPLOT Plots seismic travel time curve(s). % 1) CURVEPLOT(PHASE,MODEL,SOURCE_DEPTH,VARIABLE,COLOR) % Generates a CURVEFILE and plots travel time (seconds) versus range % (degrees) for the desired inputs. PHASE is a string corresponding % to the seismic phase to plot (as generated by MKPHASE). MODEL is a % string naming the desired velocity model and SOURCEDEPTH is the % earthquake depth in km which can be multi-valued. VARIABLE is a depth % variable for the phase given (i.e., PHASE='Pds' and VARIABLE=410 will % generate a travel time curve for "P41 Os" as "d" corresponds to a % compression-to-shear conversion at 410 km). COLOR is a string % argument that defines the plot style (i.e.,'k' or 'r*'). % % 2) CURVEPLOT(CURVEFILE,COLOR) % Plots travel time (seconds) versus range (degrees) based on the % variables within the CURVEFILE (as generated by TIMETOOL). % % EXAMPLES: % % curveplot('Pds','iasp91',33,410,'k') % curveplot('Pds_iasp9r,'rd') % curveplot('P','iasp91',33,'g') % load dirjjath abcde=findstr('.mat',phase); if length(abcde)>0 %kill ".mat" extension phase=phase(l :length(phase)-4); end if nargin0 %kill ".mat" extension model=model(l :length(model)-4); end if nargin=3 color='k'; d=[]; elseif nargin=4 color=d; d=[]; else end if nargin>2 for i=l :length(source_depth) [time,raypar]=timetool(phase,d,model,[10source_depth(i)],[0]); load([wherecurvefiIes 'f phase '_' model 'curves.mat'])
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hold on plot(curves.ranges,curves.times,color,'LineWidth',2) end
else piot(curves.ranges,curves.times,color,'LineWidth',2) end ff=findstr('d',lower(phase)); if isempty(ff) phase2=phase; else if length(d)>l ;dd='d';else;dd=int2str(d);end phase2=[phase(l :ff-l) dd phase(ff+I :length(phase))]; end strl=[phase2 ',' (model)',' ]; str2=['source:' int2str(source_depth)' km']; strr=rm_([strl str2]); title(strr,'FontWeight*,'Bold') xlabel('arc distance (degrees)','FontWeight','Bold') ylabel('time(seconds)','FontWeight','Bold') grid on hold off Location: /MatTimes/Graphics/mkearth.m function mkearth(model,flag) %MatTimes Tool: %
%MKEARTH Generates a graphical representation of the Earth. %MKEARTH(MODEL,FLAG) % Uses MODEL to create a graphical representation of the Earth % based on the location of the interfaces of the major components 0, % of the Earth: upper mantle/crust, lower mantle, outer core and % inner core. MODEL is a string argument naming the desired % velocity model. FLAG indicates the type of Earth to generate. % FLAG=1 creates a simple plot. FLAG=2 creates a patch-generated % Earth. FLAG=3 creates a line version like FLAG=1 except the % radii of the interfaces are labelled. FLAG=4 creates a patch % Earth with the interface radii labelled. % EXAMPLES: %
% mkearth(model,I); plot % mkearth(model,2); solid % mkearth(model,3); plot with text % mkearth(model,4); solid with text model=modelck(model, 1); warning off load dirjjath load([wheremodelfiles'/' model]) maxx=[ 1; breaks(2:4)/max(v_model(:, 1))]; %maxx=[l .8964.5465.191] color=[ .75 0 0; I 0 0; 1 .7 0 ; 1 .9 0]; for k=l :length(maxx); kk=maxx(k); a=l; x=[-kk:.001:kk]; y=(sqrt((kk.'^2-x.^2))); x=[x fliplr(x)]; y=[y -fliplr(y)]; hold on
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ifflag=2|flag=4 patch(y,x,color(k,:)) elseif flag=l | flag=3 plot(y,x,'k','Line Width', 1.2) end end axis equal axis off hold off if flag=3 I flag==4 text(0,-l,int2str(max(radii)),'FontWeight','bold') text(0,-breaks(4)/max(v_model(:,I)),int2str(breaks(4)),'FontWeight','bold') text(0,-breaks(3)/max(v_model(:,l)),int2str(breaks(3)),'FontWeight','bold') text(0,-breaks(2)/max(v_model(:,l)),int2str(breaks(2)),'FontWeight','bold') end hold off Location: /MatTimes/Graphics/moviemap.m function frames=moviemap(curvefile,increment,ntimes,mappref) %MatTimesTool: %
%MOVIEMAP Generates and plays a movie of a mapped phase on a spinning Earth. %
% FRAMES=MOVIEMAP(CURVEFILE,INCREMENT,NTIMES,MAPPREF) % Generates and plays a movie clip after plotting the phase path within % CURVEFILE. CURVEFILE is a string argument naming a curve file originally % generated by TIMETOOL. ARCTOOL and TRACETOOL must have been executed % on the curve file before executing MOVIEMAP INCREMENT is the longitude % increment between movie frames. MAPPREF is a string argument of map % preferences (See: MAPPHASE). If MAPPREF is left off, MOVIEMAP use a % default file. NTIMES is the number of times to play the movie. See % movie to uses FRAMES independantly. If NTIMES is negative, the movie % plays forward and reverse NTIMES. Else if NTIMES is left off or empty % ([]), the movie is saved for later play to a file named: CURVEFILEMOVIE.mat. % PLAYMOVIE is a mattimes tool to play a previously saved movie. % % EXAMPLES: % % tongamovie=moviemap('tonga',5,2); %(try moviemap('tonga',l,10) for fast machines) % moviemap('tonga',5,1 ,'mapdefault') %(uses MAPPHASE defaults) % tongamovie=moviemap('tonga',5) disp(['MOVIEMAP.. .Working']) if nargin=3 mappref='movieprefmat'; end load('dir_path.mat') load(mappref) load([wherecurvefiles'/' curvefile 'curves.mat']); model=input.modeI; raypar=output.raypar; phase=input.phase; event=input.event; receiver=input.receiver; d=input. depths; wave=output. wave; latitude=output.pplat; longitude=output.pplon; if length(origin)=l origin=[0 origin 0];
