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DETECTION OF SEDIMENTARY CYCLICITY AND STRATIGRAPHIC COMPLETENESS BY WAVELET ANALYSIS: AN APPLICATION TO LATE ALBIAN CYCLOSTRATIGRAPHY OF THE WESTERN CANADA SEDIMENTARY BASIN ANDREAS PROKOPH1 AND FREDERIK P. AGTERBERG2 1

Department of Earth Sciences, University of Ottawa, P.O. Box 450, Stn. A, Ottawa, Ontario K1N 6N5, Canada e-mail: [email protected] 2 Geological Survey of Canada, 601 Booth Street, Ottawa, Ontario K1A OE8, Canada

ABSTRACT: On the basis of the time–frequency scaling property of the wavelet transform, accumulation rates and stratigraphic completeness can be calculated for various observation time spans (ot) by using wavelet analysis. Wavelet analysis also allows automatic detection of high-frequency sedimentary cyclicity, and abrupt and gradual variations in sedimentation rate. The preservation of different frequency cycles is strongly dependent on variations of the intensity-to-noise ratio of the original cycles and accumulation rate through time, as demonstrated by computer models. Wavelet analysis was used to detect and correlate periodic–cyclic successions of marine sediments in the Western Canada Sedimentary Basin in observation time spans ranging from 100 kyr to 3.8 Myr. Cycles in gamma-ray data are in accordance with sonic logging, lithology, and biotic change. Cyclic units embedded in the upper Albian Westgate and Joli Fou Formations are almost periodic with 11 and 10 repetitions, respectively. Accumulation rates at ot 5 100 kyr vary from 5–7 cm/kyr in mudstone successions to 29 cm/kyr in sandstone successions of the Rocky Mountains Foothills. These 100 kyr cycles are preserved from 30% in the Manitoba Escarpment to 100% in SE Alberta in the Westgate Formation. These cycles can be correlated throughout facies belts of siliciclastic sedimentation in the entire basin. In gamma-ray logging the cyclicity is most pronounced in the foredeep succession and almost without fluctuations in the basin center. Cyclic changes from wet to dry climate probably forced by Milankovitch cycles of 100 kyr eccentricity may have controlled the stable periodic sedimentary cyclicity.

i.e., eccentricity, obliquity, and precession (Milankovitch 1941; Berger and Loutre 1989) are more suitable for studying marine deposition, especially pelagic facies (e.g., Schwarzacher 1993). The purpose of this study is the characterization of sediment accumulation and its preservation potential by wavelet analysis at resolutions higher than can be provided by biostratigraphy, chronostratigraphy, or sequence stratigraphy. In this paper, we present methods, models, and applications that demonstrate that high-frequency cycles, discontinuities, and gradual sedimentary changes can be detected both in their position (depth) and with respect to their dynamics. Gamma-ray logging applications from Upper Albian siliciclastic successions in the Western Canada Sedimentary Basin (WCSB) were selected for this study, because an extended stratigraphic framework already exists for these successions (Obradovich 1993; McNeil and Caldwell 1981; Schro¨derAdams et al. 1996; Leckie and Reinson 1993). Late Albian high-frequency cyclicity has been investigated by various research groups in various regions in the ALBICORE program (Premoli-Silva et al. 1989; Schwarzacher 1994; BCCP Group 1994). Previous cyclostratigraphic studies showed strong evidence for Milankovitch cyclic forcing of Cenomanian and Turonian marlstone/limestone sequences in the Western Interior Seaway (e.g., Fischer 1993; Sageman et al. 1997). However, no comparable cyclostratigraphic study had been carried out in the marine mudstone successions of the Western Canada Sedimentary Basin to extend the global view of Late Albian cyclicity. MODELS AND METHODS

Preservation of Cyclicity and the ‘‘Paradox of the Sedimentation Rate’’ INTRODUCTION

Well-logging data are well known tools in the discrimination of sedimentary subsurface rock properties and their changes through depth (Serra 1984). However, they suffer from uncertainty in exact distinction of rock types and sedimentary changes (cycles, trends) through time. Additionally, stratigraphers have to face uncertainties in time measurements (stratigraphic accuracy) of proposed stratigraphic intervals, as explained by Gradstein and Agterberg (1998). For poorly dated radiometric and biostratigraphic successions this implies that only interpolated ages can be used to determine accumulation rates. One of the crucial purposes of quantitative stratigraphy is the detection of deterministic patterns (i.e., cycles and their bundling) in sedimentary successions, and of the processes responsible for their formation and their correlation. The stratigraphic feasibility of sedimentary cycles generated by the same controlling mechanism depends on their regional and global extension (i.e., correlativity). Any signal of a time series can be transformed in frequencies or cycles by Fourier transformation (Davis 1986), which is commonly used to analyze trends and cyclic behavior, and to distinguish between nonlinear and stochastic characteristics of sedimentary successions (e.g., Schwarzacher 1993). ‘‘Random walk’’, ‘‘fractal Brownian motion’’ or other nonlinear models are studied by methods of spectral analysis (power spectra) to describe fluvial deposition (Pelletier and Turcotte 1996, 1997). However, cyclic models implementing the frequencies of the Earth’s orbital elements, JOURNAL OF SEDIMENTARY RESEARCH, VOL. 69, NO. 4, JULY, 1999, P. 862–875 Copyright q 1999, SEPM (Society for Sedimentary Geology) 1073-130X/99/069-862/$03.00

