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Key words: H/V ratio, Kappa, Kobe earthquake, Non-Linearity. Abstract. Simple straightforward methods are applied to test their ability to detect the non-linear ...
Journal of Seismology 4: 161–173, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

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Straightforward methods to detect non-linear response of the soil. Application to the recordings of the Kobe earthquake (Japan, 1995) C. Lacave-Lachet1,2 , P.Y. Bard1,3 , J.C. Gariel4 & K. Irikura5 1

Laboratoire de G´eophysique Interne et Tectonophysique, Grenoble, France; 2 R´esonance, Ing´enieurs-Conseils SA, Gen`eve, Switzerland; 3 Laboratoire Central des Ponts et Chauss´ees, Paris, France; 4 Institut de Protection et de Sûret´e Nucl´eaire, Paris, France; 5 Disaster Prevention Research Institute, Kyoto, Japan Received 16 April 1998; accepted in revised form 18 May 1999

Key words: H/V ratio, Kappa, Kobe earthquake, Non-Linearity

Abstract Simple straightforward methods are applied to test their ability to detect the non-linear response of the soil. Recordings of the main shock and aftershocks of the 1995, Hyogo-ken Nanbu (Kobe) earthquake are used. Non-linear effects are investigated using two different techniques, on a collection of data for 12 sites situated on different geological structures in the Kobe and Osaka areas. The first method used is the so-called receiver functions technique (Langston, 1979), which consists of computing the spectral ratio between horizontal and vertical components of motion. This ratio has been shown to reveal the fundamental frequency of a site (Lachet and Bard, 1994; Lachet et al., 1996; Theodulidis et al., 1995, 1996). For each site, recordings of the main shock and a set of aftershocks are considered. The variation of this spectral ratio for different values of the maximum acceleration recorded at a site is investigated. Both variations of the amplitude of the H/V ratio (due to non-linear behavior, on the horizontal components in particular) and of the frequency position of the amplified band-width are observed. The second technique used in this study is related to the variation of the high frequency content of the recordings during the main-shock and its aftershocks. The high frequency spectral decay of the motion, characterized by κ parameter, is assumed to be related mainly to the near-surface attenuation. It should then increase with increasing peak velocity, in case of non-linearity. The value of kappa is calculated for the 12 sites in the Kobe area, for different types of soil conditions, and again different values of peak ground acceleration. Variations of kappa are then related to non-linear behavior of the soil during the Kobe earthquake.

Introduction The 1995 Hyogo-ken Nanbu (Kobe) earthquake is one of the most investigated recent earthquake, due to the considerable damage that occurred in the city of Kobe and the great number of available data. One of the most investigated issues is the location of the ‘damage belt’. It has been shown to be related both to the general basin structure and to strong directivity effects. Another important issue is the non-linearity and liquefaction phenomenon that occurred mainly on coastal sites and reclaimed land islands. Various studies have been conducted about this problem, in particular by Aguirre and Irikura (1997), using recordings at different depths in a bore-hole at Port Island. They show

a permanent change in the value of the shear wave velocity after the main shock, in the liquefied layer. Non-linear behavior of the ground motion is an important issue which should systematically be taken into account by seismologists and geotechnical engineers when evaluating the seismic hazard related to a given site. The case of the Kobe earthquake is a dramatic example of how important these phenomena can be, regarding the damage distribution during an earthquake. A large area in the city of Kobe, seems indeed to have suffered significant non-linear effects, as evidenced by the extensive liquefaction along the sea shore and on the artificial reclaimed land islands, such as Port Island and Rokko Island. While non-linearity is obvious in case of liquefaction, what about non-linear