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end wb=waitbar(0,'Please wait...Building Movie'); samps=max(longitude):-increment:min(longitude); for i=l:length(samps) waitbar(i/length(samps),wb) figure(lOOO) whitebg(IOOO,'k'); set(1000,'NumberTitle','ofir,'Name','Movie'); origin(2)=samps(i); axesm('MapProjection',projection,'Origin',origin); hold on plotm(latitude(I),longitude(2),char(marker(l)),'MarkerSize',symbolsize,... 'MarkerFaceColor'.facecolor); plotm(latitude(length(latitude)),longitude(length(longitude)),char(marker(2)), 'MarkerSize',symbolsize,'MarkerFaceColor',facecolor); iflower(mtype(l))='r load coast fi-amem('b') plotm(lat,long,'LineWidth',.5); elseif lower(mtype( 1 ))='t' load topo meshm(topo,topolegend); demcmap(topo) end a=find(abs(diflF(wave))=I); a=[2; a; length(latitude)]; iflength(a)>l; k=length(a)-I; else ; k=l; end for iii=l:k lati=latitude(a(iii)-I:a(iii+l)); loni=longitude(a(iii)-l:a(iii+l)); if wave(a(iii)+l )==0 plotm(lati,loni,char(colors(I)),'LineWidth',linewidth); else; plotm(lati,loni,char(colors(2)),'LineWidth',linewidth); end end gridm on strl=['Event:' int2str(event(I))',' int2str(event(2))',' int2str(event(3))]; str2=[', Receiver:' int2str(receiver(I))',' int2str(receiver(2))',']; fi=findstr('d',lower(phase)); if isempty(ff) phase2=phase; else phase2=[phase(l :fr-l) int2str(d) phase(ff+l :length(phase))]; end str3=[int2str(receiver(3))', Phase:' phase2 ', Model:' upper(model)]; title([strl str2 str3],'FontWeight','bold','Color','w') hold off frames(i)=getframe; ax=axis; close end close(wb) if nargin>=3 & isempty(ntimes)=0 figure(lOOO)
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whitebg(1000,'k'); set( 1000,'NumberTitle','ofF,'Name','Movie'); axesm('MapProjection',projection); title([strl str2 str3],'FontWeight','bold','Color','w') movie(frames,ntimes) else save([curvefile'_movie'],'frames','projection','strr,'str2','str3','ax'); end disp(['MOVIEMAP...Done']) Location: /MatTimes/Graphics/playmovie.m function playmovie(curvemovie,ntimes) %MatTimes Tool: % %PLAYMOVIE Plays a movie generated by MOVIEMAP. % % PLAYMOVIE(MOVIE,NTIMES) See help on MOVIEMAP. MOVIE is % a string argument naming a movie generated by MOVIEMAP. load(curvemovie) figure(lOOO) whitebg(IOOO,'k'); set( 1000,'NumberTitle','off ,'Name','Movie'); axesm('MapProjection',projection); axis(ax); title([strl str2 str3],'FontWeight','bold','Color','w') movie(fi'ames,ntimes) Location: /MatTimes/Graphics/plot3comp.m function plot3comp(file); %MatTimes Tool: %
%PLOT3COMP Plots seismic data and markers from a data file. % PLOT3COMP(DATAFILE) will plot the data file with the % time markers existing in the structured array. DATAFILE % is a string argument naming a MatTimes data file that % may have more than one component. If more than one % component exists, then all data is plotted on one figure. % % % % EXAMPLES: % % %import and plot a single component from SAC with P % % marker % sactool('event0920z') % [time,raypar]=timetool('P',[],'iasp91 ','event0920z.mat') % plot3comp('event0920z') % % %import and plot 3 component file from SAC with P, P41 Os % and P660s markers: % LIST3=[dir('event0920e') dir('event0920n') dir('event0920z')]; % DIRECTORY=[]; % NAMES.name='event0920'; % sactool(LIST3,DIRECTORY,NAMES); % [time,raypar]=timetool('P',[],'iasp9r,'event0920.mat') % [time,raypar]=timetool('Pds*,[410 660],'iasp9r,'event0920.mat') % plot3comp('event0920')
abcde=findstr('.mat',file); if length(abcde)>0 %kill ".mat" extension file=file(l:length(file)-4);
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end load([file '.mat']) b=fieldnames(data(l)); fori=I:length(b); a=findstr('_time\char(b(i))); if isempty(a)==0; aa(i)=i; else aa(i)=0; end end if a n y ( a a ^ ) & isempty(b)=0 fnames=b(aa(aa~=0)); else fhames=n; end ldata=length(data); fori=l:ldata subplot(ldata,l,i) plot(0:.2:data(i).streamtime,data(i).data); a=axis; hold on if isempty(fhames)=0 for jj=I :length(fnames) nn=char(fhames(jj)); xx=getfield(data(i),nn); ck=findstr('_',nn); mod=nn(min(ck)+I :max(ck)-I); ph=nn(I:min(ck)-I); forjk=I:length(xx) plot([xxOk) xx0k)],[a(3) a(4)],'r'); ab=findstr('d',ph); if isempty(ab)=0; dd=(getfield(data(i),[ph'_' mod '_dpth'])); ph2=[ph(l:ab-I) int2str(dd(jk)) ph(ab+l:length(ph))]; else ph2=ph; end text(xxOk),a(4)+. 15*a(4),ph2,'FontSize',7); end end end axis(a); lg=data(i).name; lg=lower(rmmat(lg)); lg=rm_(lg); legend(lg,l); ylabel('amp'); end xlabel('secs');
Location: /MatTimes/Graphics/plotphase.m function plotphase(phase,model,raypar,source_depth,d,flag,color) %MatTimes Tool: %