Sadler (1981) quantified sedimentation rate (sr) as a power-law function of time span (observation time interval ot). The total stratigraphic time interval (T) is defined as the difference between the ages of the base and the top of a sedimentary succession. The sedimentation rate (sr) can be described by (1) observation time interval (ot) as a fraction of total stratigraphic time (T), (2) numbers (a) of observation time intervals (ot) found, or (3) total thickness (s) of the section investigated (Fig. 1). It follows that sr 5 f(ot) 5 a*ot/s The completeness c is the ratio of overall accumulation rate, sr(T), to the average rate at time span, i.e., observation time interval ot (Sadler and Strauss 1990). Therefore, the stratigraphic completeness (c) generally is given by c(ot) 5 (a*ot)/T and in relation to the sedimentation rates (sr) by c(ot) 5 sr(T)/sr(ot) Therefore, estimation of the stratigraphic completeness of sedimentary sections depends significantly on total stratigraphic time (T) investigated and (maximum) time resolution given by the observation time interval (ot). Consequently, the completeness becomes reduced with higher stratigraphic resolution, because of the increasing number of detected short time intervals of nondeposition and erosion (Ivanov 1996). Therefore, sedimen-

WAVELET ANALYSIS OF SEDIMENTARY SUCCESSIONS

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FIG. 1.—Transformation from depth dependence to time dependence of a synthetic sedimentary column with thickness of the section (s 5 100 m), total time T 5 1 Myr, and three observation time intervals (ot 5 0.5 Myr, 0.167 Myr, 0.056 Myr), and their completeness c(ot).

tation rates in the preserved time intervals increase with stratigraphic resolution, a phenomenon that was by Korvin (1992) called the ‘‘paradox of the sedimentation rate’’. Wavelet Analysis of Sedimentary Time Series In sedimentary time series the wavelet transform can be used for detection of gradual and abrupt changes in the sedimentation rate, discontinuities, and superimposed periodic cycles (Prokoph and Barthelmes 1996). Wavelet transform permits automatic localization of attributes (e.g., periodic–cyclic sequences) both in time (the time domain) and according to their frequency (the frequency domain). It uses narrow windows at high frequencies and wide windows at low frequencies (Fig. 2). In contrast, the Fourier transform uses a single analysis window for all frequencies. A shifted single-size analysis window is used for sliding-window Fourier transforms (Rioul and Vetterli 1991) as well as for ‘‘evolutionary spectral analysis’’. The wavelet transform (L1 norm) of a time series is defined as W(a, b) 5

1a 2 E f(t)c 1 1

2

t2b dt a

where c(a, b) is the basic wavelet with an effective length that usually is much shorter than the length of the entire time series f(t). The variable a is a stretching/compression scale factor to determine the characteristic frequency so that varying a gives rise to a ‘‘spectrum’’; b represents translation in time, and varying b yields the ‘‘sliding window’’ of the wavelet over f(t) (Chao and Naito 1995). The continuous wavelet transform with the Morlet wavelet as the mother function was used in this study (Morlet et al. 1982), because its shape is similar to that of a periodic sinusoidal function. An additional parameter (l) enables an arbitrary shift of the wavelet transform resolution in favor of time or in favor of frequency (‘‘scale’’) without changing the (central) frequency for a fixed ‘‘scale’’ value a. Then the Morlet mother wavelet is defined as

cla,b (t) 5 p(21/4) (al)(21/2) e2i2p (1/a)(t2b) e2(1/2)((t2b)/al)2 The values of l support higher resolution in time (depth) or frequency due to the Heisenberg-type uncertainty DaDb $ 1/4p The sampling along the a and b axes controls the resolutions in time and frequency, Db and Da (cf. Rioul and Vetterli 1991): Db $ a1/Ï2;

Da $ Ï2/4pa1

Sufficiently precise results in both time and frequency are obtained by choosing l 5 10. The first-order trend is removed before wavelet analysis is applied, separating frequencies (e.g., from climatic signals) from superimposed ‘‘red noise’’. ‘‘Red noise’’ primarily is low-frequency background noise (Mann and Lees 1996). To transform a measured and hence limited and discrete time series, the integral in the wavelet transform has to be modified by using the trapezoidal rule for unevenly sampled points to evaluate the wavelet transform, and this provides W*l(a, b). The interpolated W*l(a, b) can be graphically visualized with appropriate colors or shades of gray. This graphic representation in time–frequency space is called a ‘‘scalogram’’, because the wavelet transform uses mostly nonperiodic mother wavelets (e.g., ‘‘Daubechies’’ wavelets) in other signal-processing applications (Rioul and Vetterli 1991). In this paper, we use shades of gray, with black representing 75–100%, dark gray for 50–75%, light gray for 25–50%, and white for 0–25% of maximum W*l(a, b), as shown in Figure 4A. The wavelet analysis method and computer program CWTA.F are explained in more detail in Prokoph and Barthelmes (1996). Model 1 (Fig. 3) illustrates the preservation of Earth’s orbital cycles of about 100 kyr, 41 kyr, and 21 kyr (Milankovitch 1941) in wavelet analysis and spectral analysis with fast Fourier transform. These simulated Milankovitch cycles of equal amplitude have been transformed by two sinusoidal cycles, which can be related to low sediment supply–high sediment supply cycles with mean sedimentation rate of 50 cm/kyr and range from 0 cm/

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FIG. 2.—Analysis windows for A) Fourier analysis and B) wavelet analysis with a mother wavelet. Notice that there is only a single analysis window for Fourier analysis in the time domain (xo-xn) for each frequency. The analysis window width b of the wavelet transform is adjusted to a distinctive time (xi) and scale a by centering the Morlet mother wavelet with scale a at xi.