162 or linear response of the soil in other places which did not suffer liquefaction? As this earthquake occurred in a well instrumented area, a great amount of data is available. The goal of this study is to investigate the ability of simple experimental methods to detect the occurrence of non-linear phenomena. In that sense, Aguirre and Irikura (1995) used recordings of the Port Island down-hole vertical array to show significant non-linear effects on the horizontal components of motion, the vertical component having an apparent linear behavior. These results explain the disproportion observed between amplitudes of the horizontal and vertical motions, particularly on the reclaimed land areas. Aguirre and Irikura (1997) also showed a clear change in the S wave velocity during and after the main shock. Using several aftershock recordings at different times, they proposed a curve of the S wave velocity change in the liquefied layer as a function of time. From a more geotechnical point of view, Cubrinovski and Ishihara (1996) also investigated the problem of liquefaction on Port Island, using an effective stress analysis. They showed that the major part of the liquefaction occurred in the ‘Masado’ layer, between 5 and 15 meters from the ground surface. A study by Yasuda et al. (1996) clearly showed the efficiency of soil improvement against liquefaction phenomena. These authors indeed pointed out a clear correlation between the areas on the Port and Rokko islands where no liquefaction occurred and the specific soil improvement that had been done before the construction of buildings at these places. Mohammadioun (1997) proposed a mathematical method for detection of non-linear behavior of the soil from seismic recordings. He considers the time derivative of the phase of the signal that represents the instantaneous angular frequency. This function gives an image of the evolution of the predominant frequency along the signal. An application on the Port Island vertical array recordings shows that this method gives a good indication of the occurrence of non-linearity along a seismic recording that is characterized by an abrupt decrease of the apparent frequency. The study presented here is based on the use of several recordings of the Kobe main shock and aftershocks at different sites in the cities of Kobe and Osaka (Figure 1 and Table 1). The aim is to test straightforward methods to investigate their ability to reveal non-linear phenomena. Two different techniques are used: the H/V ratio (spectral ratio between horizontal and vertical components of motion) and the

high frequency spectral decay of acceleration spectra (parameter ‘kappa’). These methods and the obtained results are presented in the following sections.

H/V ratio The H/V ratio method consists of the calculation of the spectral ratio between the horizontal and vertical components of the motion at a given site. This technique was first introduced as the receiver function method (Langston, 1979), and it was later used on ambient noise recordings to determine the fundamental frequency and amplification level of a site (Nakamura, 1989). Further studies conducted by other authors (Lachet and Bard, 1994; Field and Jacob, 1995; Lachet et al., 1996; etc.) confirmed that H/V ratio is an effective tool to estimate the fundamental frequency of a site independent of the kind of signal used; real earthquakes or ambient noise. On the contrary, these same studies indicate that one must be very careful with the use of the H/V ratio amplification level whose significance is still not well understood. Bard et al., 1997 conducted a statistical analysis on many data sets, showing a general trend for the noise H/V ratio underestimating the amplification level with respect to the classical spectral ratio. It is then not reliable to consider absolute values of amplification given by this technique. This is the reason why we suggest the use of the H/V ratio amplitude only as a relative indicator of site amplification, in comparison of one site with another or one period with another. One of the aims of this study is to test the ability of the H/V ratio technique to indicate the occurrence of non-linearity, when applied on data from the main shock and aftershocks of a big earthquake. In the case of the Kobe earthquake, the H/V ratio of the main shock and of a collection of available aftershock recordings have been calculated for each site. A signal to noise ratio threshold value of 3 has been applied to the data. If these H/V ratios present a relative decrease of the amplification level for higher peak ground accelerations (PGA), it would indicate a non-linear behavior of the soil characterized by a loss of energy on the horizontal components. Figure 2 (a and b) presents the H/V ratios obtained, for the main shock (continuous line) and for the aftershocks (dotted lines) for different sites considered in this study. Looking at these results, it appears that for some sites the H/V ratio of the main shock is lower than that of the aftershocks, particularly at high frequencies (greater than 2 Hz). On the

163

Figure 1. Map of the location of the recording sites, in the Kobe and Osaka areas.