%PLOTPHASE Plots seismic raypath in a 2D cross-section of Earth. % 1) PLOTPHASE(PHASE,MODEL,RAYPAR,SOURCE_DEPTH,VARIABLE.FLAG,COLOR) % Determines progressive arc values for a seismic phase and plots % the ray path through a graphical Earth. PHASE and MODEL are string % arguments naming an existing phase (i.e., 'PKP') and a velocity % model respectively (i.e., 'iasp91'). RAYPAR is the pre-determined % ray parameter in radiians/second (angular ray parameter based on the
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Vo Earth flattening transformation (i.e.. (sec/km)*rO where rO is the '/o radius of the Earth). S O U R C E D E P T H is the depth, in kilometers, of the •/o proposed earthquake. VARIABLE refers to the depth of the variable '/o as designated in MKPHASE. In the case that the input phase does not % have a variable, the input should be set to an empty variable (Q). % FLAG indicates the type of graphical Earth to plot. See MKEARTH for % details. COLOR is a string argument setting the plot color (i.e., 'k'). % Ifleft off, COLOR is'b'. % % 2) PLOTPHASE(CURVEFILE,FLAG,COLOR) Plots the ray path, as indicated in CURVEFILE, through a graphical Earth. 0, % CURVEFILE is a string argument naming an existing curve file as generated % by TIMETOOL (i.e.,'PKKPJasp91'). FLAG is the same as above. This call % method removes the need to re-calculate arc values. ARCTOOL must have % been used previously, saving arc values to the CURVEFILE. % % EXAMPLES: % % PL0TPHASE('Pds','iasp91 ',300,250,660,4,'b') % PLOTPHASECPdsJasp9r,3,'k') disp(['PLOTPHASE...Working']) load dir_path if n a r g i n = 2 | nargin^=6, color='b', end if nargin>3 [x,z,t,wave]=arctool(modeI,raypar,phase,source_depth,d); else color=raypar; curvefile=phase; flag=model; load([wherecurvefiles'/" curvefile 'curves.mat']) phase=input.phase; model=input.model; raypar=output.raypar; source_depth=input.event(length(input.event)); d=input. depths; x=output.x; z=output.z; wave=output.wave; end ; a=find(abs(diff(wave))=l); a=[2; a; length(x)]; iflength(a)>l; k=length(a)-l; else ; k=l; end; ifflag~=0 mkearth(model,flag) end hold on for iii=l:k xi=x(a(iii)-l:a(iii+l)); zi=z(a(iii)-I:a(iii+I)); ifwave(a(iii)+l)=0 polar((xi+90)*pi/180,(6371 -zi)/6371 ,[color]); else; polar((xi+90)*pi/l 80,(637 l-zi)/6371,[color •:•]); end; end ; style l=[color'*']; style2=[color '^']; a=polar((x(l )+90)*pi/l 80,(6371-source_depth)/637 Lst>le 1); b=polar((x(length(x))+90)*pi/180,l,style2);
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set(a,'MarkerSize',10) ff^findstr('d',lower(phase)); if isempty(ff) phase2=phase; else phase2=[phase(l:ff-l) int2str(d) phase(ff+l;length(phase))]; end title([phase2 ', • model', source:' int2str(source_depth)' km'],'FontWeight','bold'); ifmax(x)>180 xx=abs(3 60-max(x)); else xx=max(x); end xlabel(['gcarc:' int2str(xx)' deg, rayp:' int2str(raypar)' sec/rad'],'FontWeight','bold'); hold off maxx=xx; save([whereami'/phases/pptemp.mat'],'maxx'); disp(['PLOTPHASE...Done']) Location: /MatTimes/Graphics/vplot.m function h=vplot(model,color) %MatTimesTool: %
%VPLOT Utility used by MKPHASE to plot a velocity model. % VPLOT(MODEL,COLOR) load dir_path abcde=findstr('.mat',model); if length(abcde)>0 %kill ".mat" extension model=model(I :length(model)-4); end load([wheremodelfiles'/' model '.mat']) radii=v_model(:,l); vp=v_model(:,2); vs=v_model(:,3); h=plot(vp,radii,color); hold on plot(vs,radii,[color':']) xlabel('veIocity(km/s)','FontWeight','bold') ylabel('radius(km)','FontWeight','bold') axis([-I max(vp)+l 0 max(radii)]) hold off
Location: /MatTimes/Intemal/findseg.m function [segbegin,segend,segments]=findseg(seg); seg=lower(seg); tum=IOOOO; t=IOOOO; depths=9999; d=9999; variable=9999; source=9998; s=9998; inner_core=9997; ic=9997; icore=9997; outer_core=9996; oc=9996;
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ocore=9996; lower_mantle=9995; lm=9995; lmantle=9995; moho=9994; m=9994; mh=9994; upper_mantle=9994; umantle=9994; um=9994; segments=[]; segbegin=[]; segend=[]; %remove blank lines [a,b]=size(seg); seg(sum(seg,2)/b=32,:)=[]; [a,b]=size(seg); %account for innercore and inner core, etc. for k=l:length(seg(:,I)) ss=seg(k,:); fn=findstr('rc',ss); ifisempty(fn)=0 seg(k,fn+!)='_'; end flf2=findstr('r m',ss); ifisempty(ff2)=0 seg(k,ff2+l )=•_•; end end segbegin=seg(I:2:a-2,:); segend=seg(3:2:a,:); segments=seg(2:2:a-l,:); segments(segments=' ')=[]; %figure out what each segment end is [a,b]=size(segend); for i=l:a segtemp=segend(i,:); segtemp(segtemp=' ')=[]; if isempty(segtemp) segtemp2(i)=[]; elseif i = a & isempty(segtemp)=0 segtemp2(i)=0; %set last one to zero elseif i~=a& isempty(segtemp)=0 segtemp2(i)=eval(segtemp); end end segend=segtemp2; [a,b]=size(segbegin); for i=l:a segtemp=segbegin(i,:); segtemp(segtemp=' ')=[]; if isempty(segtemp) segtemp2(i)=[]; elseif i = l segtemp2(i)=9998; elseif i~=l & isempty(segtemp)=0 segtemp2(i)=eval(segtemp); end end segbegin=segtemp2; Location:/MatTimesAntemal/getmodel.m
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function model=getmodel %MatTimes Tool: %