FIG. 3.—The transformation of Milankovitch cycles of 100 kyr, 41 kyr, and 21 kyr related to A) two sinusoidal cycles of changes in sedimentation rate from the time domain into the depth domain is shown by B) spectral analysis (Fourier transform) and C) wavelet analysis for Model 1. The two-dimensional gray-shade picture is ‘‘scalogram’’, which shows dark gray and black color at high-intensity periodicity a in a distinctive time interval b. No cyclicity of period a appears in time interval b at white areas in the scalogram.


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FIG. 4.—A) Four-step intensity scale for wavelet scalograms. B) Wavelet scalogram of Model 2; t 5 33 and t 5 47 mark short-time random cyclicity. C) Model 2: random noise data. D) Model 3 shows the preservation of periodic cyclic signals of t 5 40 and t 5 250 with the appearance of random noise F(t). The black triangle shows the amplitude variability (0–2) of the random noise compared to the amplitudes of the periodic signals (black bars) of 0.4. E) wavelet scalogram of Model 3 (for interpretation, see Figure 3).

kyr to 100 cm/kyr. The Fourier transform from the time to the depth domain leads to broad spectra of frequencies, because of phase shifting for each primary Milankovitch signal, which cannot be clearly related to the original cycle ratios (5:2:1). On the other hand, wavelet analysis traces the gradually transformed Milankovitch cycles throughout the modeled data. Periodicities of Milankovitch cycles are better preserved in depth intervals with relatively high accumulation rates (100 cm/kyr). Cycle preservation is fuzzy at very low accumulation rates. The primary signal ratio of about 5 (5 100 kyr): 2 (5 41 kyr): 1 (5 21 kyr) becomes approximately 4: 1.8: 1 5 80 m: 36 m: 20 m, as follows from the major peaks in the power spectra and the wavelet scalogram. Confidence levels cannot be constructed for gradual ‘‘deterministic’’ shifts in the accumulation rate detected by wavelet analysis as used for stationary signals (Davis 1986; Mann and Lees 1996). Therefore, subjective interpretation remains necessary to link gradual frequency shifts to a single controlling factor in sedimentary depthdependent data series. Another difficulty for geologists is the prominence of noise in welllogging data. Noise can be caused by measurement errors, unstable borehole walls, and random sedimentary events such as bentonites, turbidites,

and tempestites. These effects and, therefore, the signal/noise ratio can change through time and depth. In the second model used (Model 2), random noise F(t) with amplitude from 0 to 2 (Fig. 4C) provides mostly scattered high frequencies (cycle length t , 10) without stationarity, but short-time stationarity at weak intensity of t 5 33 and t 5 47 is shown as dark gray patches in Figure 4B. These random ‘‘cycles’’ are less intense than the superimposed highfrequency noise. However, these ‘‘cycles’’ also appear in marine mudstone sedimentation. Random noise F(t) of amplitude from 0 to 2 was added in Model 3 to two periodic signals (period t 5 250 and t 5 40), both with amplitudes of 0.4 (Fig. 4D). The scalogram (Fig. 4E) illustrates enhanced preservation of the higher-frequency cycle (period t 5 40), possibly because the noise F(t) enhances the amplitude of these frequencies as an effect of stochastic resonance, as demonstrated by Wiesenfeld and Moss (1995). The noise provides high-frequency signals and low-frequency interference, shown as dark patches in the scalogram. The three models suggests that wavelet analysis permits one to distinguish better than spectral analysis between continuous, nonstationary, and

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A. PROKOPH AND F.P. AGTERBERG The Upper Albian marine mudstone successions are from east to west: Skull Creek, Joli Fou, Westgate, Lower Shaftesbury, Hasler, and Goodrich Formations. They are subdivided by the deltaic, fluvial, and shoreface sandstones of the Newcastle Sandstone, the Viking Formation, the Paddy Member, and the Boulder Creek F. (Fig. 7). The mudstone succession of the basin center forms the basal part of the ‘‘Lower Colorado Group’’. The thickness of the Upper Albian succession varies from about 550 m in the Foothills of NE British Columbia to about 84 m on the Manitoba Escarpment, corresponding to mean sedimentation rates of about 14 to 2.2 cm/ kyr, respectively. Correlation of Cycles

FIG. 5.—Paleogeography of Western Interior Seaway of America, after Schro¨derAdams et al. (1996). The gray area illustrates the land mass, and the shaded line shows the outline of the Late Albian Mowry sea.

