THE ESTIMATION OF SIGNAL SPECTRA AND RELATED QUANTITIES BY MEANS OF THE MULTIPLE COHERENCE FUNCTION *

A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χ_j(t), from a set of traces, can be broken down into two stationary components: a signal sequence, α_j(t) *s(t—τ_j), which correlates from trace to trace, and an incoherent noise sequence, n_j(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χ_j(t) =α_j(t) * s(t—τ_j) +n_j(t) where the signal wavelet α_j(t), the lag (moveout) of the signal τ_j, and the noise sequence n_j(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented. The method requires the calculation of the multiple coherence function γ_j(f) of each trace. γ_j(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρ_j(f) by where K_j(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix. Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described. Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.     

Ambient vibration tests of a seven-story reinforced concrete building in Van Nuys, California, damaged by the 1994 Northridge earthquake

Results of two detailed ambient vibration surveys of a 7-story reinforced concrete building in Van Nuys, California, are presented. Both surveys were conducted after the building was severely damaged by the 17 January 1994, Northridge earthquake (M_L=5.3, epicenter 1.5 km west from the building site) and its early aftershocks. The first survey was conducted on 4 and 5 February 1994, and the second one on 19 and 20 April 1994, about one month after the 20 March aftershock (M_L=5.3, epicenter 1.2 km north–west from the building site). The apparent frequencies and two- and three-dimensional mode shapes for longitudinal, transverse and vertical vibrations were calculated. The attempts to detect the highly localized damage by simple spectral analyses of the ambient noise data were not successful. It is suggested that very high spatial resolution of recording points is required to identify localized column and beam damage, due to the complex building behavior, with many interacting structural components. The loss of the axial capacity of the damaged columns could be seen in the vertical response of the columns, but similar moderate or weak damage typically would not be noticed in ambient vibration surveys. Previous analysis of the recorded response of this building to 12 earthquakes suggests that, during large response of the foundation and piles, the soil is pushed sideways and gaps form between the foundation and the soil. These gaps appear to be closing during “dynamic compaction” when the building site is shaken by many small aftershocks. The apparent frequencies of the soil–foundation–structure system appear to be influenced significantly by variations in the effective soil–foundation stiffness. These variations can be monitored by a sequence of specialized ambient vibration tests.     

A probabilistic model of seismicity: Kamchatka earthquakes

The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω _i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω _i is characterized by a system of random variables, viz., energy class k_i, latitude φ _i , longitude λ _i , and depth h _i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k ₀) is the basic data [Bogdanov, 2006] rather than the seismic activity A ₀, we proceed to show that for different intervals of coordinates and time the distribution f _elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f _full(k), which corresponds to the full catalog. It follows from our calculations that f ₀(k) takes on nearly identical numeral values for different initial values of energy class k ₀ (8 ≤ k ₀ ≤ 12) f(k ₀). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k ₀) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k ₀) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods     

小波分析在电磁数字化资料分析处理中的应用

基于小波变换理论,分析了数字信号f(x)近似地表示为近似部分ak^jf(x)与分解(或细节)部分dk^jf(x)的理论,建立了数字化资料的干扰识别与消除、高频信息与低频信息提取的分析方法。本给出了小波分析方法应用于电磁数字化前兆的实例,说明小波变换可作为电磁数字化资料分析处理的一种有效方法。     

Long period microtremors, microseisms and earthquake damage: Northridge, CA, earthquake of 17 January 1994

Three studies of site amplification factors, based on the recorded aftershocks, and one study based on strong motion data, are compared one with another and with the observed distribution of damage from the Northridge, CA, earthquake of 17 January 1994 (M_L=6.4). In the epicentral area, when the peak ground velocities are larger than v_m≈15 cm/s, nonlinear response of soil begins to distort the amplification factors determined from small amplitude (linear) wave motion. Moving into the area of near-field and strong ground motion (v_m>30 cm/s), the site response becomes progressively more affected by the nonlinear soil response. Based on the published results, it is concluded that site amplification factors determined from small amplitude waves (aftershocks, small earthquakes, coda waves) and their transfer-function representation may be useful for small and distant earthquake motions, where soils and structures respond to earthquake waves in a linear manner. However in San Fernando Valley, during the Northridge earthquake, the observed distribution of damage did not correlate with site amplification determined from spectra of recorded weak motions. Mapping geographical distribution of site amplification using other than very strong motion data, therefore appears to be of little use for seismic hazard analyses.     

Earthquake damage detection in the Imperial County Services Building III: Analysis of wave travel times via impulse response functions

The majority of structural health monitoring methods are based on detecting changes in the modal properties, which are global characteristics of the structure, and are not sensitive to local damage. Wave travel times between selected sections of a structure, on the other hand, are local characteristics, and are potentially more sensitive to local damage. In this paper, a structural health monitoring method based on changes in wave travel times is explored using strong motion data from the Imperial Valley Earthquake of 1979 recorded in the former Imperial County Services (ICS) Building, severely damaged by this earthquake. Wave travel times are measured from impulse response functions computed from the recorded horizontal seismic response in three time windows—before, during, and after the largest amplitude response, as determined from previous studies of this building, based on analysis of novelties in the recorded response. The results suggest initial spatial distribution of stiffness consistent with the design characteristics, and reduction of stiffness following the major damage consistent with the spatial distribution of the observed damage. The travel times were also used to estimate the fundamental fixed-base frequency of the structure f₁ (assuming the building deformed as a shear beam), and its changes during this earthquake. These estimates are consistent with previous estimates of the soil–structure system frequency, f_sys, during the earthquakes (f₁<f_sys as expected from soil–structure interaction studies), and with other estimates of frequency (f₁ from ETABS models, and f_sys from ambient vibration tests, and “instantaneous” f₁ from high-frequency pulse propagation).     