Table 1. Available data for each site considered Site name

Soil type

Number of available events

Range of PGA (m s−2 )

Owner organization

KBU MOT KOB AMG FKS OSA MKT YAE ABN SAK PR1 RKI

granite alluvium alluvium alluvium alluvium alluvium alluvium alluvium alluvium alluvium reclaimed land reclaimed land

11 10 2 9 9 2 10 7 11 4 11 11

4.44–0.075 7.77–0.17 8.2–0.2 3.29–0.016 2.10–0.014 0.81–0.12 2.09–0.015 2.58–0.037 2.26–0.014 0.47–0.13 6.78–0.027 2.91–0.02

KISSAN KISSAN JMA KISSAN KISSAN JMA KISSAN KISSAN KISSAN KISSAN Kobe City Sekisui House Co. Ltd.

164

Figure 2a. H/V ratios calculated on the main shock recordings (thick line) and on the aftershocks recordings (dotted lines).

165

Figure 2b. H/V ratios calculated on the main shock recordings (thick line) and on the aftershocks recordings (dotted lines).

166

Figure 3. a: For each site: ratio of the H/V ratio of the main shock over the mean H/V ratio of the aftershocks. The thick line is the average of all the curves obtained. b: For each site: ratio of the H/V ratio of one particular aftershock over he mean H/V ratio of the other aftershocks.

167 contrary, some sites present the inverse trend, with a higher H/V ratio for the main shock, at low frequencies. In order to visualize better the relative differences between the H/V ratio on the main shock and those of the aftershocks, the following ratio was calculated and is plotted on Figure 3a for each site: (H/V ratio of the main shock) / (average H/V ratio of all aftershocks) The thick curve indicates the average of all curves (for each site), the dotted line is the line corresponding to a value of the H/V ratio that is the same for the main shock and for the aftershocks. By looking at this figure, the following general trends can be pointed out. In the low frequency range (below 2 Hz) the H/V ratio for the main shock is slightly larger than for the aftershocks. On the contrary, for frequencies higher than 2 Hz, this tendency is reversed, giving an H/V ratio for the main shock nearly systematically lower than that of the smaller aftershock events. This last trend is consistent with what could be expected in case of non-linearity of the soil layers, as discussed before. Figure 3b shows, as a control comparison, the following ratio for each site: (H/V ratio on a particular aftershock) / (average H/V ratio of all other aftershocks) This comparison confirms the that the trends observed previously are related to the difference between the main shock and the aftershocks. Figure 3b indeed shows a symmetric distribution of the curves, when comparing the H/V ratio of a particular aftershock with those of all other aftershocks. These results indicate a general occurrence of non-linear behavior of the soil in the case of Kobe earthquake when all sites are considered together. One also might expect a shift of the H/V peaks in the frequency domain, towards lower frequencies, due to the occurrence of non-linearity. No such tendency was observed in the data set used. However, such variations were investigated for the particular case of the site PR1. This site is indeed situated on Port Island, an artificial island which suffered extreme liquefaction phenomena during the Kobe earthquake. It is interesting to look at the evolution of non-linear response of the soil along the main shock signal (Mohammadioun, 1997). The H/V ratio for this site was calculated on a moving time window of 5 seconds, along the signal of the main shock. Figure 4 shows the time evolution of the H/V ratio obtained during the main shock on Port Island, with respect to the maximum acceleration in

the time window considered for each calculation. This shows a very big variability of the H/V ratio depending on the chosen time window. A high peak occurs at 0.6 Hz, at the beginning of the signal (high acceleration level). Then, for frequencies higher than 1 Hz, the amplitude tends to decrease, as one goes further along the signal, due to the fact that there is less and less energy on the horizontal components.