random signals in dependence of the observation time and depth intervals. Wavelet analysis also provides almost no edge effects (see Figs. 3C, 4B, and 4E) because of centering of the highest amplitudes of the Morlet mother wavelets around the data window analyzed. CYCLICITY AND THE PRESERVATION OF THE STRATIGRAPHIC RECORD IN THE UPPER ALBIAN OF THE WESTERN CANADA SEDIMENTARY BASIN

(WCSB) Geological Setting The Western Interior Seaway of North America is one of the largest foreland basins of the world (Kauffman and Caldwell 1993) extending from the Gulf of Mexico to the Arctic Ocean for about 6000 km (Fig. 5). The Canadian part of the seaway, the Western Canadian Sedimentary Basin (WCSB), extended during the Cretaceous from British Columbia to western Ontario for about 1600 km (Fig. 6; Williams and Stelck 1975; Leckie and Smith 1992). Transgressions during the Late Albian generated the Kiowa Skull Creek cycle and the Greenhorn cycle in the WCSB (Kauffman and Caldwell 1993). Late and Middle Albian stratigraphy of the WCSB is characterized by biostratigraphic and lithostratigraphic inconsistencies, especially in the Rocky Mountain Foothills (Leckie and Reinson 1993). For example, the widely correlative Base of Fish Scales (BFS) marker bed is not observed in the Foothill sections. In the global time scale, the Albian/Cenomanian boundary is placed at the base of the Neohibolites haasi subzone at about 98.9 Ma (Gradstein et al. 1994) and not at the Base of Fish Scales (97.6 Ma; Obradovich 1993). It means that the Late Albian for the WCSB is of the same age as the Early Cenomanian defined by Gradstein et al. (1994). Therefore, we have used for biostratigraphic and lithostratigraphic correlation a ‘‘common sense’’ chart that is in agreement with the most recent publications on the WCSB (Schro¨der-Adams et al. 1996; Leckie and Reinson 1993; Leckie at al. 1997).

Sedimentary cycles are defined in various ways. Schwarzacher (1993) suggests that sedimentary cycles are externally produced, periodic repetitions of sedimentary rock types (e.g., facies ABCD) detected from lithofacies and bedding rhythm. Vertical geophysical well logging (e.g., gammaray) cycles in the subsurface cannot directly be related to bedding rhythms. It is also hard to rule out that periodic repetitions in logging data are not produced by stochastic processes unrelated to external forcing. Therefore, gamma-ray cyclicity should: (1) be comparable with lithofacies cycles from cored sections; (2) be correlative to other geophysical logs of the same succession; and (3) show periodic repetition in relatively high or low signals (i.e., peaks) for the major period. Gamma-ray cycles, feasible for stratigraphy, should also show bundling in the frequencies or be bounded by chronological marker horizons detectable in the well studied. In this study, negative gamma-ray peaks are used for primary correlation of wells, because they are easy to identify in the logging curves. The sedimentary and stratigraphic significance of these negative peaks is discussed later in the text. An east–west cross section (A–B) spans the southern basinal part of the WCSB and covers parts of southeastern Saskatchewan (well 11-11-2022W2) to southern Alberta (well 3-22-7-24W4). Up to 10 gamma-ray cycles in the Joli Fou and Skull Creek Formations (J1–10) and 11 gammaray cycles in the Westgate and Shaftesbury Formations (W1–11) can be detected (Fig. 8). However, it cannot be determined whether or not preservation of the two cyclic units is limited by erosion at the top, at the base, or somewhere in between. For practical reasons, the cycle counts are tied to the tops. Later in the text these two cyclic units are called ‘‘Westgate cycles’’ and ‘‘Joli Fou cycles’’, respectively. Partially, the transgressive bases of these formations have noncyclic units described as ‘‘Jtr’’ and ‘‘Wtr’’. The Viking Formation is noncyclic or nonperiodic–cyclic. In the wavelet scalogram the gamma-ray log of well 3-22-7-24W4 of the Viking formation data displays an abrupt transition from the predominant 4.9 m and 20 m cycles of the Joli Fou Formation to 3.7 m and 14 m cycles of the Westgate Formation, respectively. The southeast (C)–northwest (D) correlation from southern Alberta to NE British Columbia provides a different cycle pattern (Fig. 9). There the preservation of the Joli Fou cycles decreases from the southeast (10 cycles) drastically to nonperiodic cyclicity in the Rocky Mountain Foothills. The Lower Shaftesbury Formation of the Peace River Area most likely provides the most complete marine succession of the late Late Albian. Two distinctive parts (Wtr and Wtr(e)) of cyclic mudstone sedimentation below the 11 Westgate cycles are present in relatively few wells. Cyclicity of the Hasler Formation is less pronounced than that of the Goodrich Formation (29 m, 19 m) in well 14-20-77-23W6. Generally, the top of the Westgate Formation is easily detectable by its positive gamma-ray peak at the Base of Fish Scales. However, positive precursors can appear in cycles W1 to W3, which are probably not synchronous. The cycles are easier to detect in the incomplete western sections (3-22-7-24W4) than in the complete but monotonous central sections (e.g., 12-22-14-14W3).


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FIG. 6.—Map of the study area showing the location of wells studied (black circles) and cross sections A–B and C–D.