%GETMODEL Ufility used in MKPHASE to select a velocity model. % MODEL=GETMODEL load dirjjath d = dir([wheremodelfiles ^*.mat']); str= {d.name}; [s,v] = listdlg('PromptString','Select a file:',... 'SelectionMode','single',... 'ListString',str,'name','MODEL FILE SELECTION'); modeI=getfield(d(s),'name') Location: /MatTimes/Intemal/mktau.m function mktau(vmodel); %MatTimes Tool: %
%MKTAU Generates Tau(P) files for seismic travel time calculation. % MKTAU(MODEL) uses the Tau(P) method outlined by Buland and Chapman, % 1983, in "Bulletin of the Seismological Society of America". % MODEL is a string argument name of a velocity model file generated % by MKMODEL. MKMODEL calls this function to complete the velocity % model files used in travel time calculation. % disp(['MKTAU.. .Working']) load dir_path warning off abcde=findstr('.mat',vmodel); if length(abcde)>0 %kill ".mat" extension vmodel=vmodel(l :length(vmodel)-4); end %load and define variables of velocity model load(vmodel) radii=v_model(:,l); mrad=max(radii); vp=v_model(:,2); vs=v_model(:,3); %find interfaces branches=sort([gradbreaks gradbreaks+1 ]); %find ray parameters to calculate for P and S independantly prayp=radii.'*(I./vp);%all slownesses for P prayp(length(prayp))=0; srayp=radii.*(l ./vs); %all slownesses for S sray p(l ength(sray p))=0; sraypbreaks3=srayp(find(radii=breaks(3))); sraypbreaks4=srayp(find(radii=breaks(4))+I); %add in no-tum ray parameters (partial reflections) maxprayp=prayp(branches(1:2:length(branches)-l)); minprayp=prayp(branches(2:2:length(branches))); maxsrayp=srayp(branches(l :2:length(branches)-l)); minsrayp=srayp(branches(2:2:length(branches))); newrayp=[]; newsrayp=[]; for jj=l :length(maxprayp) aa=maxprayp(ij); bb=minprayp(jy); aaa=maxsrayp(jj); bbb=minsrayp(jj); if(aa-bb)>le-2
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newrayp2=[aa-.001 bb+.OOl linspace(aa,bb,5) linspace(aa,aa-.05*abs(aa-bb),3)... linspace(aa,aa-. 10'»abs(aa-bb),3)]; newrayp2(find(newrayp2>=aa-Ie-5 | newrayp2=aaa-le-5 | newsrayp2=raypend( 1))); otherwise rayp=rayp(find(rayp=raypend(3))); end case 'reflection' switch lower(WaveType) case 'p'^Uowest tuming point achieved by P rayp=prayp2; raypend=prayp_breaks_end; raypbegin=prayp_bfeaks_begin; flag=T»'; case 's'%lowest tuming point achieved by S instead rayp=srayp; raypend=srayp_bfeaks_end; raypbegin=srayp_breaks_begin; flag='S'; end SMritch lower(Branch) case 'inner_core' rayp=Ttiyp(find(rayp180) & any(rr=3 & isempty(isitaphase)%use data file pptool(file,phase,model,depths) file=phase; phase=model; model=wave; load([file '.mat']) raypar=getfield(data(l),[phase ' J model 'J 'rayp']); load([wherephasefiles 'P phase '_phase.mat']) wave=segments(length(segments)); if nargin=3 depths=getfield(data(l),[phase 'J model 'J 'dpth']); end end %choose 2nd end of two-ended model model=modelck(model,2); %load in tau table load([wheretaufiles'/' model 'Jau.mat']) %determine ray parameter range [rayp,prayp2,pJime2,pJau2,p_range2,sJime2,sJau2,s_range2]=ra\ptool( phase,mod^ %reshaping values for input [a,b]=size(depths); [aa,bb]=size(raypar); ifaa+bb>a+b«&a+b>0 a=aa; b=bb; elseif a+b^O a=l; b=l; end raypar=raypar(:); depths=depths(:); switch lower(wave) case 'p' %p-wave x=interp2(radii,rayp,p_range2,max(radii)-depths,raypar); t=interp2(radii,rayp,pjime2,max(radii)-depths,raypar); case 's' %s-wave x=interp2(radii,rayp,s_range2,max(radii)-depths,raypar); t=interp2(radii,rayp,sjime2,max(radii)-depths,raypar); end %define output x=reshape(x,a,b)'* 180/pi; t=reshape(t,a,b); z=reshape(depths,a,b);
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if nargin=3 & isempty(isitaphase)%save to data file forjk=l:length(data) data=setfield(data,{ljk},[phase ' J model '_pptx'],x); data=setfield(data,{ljk},[phase ' J model '_pptz'],z); data=setfield(data,{ljk},[phase 'J model '_pptt'],t); end save(file,'data','-append') disp(['New fields set in variable "data" in file:' file '.mat']); disp(['']); disp([phase ' ' model '_pptx.mat']); disp([phase 'J model 'jjptz.mat']); disp([phase ' ' model '_pptt.mat']); disp(['']); tracetool(file,phase,model,'ppt'); end Location: /MatTimes/Tools/sactool.m function []=sactool(filename,directory,oname,flag) %MatTimes Tool: %
%SACTOOL Imports Seismic Analysis Code files (SAC). % 1) SACTOOL(FILENAME,DIRECTORY) Imports a singlefilefi-omthe SAC format to a Matlab data file (.mat) as a structured array (variable % with fields). The output name is the same as the string argument % FILENAME and the file is saved in the current directory. DIRECTORY % is a string argument naming the directory (i.e., 'C:/MatTimes/Data/'). % If DIRECTORY is left off, it is assumed that the current directory % contains the file. % % % 2) SACTOOL(LIST,DIRECTORY) Imports mulfiple files contained within the list. % To generate LIST, simply use the Matlab DIR command like the following: % % %
% %
LIST=dir(FILES) where FILES is a string argument that uses the wildcard (•*) to make a list. LIST will be a structured array consisting of one column.