Generalized inversion A generalized inversion was also performed on the whole data set. The code used (Riepl et al., 1998) is based on the use of k recordings (i events recorded at j stations: k > i + j ), for which the i + j unknown site and source spectra are simultaneously solved, using a singular value decomposition of the k recordings. This technique presents the advantage to simultaneously invert all available data, even if not all events are recorded at all sites. Furthermore, some events can be included in the inversion even if they are not recorded at the reference site, this offers a very complete exploitation of the data set. Site KBU was considered as the reference site, despite the fact that it is not a ‘perfect’ reference site, due to the weathering of surface rock. Unfortunately, for sites KOB, SAK and OSA, very few aftershock recordings were available (1, 3 and 1 respectively). The results concerning these site must then be considered with much care and should not be regarded as conclusive on their own. The generalized inversion was performed twice. First, using all the available recordings; and second, without including the main shock recordings. Figure 5 presents the results of the two inversions, for the sites where recordings were available. The thick lines are the amplification spectra obtained using all recordings, and the dashed lines are those obtained without the main shock recordings. It is very interesting to compare these two sets of results. One can indeed see the effects of non-linearity that occurred during the main shock, for some of the sites. For example, site PR1 (located on reclaimed land and well known for liquefaction phenomena) shows a much lower amplification level when including the main shock recordings, compared to that obtained for smaller events. Sites SAK and OSA, which are situated on the Osaka side, also show the same characteristics. Despite the reserve that one should take regarding these sites (very limited number of available recordings), this might be interpreted as due to their location on very thick sed-

168

Figure 4. H/V ratios calculated on a 5 second moving window along the main shock signal at site PR1.

imentary deposits of the Osaka basin. Finally, sites FKS, AMG, MKT and YAE, seem to be much less affected by such non-linear effects, the generalized inversion with and without the main shock recordings tends to give the same amplification spectra.

on an elastic half-space, following the approach by Anderson and Hough (1984): A(f ) = A(r) · e−πf t with ∗

t =

High frequency spectral decay In a second stage, the parameter ‘kappa’ was investigated. It was introduced by Anderson and Hough (1984) as a measure of the high frequency decay of the acceleration spectrum. When plotted as a function of linear frequency, the acceleration Fourier spectrum exhibits a quasi-linear decrease at high frequencies. The kappa parameter is defined as follows: ln(A) = C − πκ f

(1)

where C is a constant, A is the acceleration spectrum, and f is the frequency. In the case of a single layer

Z

dr Q(r) · β(r)



(2)

(3)

A being the amplitude of the spectrum, Q the quality factor and β the S wave velocity in the sediments. In the case of a soft layer over a half-space, the quality factor Q can be decomposed as: 1 1 1 = + Q Qi As · f 1 Qi

(4)

corresponding to the shallow deposits and As1·f to the deep crust (half-space). Then, t ∗ can be decomposed as following, h being the thickness of the

169

Figure 5. Amplification spectra obtained with a generalized inversion technique, performed on the whole data set (thick line), and only on the aftershocks (dashed line). Reference station: KBU. NS component.

170

Figure 6. Example of the logarithm of the horizontal acceleration spectrum used to calculate kappa: slope of the spectral decay.

sediment layer: t∗ =

R

=

dr Qi ·β(r)

h Q¯ i ·β¯

+

+

R

1 f ·As

dr As ·β(r)·f

·

R

(5) dr β(r) .

Finally: ∗

e−πf t = e

−πf

h Q¯ i β¯

·e

− Aπs

R

dr β(r)

.

(6)

The second term of Equation 6 is independent of frequency, so that the linear decrease of the acceleration spectrum A(f ) with frequency is proportional to: h . ¯ Qi β¯ Thus, κ corresponds to the slope of the high frequency spectral decay and may be interpreted as linked with damping in the upper layers. Figure 6 shows an example of the logarithm of the horizontal acceleration spectra used to calculate κ. Durward et al. (1996) have used this parameter on data from Imperial Valley (California). They first pointed out that the significance of κ is still under discussion, since it is not known whether κ depends more on the source effects or on the attenuation of the waves between the source and the receiver. Making the hypothesis that the parameter κ is a function of the attenuation in the surface sediments implies that κ depends on the strain amplitude if the soil response is non-linear. Following the linear equivalent theory (used in SHAKE codes for example), the quality factor Q decreases when the strain increases, thus κ increases with increasing strain, if non-linear effects occur. Consequently, if κ varies as a function of