FIG. 7.—Stratigraphic nomenclature for the Late Albian of the Western Canada Sedimentary Basin with comparison to Northern Europe. Nomenclature compiled after Leckie and Reinson (1993), Schro¨der-Adams et al. (1996), McNeil and Caldwell (1981), and Gradstein et al. (1994).

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FIG. 8.—Cross section A–B; location is shown in Figure 6. Two-dimensional gray-shade picture at the left shows the wavelet scalogram of gamma-ray log from well 322-7-24W4. Horizontal scale is the logarithmically ordered cycle length (5 period), and vertical scale is correlative to the depth in the borehole. Vertical lines in the scalogram mark significant cycle lengths, and horizontal lines mark distinctive abrupt changes in cyclicity at a distinctive depth. The black bar gives the 50 m depth scale. Dotted lines mark high-frequency cycles in the wells. Sampling intervals of the gamma-ray logs are 0.5 ft or 20 cm.

Gamma-Ray Cyclicity versus Lithological Cyclicity A detailed bed-by-bed description of core 10-35-45-2W4 north of the central part of the basin shows two distinctive lithofacies evolutions in the Westgate Formation: The lower part (500–480 m depth) displays a transition from intensely bioturbated (Teichichnus, Planolites, Zoophycos) sandstones and siltstones to weakly bioturbated (Chondrites, Planolites) mudstones, which are slightly calcareous at about 480 m. The periodic cycles W11 to W7 are correlative with the occurrence of siderite layers and nodules (Fig. 10). In the upper part, from about 480 m to 455 m, slightly calcareous mudstones change to thick-bedded glauconitic and bioturbated (‘‘Spreitenbauten’’) sandstones, siltstones, and intercalated thin beds of moderately bioturbated mudstones. The boundaries of cycles W7 to W4 coincide again with siderite layers, but the other boundaries are more in accordance with coarser-grained beds. Near the top (cycle W1), mudstones enriched in fish scales and pyrite dominate, evolving to the condensed sedimentation of the Base of Fish Scales (BFS), which consists of nonbioturbated siltstones enriched in fish scales, and iron concretions. Consequently, lithologcal cycles

can be defined as fluctuations between (A) coarser grained sandstone/siltstone or siderite layers providing negative gamma-ray peaks, and (B) finegrained, pyrite-enriched mudstones providing positive gamma-ray values. Lithological core descriptions of the Joli Fou cycles suggest fluctuations between poorly bioturbated mudstones and siltstones (high gamma-ray values) and highly bioturbated and glauconitic sandstones (negative gammaray peaks) in the Manitoba Escarpment and in the basin center (McNeil and Caldwell 1981; Leckie and Reinson 1993). Gamma-Ray Cyclicity versus Cyclicity in Foraminiferal Assemblage The paleontological and biological response to sedimentary changes depends on (1) the primary sensitivity of a species or fossil group to facies changes, (2) preservation of these variations due to diagenesis, (3) the continuous sampling of a statistically significant number of specimens through time, and (4) the exact taxonomy of these specimens. The distribution and abundance of two easy-to-distinguish benthic agglutinated foraminifera (Miliammina manitobensis and Gaudryina canadensis) of the Upper Albian marine hemipelagic succession in the Manitoba


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FIG. 9.—Cross section C–D; location is shown in Figure 6. Two-dimensional gray-shade picture on the left shows the wavelet scalogram of gamma-ray log from well 14-20-77-23W6. For interpretation of the scalogram see Figure 8. Notice the 50 m scale change between well 14-20-77-23W6 and well 11-21-72-12W6 as well as the change of formation names (see Figure 7). For further remarks, see text.

Escarpment (well 1-24-20-33W1) were taken from data by McNeil and Caldwell (1981) as shown in Figure 11. These species are common in the entire basin all the way to the Arctic Sea (Caldwell et al. 1993). High relative abundances of these two species (. 40 specimens/sample) are correlative with relatively high gamma-ray values in cycles J2–J5, and probably indicate clay-rich parts of the section (shales), whereas low abundances are most likely related to sandstones and siltstones. The occurrence of G. canadensis is stratigraphically restricted to the Skull Creek Formation. G. canadensis varies with the periodic 7 m cycles J6–J2 and, additionally, in accordance with M. manitobensis in cycles J5– J2. The continuous occurrence of Haplophragmoides gigas (see McNeil and Caldwell 1981) make it unlikely that these variations are due to diagenetic variations. In the Westgate Formation the number of samples is too small for significant correlation. However, there is also a positive correlation between the 7.6 m cycles and the variable abundance of M. manitobensis.

on both gamma-ray and sonic logging curves of well 11-11-20-22W2 (Fig. 12). The fact that the other cycles (1.7 m, 2 m, 4 m, and 26 m) appear in only one of the logging curves may be due to frequency interference effects, as described by Sanchez and Vos (1994). The Viking Formation exhibits 26 m cyclicity in sonic logs and 7 m in gamma-ray logs. The 7 m gamma-ray cyclicity spans two repetitions with weak negative ‘‘peaks’’ at depths of about 611 m, 618 m, and 625 m. The 26 m sonic cycle spans the interval between two distinctive positive peaks at 629 m (still in the Joli Fou Formation) and 623 m. The base of the Westgate Formation (Wtr) is characterized by high-frequency fluctuations. Generally, the sonic logs are less sensitive to sedimentary variations in this example, indicating relatively poor cyclicity but also less noise, as illustrated in Model 3 (Fig. 4).