% 3) SACT00L(LIST3,DIRECT0RY,NAMES) % LIST3 is similar to LIST except that it is designed to load in three % seismic components to save to a single file as a multi-dimensional % structured array. NAMES is a structured list of file names for each % row in LIST3. A row of files in LIST3 will be combined into a single % file in the corresponding row or column in NAMES. The three components % will saved within NAMES as data(1:3) where "data" is a structured array. % See example below. %
% % % % % %
IMPORTANT NOTES: In order to import SAC files for proper usage in MatTimes,SAC fields: User5, User6, User7 and User8 must have actual event time information so that MatTimes can determine travel time markers for the imported data stream. User5 = Julian Day, User6 = event hour, User7 = event minute, UserS = event seconds. All of these fields will be combined during
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/o
% % % %
importation to a field named "evtime" The actual data stream beginning fime will be in the field named "beginfime" "Streamfime" will contain the data stream length in seconds. If you must import "as is", this can be done wifli a fourfli input: SACT00L(A,B,C,1). This will import with no problem, but there is no guarantee that all MatTimes functions will support it. Currently, SACTOOL assumes that the beginning time in the SAC file corresponds to the first data point in the data.
% EXAMPLES: Vo
% %
% % % % % % % % % % % % % % %
%Load in a z-component data file load dir_path %(file generated with SETUP with path names for example only) FILENAME=[whereami '/Data/event0920z']; %(whereami from dir_path) sactool(FILENAME) %create Matlab file %Load in all three components for the same event, 0920. load dir_path %(this does not have to be used in real situations) DIRECTORY=[whereami '/Data/"]; LIST=dir([DIRECTORY'event0920*']); sactool(LIST,DIRECTORY) %Load in three components for a multi component file creation %Try this in the "Data" directory (delete all example ".mat" files first) LIST3=[dir('ev*e') dir('ev*n') dirCeV^z')]; DIRECTORY=D; NAMES .name='event0920'; sactool(LIST3,DIRECTORY,NAMES); %look at some input load(NAMES(l).name) data(2) ploGcomp(NAMES(l).name)
% % % % % % % % character %
%if LIST3 is long, it is not convenient to type in all output names, in such %a case you could do a form of the following for your file name stmctures:
%
end
LIST3=[dir('ev*e') dir('ev*n') dir('ev*z')]; %make data file list [a,b]=size(LIST3); for i=l:a lname=length(LIST3(i).name); NAMES(i).name=LIST3(i).name(l:lname-l) %use same name minus last %as a file name
disp(['SACTOOL...Working']) %directory is ./ if nargin=l if nargin=l, directory="; end %make input a structured array if it is not if isstmct(filename)=0 filename.name=filename; end if nargin=3 & isstmct(oname)==0 oname. name=oname; end %wb=waitbar(0,'lmporting...'); %determine how many files and if mulfi comp [a,b]=size(filename); %loop through files to output for i=l:a %loop through components forj=l:b %determine string file name name=[directory filename(ij).name]; %waitbar(i/a,wb); %check if maflab file already or if a maflab file exists
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3^"!
ifnargin>=3 abcde=findstr('.mat',oname(i).name); abcde2=dir([oname(i).name '.mat']); else abcde=findstr('.mat',name); abcde2=dir([filename(ij).name '.mat']); end if isempty([abcde abcde2]) [hl,h2,h3,data2]=readsac(name); h=[h2(l:6) round(hl(l)*100)/100 hl(6:7) hl(l 1:17) hl(32:37) hl(39) hl(46:54) hl(58:59)]; h(19:20)=h(19:20)/1000; if nargin=2 disp([oname(i).name ': Maflab file already exists.']) else disp([name ': Matlab file already exists.']) end end end if nargin=3 fhame=oname(i).name; end if isempty([abcde abcde2]) ifb>l disp(['New Matlab Multi-component Data File Created:' fhame]), else
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disp(['New Maflab Data File Created:' ftiame]); end save(fname,'data') end fclose('air);%avoid "too many files open" problem end %close(wb) disp(['SACTOOL...Done'])
Location:/MatTimes/Tools/timetool.m funcfion [time,raypar]=timetool(phase,d,model,event,receiver,curvefilename) %MatTimesTool: %TIMETOOL Calculate seismic travel fime(s) and ray parameter(s) for a given phase. %1) [TIME,RAYPAR]=TIMETOOL(PHASE,VARIABLE,MODEL,EVENT,RECEIVER,CURVEFILENAME) Compute travel time(s) and ray parameter(s) for the desired PHASE/MODEL pair based % on the arc distance computed from EVENT and RECEIVER. Travel time curves % for all possible ranges as well as input and output are computed and saved % to CURVEFILENAME. If CURVEFILENAME is left off, a curve file is sfill saved % to the Curves directory under the name: PHASE_MODEL_CURVES.MAT (where PHASE and % MODEL are variable. PHASE is a string naming an exisfing phase (i.e., 'SKKS') % as generated using MKPHASE. VARIABLE refers to the depth(s) of the variable as % designated in MKPHASE. In the case that the input phase does not have a variable, % the input should be set to an empty vector ([]). MODEL is a string referring to % a ID spherically-symetric Earth velocity model (i.e., 'iasp9r). EVENT and % RECEIVER are the earthquake and receiver locations, respectively. If % length(EVENT)=2, EVENT(l) must be the arc distance in degrees while EVENT(2) must % be the source depth in km. With this input type, RECEIVER must be a scalar % represenfing the seismic station elevation in km. If length(EVENT)=3, EVENT(1:2) % must be the earthquake lafitude and longitude while the third element is the % earthquake depth. With this input, RECEIVER must be three elements as well. % RECEIVER(1:2) must be the station lafitude and longitude while the third element % is the station elevation in km. Note that the latter input is necessary for % mapping a phase using MAPPHASE. % % % 2)[TIME,RAYPAR]=TIMET00L(PHASE,VARIABLE,M0DEL,DATAFILE,CURVEFILENAME) % Extracts event and receiver informafion from a data file, calculates travel fime % and ray parameter then saves travel time curves to a curvefile. DATAFILE is a % string argument naming a structured array data file generated by SACTOOL % (importation from Seismic Analysis Code). New fields are set to the "data" in % DATAFILE. % % % NOTE: RAYPAR is the ray parameter in radiians/second, angular ray parameter based on the Earth flattening transformation (i.e., (sec/km)'*rO where rO is the radius of the Earth). % % % EXAMPLES: % [fime,raypar]=fimetool('P',[],'iasp9r,[35 0],[0]) % [time,raypar]=timetool('P',G,'iasp91~slowiasp9r,[35 0],[0]) %two-ended model % [fime,raypar]=timetool('P',[],'iasp9r,[35 0],[0],'temp') % [time,raypar]=timetool('P',[],'iasp9r,[35 -112 35],[2 -110 0.5]) % [fime,raypar]=timetool('Pds',[0:20:660],'iasp9r,[38 -114 35],[2 -110 0.5]) % [time,raypar]=fimetool('PKKP',[],'iasp9r,[110 0],0)% % [time,raypar]=timetool('Pds',[660],'iasp91','event0920z.mat') % To see structured array for this kind of input, type: % % %
load event0920z.mat data(l) To extract time and ray parameters, type:
Vo
% %
time=data(l).PdsJasp91Jime raypar=data( 1 ).Pds_iasp91 _rayp
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tj:--'^
.A
% %
disp(['TIMETOOL...Working']) load dir_path %path infor. opt='n'; %inifial option %condifion input abcde=findstr('.mat',model); if lengfli(abcde)>0 %kill ".mat" extension model=model(l :lengfli(model)-4); end if nargin=5 & isstr(receiver) abcde=findstr('.mat',receiver); if length(abcde)>0 %kill ".mat" extension receiver=receiver(l:length(receiver)-4); end cname=[receiver '_curves.mat']; elseif nargin=5 & isstr(receiver)=0 cname=[phase ' ' model 'curves.mat']; elseif nargin=6 abcde=findstr('.mat',curvefilename); if lengfli(abcde)>0 %kill ".mat" extension curvefilename=curvefilename(l:length(curvefilename)-4); end cname=[curvefilename 'curves.mat']; elseif nargin=4 abcde=findstr('. mat',event); if length(abcde)>0 %kill ".mat" extension event=event(l :length(event)-4); end cname=[event ' J phase ' ' model 'curves.mat']; end if isstr(event)%Earthquake and receiver info from file opt='file'; datafile=event; %avoid unix problems with ".mat" extension abcde=findstr('.mat',datafile); if length(abcde)>0 datafile=datafile(l:length(datafile)-4); end %load in data file and store variable name s=load([datafile '.mat']); load([datafile '.mat']); abcd=[];ijk=0; "/odetermine variable list in structured array while length(abcd)=0 ijk=ijk+I; df!=fieldnames(s(ijk)); dfP=(char(dff(ijk))); df^val(dff); abc=char(fieldnames(df)); abcd=strmatch('gcarc',abc); end %define event and reciever pair event=[data(l).eventlat data(l).eventJon data(I).event_depth]; abcd=strmatch('borehole_depth',abc); iflengfli(abcd)=0 receiver=[data(l).station Iat data(l).station J o n data(l).stafion_elevafion-data(I).station_depth]; else receiver=[data(l).stationlatdata(l).stafionJondata(l).station_elevation-data(l).borehole_depfli]; end end if nargin>4 & isstr(receiver) %data from curve file mkcurve='yes'; curvefile=receiver;
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elseif nargin=4 mkcurve='no'; else mkcurve-no'; end %see if library file exists ddd=dir([wherelibfiles 'P phase 'J model '_lib.mat']); iflength(ddd)=0 disp(['']); disp(['No Lib File Associated Witii the Input Phase and Model:' phase ' J model '.mat']); disp(['']); disp(['Creating Library File']) phasetool(phase,model); end load([wherelibfiles 'P phase 'J model 'Jib.mat']) if length(event)=2 range=event(l); sourced=event(2); receiver_elev=receiver; elseif length(event)=3 & opt(l)~='f range=distance(event(l),event(2),receiver(l),receiver(2)); sourced=event(3); receiver_elev=receiver(3); elseif length(event)=3 & opt(I)='f range=data(l ).gcarc; sourced=event(3); receiver_elev=receiver(3); else event receiver disp(['You must enter valid "event" and/or "receiver" variables']); end depths=l ib. depths(:); d=d(:); ld=lengtii(d); ifld=0 ld=l; end ldepths=length(lib.depths); %source and receiver ranges receiverrange=interp2(lib.elev,lib.rayp,lib.rec_range,receiver_elev,lib.rayp); sourcerange=interp2(lib.sdepths,lib.rayp,lib.source_range,sourced,lib.rayp); %source and receiver times receivertime=interp2(lib.elev,lib.rayp,lib.rec time,receiver_elev,lib.rayp); sourcetime=interp2(lib.sdepths,lib.rayp,lib.source time,sourced,lib.rayp); %source and receiver tau receivertau=interp2(lib.elev,lib.rayp,lib.rec tau,receiver_elev,lib.rayp); sourcetau=interp2(lib.sdepths,lib.rayp,lib.source Jau,sourced,lib.rayp); phase_range=lib.ph_range+(receiverrange+sourcerange)'*ones(l,ldepths); phase tau=lib.phtau+(receivertau+sourcetau)'''ones(l,ldepths); phase time=lib.phtime+(receivertime+sourcetime)'*ones(l,Idepths); iflength(lib.depths)>l phase_range=interp2(lib.depths,lib.rayp,phase_range,d',lib.rayp); phase time=interp2(lib.depths,lib.rayp,phasejime,d',lib.rayp); phasejau=interp2(lib.depths,lib.rayp,phasejau,d',lib.rayp); end pr=phase_range'* 180/pi; pr(pr> 180)=abs(360-pr(pr> 180)); raypar=zeros(ld,10); fime=zeros(ld,10);