the peak ground acceleration (PGA), it indicates that non-linear effects occur. Following the approach of Durward et al. (1996), the parameter κ was calculated for each of the available recordings at every site in Kobe and Osaka areas. Kappa is calculated in a frequency band ranging from a value higher than the maximum amplification observed on the H/V ratios (between 3 and 7 Hz depending on the site considered) to a maximum value of 25 Hz. Figure 7 presents a plot of κ, for each available recording at each site, as a function of the corresponding peak ground acceleration. For the horizontal components, as shown by Durward et al. (1996) on the data from Imperial Valley, a clear increase of the value of kappa as a function of PGA is obtained. This tendency is very pronounced for the sites made of reclaimed land (circles), it is also quite distinct for the alluvial sites (triangles), whereas κ is more diffused for the rock site KBU (crosses). But we have to notice here that this rock site KBU is actually characterized by very low S wave velocities at the surface, probably due to a very strong weathering at the surface, as noted before. These results tend to confirm the presence of clear non-linear effects, under the hypothesis proposed by Durward et al. (1996), as described above. The vertical components show a lesser increase of κ, probably indicating that non-linearity rather affects the horizontal components of motion. Another study conducted in the same area by Moya (1998) presents the variations of κ, as a function of the azimuth, incidence angle, epicentral distance and magnitude of the events. In a general way, the variations of κ obtained for different sites, as a function of these four parameters, are quite scattered, but there appear no clear correlation

171

Figure 7. Plot of the parameter kappa, for each available recording, as a function of the peak ground acceleration (PGA). Top: horizontal components, bottom: vertical components.

172 between kappa and one of these parameters: the only clear trend is its increase with increasing PGA.

Discussion The study that was conducted here about the Kobe earthquake made it possible to emphasize some interesting issues concerning the investigation of nonlinear effects, from recordings of the ground motion. The H/V ratio method, even though it should be used with lots of care, due to its unclear significance (possible sensitivity to near field effects); makes it possible to point out a general trend, for all the data used in this study. For the main shock, an average lower value for frequencies higher than 2 Hz (of a factor of about 0.5) is observed, which is consistent with what can be expected in case of non-linearity. On the contrary, at low frequencies (lower than 1 Hz), the amplification seems to be higher for the main shock (of a factor of 1.5 in average). However, it is important to point here that some sites in the Kobe area are located very close to the fault, and might be affected by directivity and near field effects. This can explain some low frequency amplification peaks on the H/V ratios during the main shock. Unfortunately, it was not possible to compare these results with some classical spectral ratios (to a reference station), because there is no station that could reasonably be considered as reference close to the sites considered. Field et al. (1997) have conducted a study of non-linear effects during the Northridge (California, 1994) earthquake, using a generalized inversion technique. They also show a reduced amplification by a factor of 2 during the main shock, compared to the amplification measured on the aftershocks. The use of a generalized inversion technique on all the available data set, also shows the same trend, with clear non-linear effects at site PR1, by comparing the results obtained with or without including the main shock recordings in the inversion. Concerning the use of the parameter κ, which characterizes the high frequency spectral decay of the recorded acceleration; a general increase of κ with increasing peak ground acceleration is shown clearly over the whole data set used in this study. This indicates the occurrence of non-linear effects, due to very soft subsurface deposits, considering the assumptions proposed by Durward et al. (1996). However, there is still a discussion concerning the real significance of κ, and it is not excluded that this parameter can also be

influenced by source effects. Moya (1998) have shown the evolution of kappa with the magnitude of the earthquakes considered. Despite the short magnitude range considered (between 2.5 and 4.9), they have not seen any clear correlation. The evidence of such non-linearity phenomena, observed in the case of many large earthquakes, addresses the problem of the use of weak motions to determine site effects (spectral ratios techniques), or to predict the ground motion for the case of big earthquakes (empirical Green’s functions techniques).

Acknowledgements We would like to thank very much T. Kagawa, CEORKA, KISSAN, JMA, Kobe City and Sekisui House Co. Ltd., for providing the data from the Kobe earthquake and aftershocks, and H. Sekiguchi (DPRI, Kyoto University) for information and transfer of the data. We are also grateful to the French Association for Earthquake Engineering (AFPS) and the French Ministry of Environment for financial support to carry out this study. And finally, we thank very much J. Riepl for kindly providing the code to perform the generalized inversion on the data.

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