Gamma-Ray Cyclicity versus Sonic-Log Cyclicity

According to Model 1 the cycles of the Joli Fou and Westgate cyclic units were deposited at the same accumulation rates through each section. The base of Joli Fou Formation to the Base of Fish Scales (BFS) spans a time interval from about 101 Ma to 97.2 Ma (Schro¨der-Adams et al. 1996; Leckie et al. 1997). The maximum possible duration of each periodic cycle W1–W11 is about 140 kyr according to the approximate time of deposition

Gamma-ray readings are more sensitive to variations in lithology and clay-mineral content than are other logging tools (Serra 1984). The results of wavelet analysis show coincidence of the 7 m cyclicity of the Joli Fou Formation and the 5 m cyclicity in the Westgate Formation

DISCUSSION AND INTERPRETATION

Cyclostratigraphy and Stratigraphic Completeness

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FIG. 10.—Correlation of gamma-ray cyclicity of well 1-24-20-33W1 with abundance of the benthic foraminifera species Gaudryina canadensis and Miliammina manitobensis. Dotted lines mark correlation with negative gamma-ray peaks, and dotted lines mark correlation with positive gamma-ray peaks. For interpretation of wavelet scalogram, see Figure 8.

for the Westgate Formation of about 98.7–97.2 Ma, providing T 5 1.5 Myr (Schro¨der-Adams et al. 1996). For well 11-21-72-23W6, the total sedimentation time span (T) of the Lower Shaftesbury is about 1.5 Myr. The total sediment thickness (s) is 156 m, and the major cycle length (sl) is 10 m (Fig. 13). In this section, the cycle preservation appears best pronounced in the middle part, probably at maximum transgression. According to Model 3, an increasing noise level superimposes cyclicity at the base and top during early transgression and late regression, respectively. In these parts the best-pronounced periodicity varies between 8 and 13 m (mean 5 10.5 m), clearly observable in the gamma-ray curve. Therefore, the observation time (ot) for these periodic cycles is estimated to be ot 5 sl*T/s 5 (10 m)(1.5 Myr)/156 m 5 0.097 Myr. According to its stable periodicity each 10 m cycle represents 97 kyr. This is close to the 100 kyr eccentricity cycle of Milankovitch (1941), which is in fact a set of periodicities varying about 93–128 kyr with major intensity at 97 kyr (Schwarzacher 1993). In the other parts of the basin, the sedimentation rates at geochronological resolution of 2 Myr and 1.5 Myr are mostly lower than the estimates with observation time spans of 1 Myr and 100 kyr, respectively. Bundles of these cycles exist in the ratio of about 4:1 (i.e., 14/3.7 m and 20/4.9 m in well 3-22-7-24W4) or 5:2:1 (7/3/1.6 m in well 1-24-20-33W1), corresponding to Milankovitch cycles of about 400 kyr: 100 kyr, and 100 kyr: 41 kyr: 21 kyr, respectively. This interpretation reduces the mean cycle duration from 140 kyr to 100 kyr, implying hiatuses or geochronological uncertainty. Table 1 shows a compilation of sedimentation rates calculated for four observation time spans (ot) ranging from (a) the whole Upper Albian suc-

cession from the base of the Joli Fou upwards (5 3.8 Myr), (b) geochronological ages for the Westgate (1.5 Myr) and Joli Fou Formations (about 2 Myr), (c) the entire Westgate and Joli Fou cycle units (ot 5 1 Myr), and (d) major cycle length (ot 5 100 kyr) from wavelet analysis. The mean sedimentation rate sr for ot 5 1 Myr was calculated by sr(1 Myr) 5 number of preserved cycles 3 (100 kyr/length of entire cyclic unit) The sedimentation rate of ot 5 1 Myr is commonly less than the major cycle (ot 5 100 kyr) in the wavelet scalogram (see Table 1) because of the effect of hiatuses and nondeposition times as shown in Model 1. Therefore, slight variations in the cycle periodicity can manifest themselves even in the cyclic units. Model of Paleogeographic Preservation of Cyclicity The small number of wells studied allows only a sketchy model of the paleogeographic preservation pattern, providing an indication of the distinction between preservation and primary sediment accumulation of highfrequency variations. Notice that the isopach maps available for these formations merge final preservation with original accumulation (i.e., Leckie and Reinson 1993). The ten Joli Fou cycles are completely preserved in southeastern Alberta and southwestern Saskatchewan, which is the northern part of the Williston (Sub-)Basin (Stott et al. 1993). The cycle number decreases only slightly to the east and more drastically toward the Foothills. In contrast, the internal sedimentation rate (ot 5 100 kyr) decreases only slightly from south-


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FIG. 11.—Correlation of gamma-ray cyclicity of well 10-35-45-2W4 and lithology. For interpretation of wavelet scalogram, see Figure 8.