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..^\
ifrange=180 range2= 180-1 e-5; else range2=range; end forj=l:ld b=pr(:J); a=b-range2; x=a(abs(a)0 & range2=min(pr(:J)) clear aa for i=I:lrow aa(i)=interplq([X(i,:)]',[Y(i,:)]',0); end kk=find(isnan(aa)~^l); iflength(kk)>0 raypar(j,l :length(kk))=aa(kk); %fix reflecfion problem if isempty(strmatch(lib.DeepestIncidence,'Reflection'))=0 & length(lib.depths)>I [ptum,stum]=tumtool(model,raypar(j,:),lib.shad); if lower(lib. WaveType)='p'; fP=find(ptum>dO)=l); else ff=find(stum>dO)=l); end rayparO.l :length(ff))=raypar(j,fO; raypar(j ,length(ff)+1: length(kk))=nan; end else raypar(j, 1 :length(kk))=nan; end else rayparO,l)=nan; end ifrange2(l)~=0 rayrow=raypar(j,:); raypf=[rayrow(find(rayrow~=0))]; else rayrow=raypar(j,:); raypf=0; end lrf=lengfli(raypf); fimeO,l:lrf)=interpI(lib.rayp,phasejime(:J),raypf); end %build matrices raypar(isnan(raypar))=0; iflengfli(d)>l n=find(sum(ray par(: ,2:10))=0)+1;
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raypar(:,n)=[]; fime(:,n)=[]; else n=find(raypar(2:10)=0)+l; raypar(n)=[]; time(n)=[]; end raypar(isnan(time))=nan; if nargin=4 %data( 1 )=setfield(data( 1 ),'name','MatTimes data( 1)'); forjk=l:length(data) dfime=data(jk).begintime-data(jk).evtime; dfime=sum(dfime.'*[31536000 86400 3600 60 l]);%convertto seconds time2=time-dtime; data=setfield(data,{IJk},'event',event); data=setfield(data,{IJk},'receiver',receiver); disp(['New fields set in variable "data" in file:' datafile '.mat']); disp(["]); data=setfield(data,{I Jk},[phase '_' model '_dpth'],d); disp([phase ' ' model '_dptii']); data=setfield(data,{ljk},[phase 'J model' time'],time2); disp([phase ' ' model 'fime']); data=setfield(data,{ljk},[phase 'J model '_rayp'],raypar); disp([phase ' J model '_rayp']); disp(['']); end save([datafile '.mat'],'data','-append') else curves.fimes=phase time; curves .tau=phase tau; curves.ranges=pr; output.fime=time; output.raypar=raypar; input.phase=phase; input.depths=d; input.model=model; input.event=event; input.receiver=receiver; save([wherecurvefiles'/' cname],'curves','input','output') disp(['New curve file created:' [wherecurvefiles '/' cname]]); end dispC'); disp(['TIMETOOL.. .Done'])
Locafion: /MatTimes/Tools/tracetool.m funcfion [lat,lon,az,gcarc]=tracetool(event,receiver,x,y) %MatTimes Tool: %
%TRACETOOL Determines the real worid path of seismic wavefront. % 1) [LAT,LON,AZ,GCARC]=TRACETOOL(EVENT,RECEIVER,X) Traces out an azimuthal path between the EVENT and RECEIVER based % on the progressive arc distances from the event. EVENT and % RECEIVER are the earthquake and receiver locations, respectively. % Each are three-element vectors where the first two elements are % latitude and longitude and the third is source depth (for EVENT) and station elevation (for RECEIVER) in km. X must be a scalar of vector of arc distances in degrees from EVENT. LAT and LON are % vectors containing computed latitudes and longitudes at X. AZ is % the azimuth calculafion from the event to the receiver. GCARC is % the great circle arc calculation for EVENT to RECEIVER in arc % degrees. Note that interchanging EVENT and RECEIVER will output % back azimuth rather than azimuth. In this case, X should be % max(X)-X if X is the arc distance vectorfi-omthe earthquake source % (the arc values in the travel time curve files are saved as % distances from the source, not the seismic stafion). %
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%
% 2) [LAT,LON,AZ,GCARC]=TRACETOOL(CURVEFILE,FLD) Uses a travel time curve file generated by TIMETOOL to trace out % the travel path from EVENT to RECEIVER. CURVEFILE is a string % argument containing the name of the desired travel fime file to % compute from. ARCTOOL must have already saved the arc distance % vector (output.x) to CURVEFILE. FLD is a string argument of the % field to use wifliin the CURVEFILE. The option are: 'ppt' and % 'arc'. If'ppt' is chosen, the progressive arc distances, % PHASE_M0DELj5ptx, are extracted from the field generated by PPTOOL. % This will find piercing point latitude and longitude locations tracing back from the receiver. If'arc'is chosen or if FLD is left off, the field of values generated by ARCTOOL will be used /o and lafitude and longitude locafions from the event will be output. % %
%3) [AZ,GCARC]=TRACETOOL(EVENT,RECEIVER) % Computes azimuth and great circle arc from EVENT to RECEIVER. % %4) [LAT,LON,AZ,GCARC]=TRACETOOL(DATAFILE,PHASE,MODEL,FLD) % Uses a structured data file named DATAFILE to trace out % travel path. FLD is the same as in option 2, except that % it a required input. PHASE and MODEL are string arguments % naming the fields to use within the variable "data" in the % DATAFILE. % % NOTE: All values are computed based on geodefic data obtained from % jpl/nasa at http://ssdjpl.nasa.gov/phys_props_earth.html. semiminor axis = 6356.752 % semimajor axis = 6378.140 % eccentricity = 0.08183; % % % EXAMPLES: % [LAT,LON,AZ,GCARC]=tracetool([30 114],[35 112],[1 3 5]) % [LAT,LON, AZ,GCARC]=tracetool('P_iasp91') % [AZ,GCARC]=tracetool([30 114],[35 112]) % % % DATAFILE USAGE EXAMPLE to find piercing point locafions for the % P to S conversion points for POs to P900s. % % %save ray parameters to data file % fimetool('Pds',[0:20:900],'iasp9r,'event0920z'); %find arc distances in degrees from receiver (pptool) % pptool('event0920z','Pds','iasp91'); % %find tme locations % % tracetool('event0920z','Pds','iasp91 ','ppt'); %observe fields % load event0920z.mat % data % % disp(['TRACETOOL...Working']) load dir_path %load in path infor. ss='n'; if isstr(event) & nargin0 %kill ".mat" extension curvefile=curvefile( I :length(curvefile)-4); end load([wherecurvefiles'/' curvefile '_curves.mat']) %trace forward for x (from arctool) and backward for ppx if nargin=l event=input.event; x=getfield(output,'x'); receiver=input.receiver;