east (. 6 cm/kyr) to northwest (. 5 cm/kyr) with a negative anomaly (sr , 5 cm/kyr) extending from SE Alberta through NE Alberta (Fig. 14). The preservation of the Westgate cycles is more patchy. A complete set of 11 cycles exists again in the Williston Basin in a slightly more extended area than that for the Joli Fou cycles. The sedimentation rate (ot 5 100 kyr) again varies in the basin part between 4.5 and 8 cm/kyr. A SW–NE-striking negative anomaly through Alberta appears as a ‘‘low-cycle-preservation’’ area and could be related to the uplift of the Sweetgrass Arch (Stott et al. 1993). In this region (e.g., well 6-21-53-14W5), only seven cycles of a total of 21 Late Albian cycles were preserved resulting in a stratigraphic completeness of 30% for ot 5 100 kyr compared to ot 5 2.1 Myr. The sedimentation rate along the Foothills increases to maximally 30 cm/kyr. According to these models, two strongly subsiding areas existed during deposition of the Joli Fou cycle but only one of these was preserved as an isopach anomaly. As many as three subbasins existed according to the models during the deposition of the Westgate Formation, of which only two remain preserved. Depositional Model According to the wavelet analysis of cyclic patterns in the WCSB, the detection of high-frequency cycles in different tectonic and lithofacies realms depends predominantly on four features:

(1) Cycle type, which is controlled by lithofacies as a result of marine productivity, terrigenous supply, and diagenesis, and the primary character of cycle deposition (event-like or continuous). (2) Periodicity of cycle preservation, which is controlled by superimposed fluctuations of sediment accumulation. (3) Intensity of cyclicity, which is controlled by lithological (or biological) variability in the cycles themselves. (4) The (stratigraphic) completeness of the cycle bundle (or ‘‘cyclothem’’), which is controlled primarily by superimposed syndepositional and postdepositional changes in sea level and base level (transgressions and regressions), tectonics (i.e., changes in relief due to subsidence variations), bottom water currents, and other factors. A model for the influence of these parameters on the formation and preservation of cyclicity is shown in the example of clastic deposition in a foreland basin with respect to a superimposed transgressive–regressive cycle in Figure 15. We avoid a sequence stratigraphic interpretation after Vail et al. (1991) of this signature, which would make the model both more sophisticated and more complex. In a sequence stratigraphic approach the cycles detected could be interpreted as fifth-order cycles or periodic parasequences. For the various sedimentary environments the optimal measurement technique with the necessary data resolution has to be taken into account

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FIG. 12.—Correlation of gamma-ray cyclicity of well 11-11-20-22W2 and sonic logging results. For interpretation of wavelet scalogram, see Figure 8.

to detect high-resolution cyclicity. These techniques range from simple bedding-rhythms counting of marl/limestone couplets (Schwarzacher 1994), multivariate statistics of fossil communities in reefs (Gro¨tsch 1994), self potential logging in chalk/marlstone successions (Niebuhr and Prokoph 1997), to analysis of gamma-ray-logging data, as in this study. Control Mechanisms for High-Frequency Cyclicity The controlling mechanism of the siliciclastic-dominated Westgate and Joli Fou cycles can be interpreted as dilution cycles, as already proposed for the Greenhorn bedding rhythms in the U.S.A. part of the Cretaceous Interior Seaway (Pratt et al. 1993). According to Pratt et al. (1993), the amount and grain size of the terrigenous sediment supply is climatically controlled. During dry periods, relatively small amounts of clay are transported into the sea, because of decreased chemical weathering of the emergent land (ROCC Group 1986). Especially the detrital minerals illite and smectite are less abundantly supplied (Sethi and Leithold 1994), resulting in negative gamma-ray peaks. In contrast, during wet periods these minerals were widely transported into the epicontinental sea, providing positive gamma-ray peaks. We have not detected a good connection between climate change and periodic cyclic occurrence of the iron-enriched concretions at negative gamma-ray peaks.

Perhaps, the primary higher porosity in the coarser ‘‘dry-climate layers’’ supports an increased primary concentration of mobile Fe ions, which became mineralized during sediment compaction. A purely tectonic control on these cycles is unlikely because up to 11 periodic repetitions appear in a marine environment without evidence of reworking or erosion. The period of the 100 kyr cycles is also much longer than those of quasi-periodic autocyclically controlled turbidite successions (Einsele 1993). Stratigraphic Significance As already mentioned, the Upper Albian Westgate Formation is correlative to the Lower Cenomanian in Europe (Gradstein et al. 1994) where Gale (1989) found 15 chalk/marlstone 100 kyr eccentricity cycles in the M. mantelli zone (basal Cenomanian). In the Lower Saxony Basin and the Anglo-Paris Basin these cycles are unconformably underlain by a glauconitic marl and covered by a coarse, condensed limestone bed interpreted as transgressive base and transgressive lag, respectively (Gale 1995). We suggest correlation of this transgressive lag with the Base of Fish Scales in the WCSB and linkage of the 1.5 Myr deposition time of the M. mantelli zone with the Westgate cycle. The controlling mechanism behind this


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FIG. 13.—High-frequency gamma-ray cyclicity of well 11-21-72-12W6 with transgressive– regressive trends. For interpretation of wavelet scalogram, see Figure 8. Bold lines mark major changes in cycle preservation. Dotted lines mark high-frequency cycles of about 100 kyr.

‘‘global’’ transgressive lag at about 97.6 Ma could be a topic for further study. CONCLUSIONS

(1) Wavelet analysis of well-logging data allows fast, single-step detection of cycles, trends, and discontinuities in sedimentary successions. The wavelet transform of gamma-ray-logging data permits automatic detection of periodic cyclicities in various observation time intervals and distinguishes cyclic from noncyclic sedimentation. (2) The preservation and stratigraphic completeness of high-frequency cyclicity can be traced through different lithofacies belts in a basin, which permits the correlation of these intervals. The interaction of preservation potential, observation time, and cycle thickness allows the distinction between primary accumulation rate and postdepositional preservation with resolution of up to 100 kyr in the WCSB. In the Westgate Formation, the

geochronologically calculated sedimentation rate varies from about 1.9 cm/ kyr to 29 cm/kyr. The sedimentation rate of the major 100 kyr cycles as calculated by wavelet analysis varies from about 4.9 to 29 cm/kyr, providing preservation potentials from 30% (intrabasinal swell) to 100% (foredeep of Rocky Mountains belt) compared to the geochronological resolution. (3) Signal/noise ratio controls the intensity (amplitude) of the periodic signal, depending on the sedimentary environment and the sensitivity of the measurement tool used, as shown in model and logging data from the WCSB. Here, gamma-ray data of from mudstone successions are more noisy but also more intensely cyclic than sonic logging data. (4) The most pronounced periodic cyclicity in the Late Albian of the Western Canada Basin is in accordance with the Earth’s orbital 100 kyr eccentricity cycle. The deposition of the cycles is interpreted as being controlled by climate fluctuations that supported the supply of clay during wet

TABLE 1.—Logged Gamma-ray sections; sedimentation rates in Upper Albian sections of the WCSB. Upper Albian

Section name

depth total (m)

1-24-30-33W1 11-11-20-22W2 12-22-14-14W3 5-7-9-19W3 6-29-7-1W4 10-35-45-2W4 10-16-11-8W4 6-34-30-8W4 3-22-7-24W4 6-21-53-14W5 11-21-72-12W6 14-20-77-23W6

303–387 540–670 922–1047 1020–1190 1310–1485 447–540 — 768–889 1557–1655 1915–1990 — 2270–2800

Joli Fou

sr (cm/kyr) ot 5 3.8 Myr 2.2 3.4 3.3 4.5 4.6 2.4 3.2 2.6 2 14

depth total (m)

sr (cm/kyr) ot 5 2 Myr

338–387 627–670 1005–1047 1115–1190 1415–1485 505–540 — 837–889 1610–1655 1977–1990

2.45 2.15 2.5 3.75 3.5 1.75

2700–2800

5

2.6 2.4 0.6

depth cyclic unit (m) 338–384 627–664 1005–1047 1115–1184 1415–1470 505–540 — 837–881 1610–1648 1977–1988

Westgate sr (cm/kyr) ot 5 1 Myr

sr (cm/kyr) ot 5 100 kyr

6.6 6.2 6 6.9 5.5 5

7 7 7.1 7.6 4.6 7.5

4.4 4.2 5.5

7.6/3.4 4.9 7.6

depth total (m)

sr (cm/kyr) ot 5 1.5 Myr

depth cyclic unit (m)

sr (cm/kyr) ot 5 1 Myr

sr (cm/kyr) ot 5 100 kyr

303–336 542–610 922–995 1020–1110 1310–1373 447–499 675–725 768–830 1557–1600 1915–1946 1475–1631 2270–2700

2.2 4.7 4.9 5.3 4.2 3.5 3 4.1 2.9 1.9 10.4 29

303–333 542–599 922–987 1015–1087 1310–1370 447–497 675–715 768–825 1557–1600 1915–1943 1475–1585 2270–2558

6 5.3 5.9 6.1 5.4 4.5 5 5.2 4.8 7 10 26

7.6 5 6.1 6.5 4.9 7.1/3.5 5.8 7.6 3.7–5.5 7.1/2.6 10–14 29

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FIG. 14.—Paleogeographic maps of the Western Canada Sedimentary Basin of A) isolines of average sedimentation rates (ot 5 100 kyr) of Joli Fou cycle, B) preservation and completeness of Joli Fou cycles, C) isolines of average sedimentation rate (ot 5 100 kyr) of Westgate cycle, and D) preservation and completeness of Westgate cycles.

FIG. 15.—Two-dimensional model of types, preservation, intensity, and completeness of high-frequency cycles with superimposed sealevel cycle in the foreland basin of Western Canada. T marks transgressive time intervals and R marks regressive time intervals.

WAVELET ANALYSIS OF SEDIMENTARY SUCCESSIONS periods and sand during dry periods. These cycles were detected in the gamma-ray log as well as in the lithology and biological response. ACKNOWLEDGMENTS

We are grateful for critical discussions with Dale Leckie (GSC Calgary) and Claudia Schro¨der-Adams (Ottawa–Carleton Geoscience Center). The paper benefited from the critical comments and suggestions provided by the reviewers Michele Kominz and Jon Pelletier. Financial support has been provided from the Geological Survey of Canada to F. Agterberg and the Deutsche Forschungsgemeinschaft (German Research Council) Grant Pr 545/1-1 for A. Prokoph. Digitized logging data were provided by Riley’s Datashare Calgary. REFERENCES

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