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elseif nargin=2 & receiver(l)^'p'; event=input.receiver; %pptool, reverse direcfion x=getfield(output,'ppx'); receiver=input.event; elseif nargin=2 &. receiver(l)='a'; event=input.event; x=getfield(output,'x'); receiver=input.receiver; end elseif isstr(event) & nargin=4 %data file input ss='f; abcde=findstr('.mat',event); if lengfli(abcde)>0 %kill ".mat" extension event=event(l :length(event)-4); end file=event; phase=receiver; model=x; load([file '.mat']) ify(I)='a' fld='arcx'; event=data(l).event; receiver=data( 1).receiver; else fld-pptx'; event=data(l).receiver;%pptool, reverse direction recei ver=data( 1 ).event; end x=getfield(data(l),[phase 'J model 'J fid]); end %geodefic data for eccentricity a=6378.140; b=6356.752; e=sqrt(a^2-b''2)/a; sma=a; geoid=[sma/6371 e]; %geoid=[l 0] %mapping utility to find azimuth (or back azimuth) az=azimuth(event(l),event(2),receiver(l),receiver(2),geoid,'degrees'); %mapping utility to find great circle arc gcarc=distance(receiver( 1 ),receiver(2),event( 1 ),event(2),geoid)* 180/pi; if nargin=2 & ss='n' lat=az; lon=gcarc; else x=x(:); xones=ones(length(x), 1); az2=az'''xones; waming off %mapping utility to find points [lat,lon]=trackl(event(I),event(2),az2,[x'*pi/180],geoid,'degrees',l); lat=lat(:); lon=lon(:); end if ss='c' %curve file output output.pplat=lat(:); output.pplon=lon(:); save([wherecurvefiles '/' curvefile 'curves.mat'],'output','input'.'curves') dispC'); disp(['New Fields (output.pplat, output.pplon) Saved in Curvefile:']); disp(["]);
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disp([wherecurvefiles 'P curvefile 'curves.mat']); dispC '); elseif ss='f %data file output forjk=I:length(data) data=setfield(data,{ljk},[phase ' J model 'J fld(l:2) •lt'],lat); data=setfield(data,{I Jk},[phase 'J model ' J fld(I:2) 'ln'],lon); data=rmfield(data(jk),[phase '_' model'_' fld]); data=rmfield(data(jk),[phase '_' model ' J fld(l:3) 't']); end save(file,'data','-append') disp(['New fields set in variable "data" in file:' file '.mat']); disp(['']); disp([phase 'J model 'J fld(l :2) 'It']); disp([phase 'J model 'J fld(l :2) 'In']); disp(['']); end disp(['TRACETOOL.. Done'])
Locafion: /MatTimes/Utilities/cutdata.m funcfion cutdata(file,phase,variable,model,window,mode) %MatTimes Tool: % %CUTDATA Cuts data about an input phase based on a time window. % 1) CUTDATA(LIST,PHASE,VARIABLE,MODEL,WINDOW,MODE) % Cuts down data within the LIST about PHASE according to % WINDOW. LIST is a structured list naming each file to % be snipped. See SACTOOL option 2 for LIST creation. PHASE % is a string argument naming the phase to center about (i.e., % 'P'). If the phase has a depth variable, such as Pds, the % input VARIABLE must be given as a value. Otherwise, VARIABLE % should be an empty cell ([]). MODEL is the velocity model % to use when determining the phase marker. WINDOW is the % window about the phase marker to keep. WrNDOW(l) is the % pre-phase fime window to keep in seconds. WIND0W(2) is the % post-phase time to keep in seconds. MODE determines whether % or not the Maflab data file is deleted. If MODE is 1, the % data file will be deleted if 1) the data file does not have the appropriate window present or 2) the phase time does not % exist for the file/phase pair (out of range). If MODE is 0 % % or left off, the ".mat" file will not be deleted in any % case. % % NOTE: The header information will be adjusted to the cut. Also, % if the data file has three components, all will be cut and % all headers will be adjusted accordingly. If the given phase % has multiple times, the cut will be about the minimum and % maximum times expanding the total stream time. % EXAMPLE: % % % % % % % %
cutdata('event0920','P',[],'iasp9r,[50 150],l) %this will cut the data file "event0920" about the %P-wave calculated based on real event time contained %within the event file. The fime window is 50 and 150 %seconds meaning 50 seconds pre-event and 150 post-event %seconds. The " 1" tells cutdata to delete the file if %the cut is unsuccesful based on the lack of the appropriate %time window.
%make input a structured array if it is not if isstruct(file)=0 file.name=file; end forj=l:lengfli(file) name=file(j)name;
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name=rmmat(name)%rm "mat" [t,rp]=timetool(phase,variable,model,name); tl=min(t); t2=max(t); load([name '.mat']) %check data window howmany=length(data); i=0;check=3; while i'^ .-encDf^l.-^-0 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
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