Experimental evidence for flexibility of a building foundation supported by concrete friction piles

This article explores the possibility to measure deformations of building foundations from measurements of ambient noise and strong motion recordings. The case under study is a seven-storey hotel building in Van Nuys, California. It has been instrumented by strong motion accelerographs, and has recorded several earthquakes, including the 1971 San Fernando (M_L=6.6, R=22 km), 1987 Whittier–Narrows (M_L=5.9, R=41 km), 1992 Landers (M_L=7.5, R=186 km), 1992 Big Bear (M_L=6.5, R=149 km), and 1994 Northridge (M_L=6.4, R=1.5 km) earthquake and its aftershocks (20 March: M_L=5.2, R=1.2 km; 6 December, 1994: M_L=4.3, R=11 km). It suffered minor structural damage in 1971 earthquake and extensive damage in 1994. Two detailed ambient vibration tests were performed following the Northridge earthquake, one before and the other one after the 20 March aftershock. These included measurements at a grid of points on the ground floor and in the parking lot surrounding the building, presented and analyzed in this article. The analysis shows that the foundation system, consisting of grade beams on friction piles, does not act as a “rigid body” but deforms during the passage of microtremor and therefore earthquake waves. For this geometrically and by design essentially symmetric building, the center of stiffness of the foundation system appears to have large eccentricity (this is seen both from the microtremor measurements and from the earthquake recordings). This eccentricity may have contributed to strong coupling of transverse and torsional responses, and to larger than expected torsional response, contributing to damage during the 1994 Northridge, earthquake.     

Variation of intrinsic and scattering attenuation of seismic waves with depth in the Bam region,East-Central Iran

The attenuation properties of the lithosphere in the Bam region, East-Central Iran, have been investigated. For this purpose, 42 local earthquakes having focal depths less than 25 km have been used. The quality factor of coda waves (Q_c) has been estimated using the single back-scattering model. The quality factors Q_p, Q_d (P and direct S-waves) have been estimated using the extended-coda normalization method. Q_i and Q_s (the intrinsic and scattering attenuation parameters) have been estimated for the region. The values of Q_p, Q_d, Q_c, Q_i and Q_s show a dependence on frequency in the range of 1.5–24 Hz for the Bam region. The average frequency-dependent relationships estimated for the region are Q_p=(36±6)f^(1.03±0.06), Q_d=(59±8)f^(1.00±0.03), Q_c=(79±5)f^(1.01±0.04), Q_s=(131±4)f^(1.01±0.04) and Q_i=(104±6)f^(1.01±0.05). A comparison between Q_i and Q_s shows that intrinsic absorption is predominant over scattering.The variation of Q has also been estimated at different lapse times to observe heterogeneities variation with depth. The variation of Q with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth.The estimated Q_o values at different stations suggest a low value of Q indicating a heterogeneous and attenuative crust beneath the entire region.     

Spatio-temporal characteristics of aftershocks and seismogenic structure of the 2011 MW9.0 Tohoku earthquake,Japan

The Tohoku megathrust earthquake, which occurred on March 11, 2011 and had an epicenter that was 70 km east of Tohoku, Japan, resulted in an estimated ten's of billions of dollars in damage and a death toll of more than 15 thousand lives, yet few studies have documented key spatio-temporal seismogenic characteristics. Specifically, the temporal decay of aftershock activity, the number of strong aftershocks (with magnitudes greater than or equal to 7.0), the magnitude of the greatest aftershock, and area of possible aftershocks. Forecasted results from this study are based on Gutenberg-Richter's relation, Bath's law, Omori's law, and Well's relation of rupture scale utilizing the magnitude and statistical parameters of earthquakes in USA and China (Landers, Northridge, Hector Mine, San Simeon and Wenchuan earthquakes). The number of strong aftershocks, the parameters of Gutenberg-Richter's relation, and the modified form of Omori's law are confirmed based on the aftershock sequence data from the M_W9.0 Tohoku earthquake. Moreover, for a large earthquake, the seismogenic structure could be a fault, a fault system, or an intersection of several faults. The seismogenic structure of the earthquake suggests that the event occurred on a thrust fault near the Japan trench within the overriding plate that subsequently triggered three or more active faults producing large aftershocks.     

Attenuation in Southeastern Sicily (Italy) by applying different coda methods

The attenuation in Southeastern Sicily has been investigated using 40aftershocks of the December 13 1990, earthquake. The quality factor ofcoda waves (Q_c) was estimated in the frequency range 1.5–24 Hz,applying three different methods in time and frequency domains. On thewhole, a clear dependence of Q_c on frequency was observed,according to the general law Q = Q₀(f/f₀)ⁿ . Thefrequency dependence relationships obtained from the analysis of codawaves at three lapse time windows (10, 20 and 30 seconds) show that, forall methods, Q₀ (Q_c at 1 Hz) significantly increases with lapsetime. In particular, Q₀ is approximately 20 at short lapse time (10s) and increases to about 70 at longer lapse time (30 s). This is attributedto the fact that larger lapse times involve deeper parts of the crust andupper lithosphere which may be characterized by larger quality factors.Moreover, the value of the exponent n decreases with increasing codalengths from about 1.3 to 0.9, suggesting a decrease in heterogeneity ofthe medium with depth.Finally, Q_c-values here found are of the same order as thosereported from other tectonic regions like the Anatolian Highlands orSouthern Spain, while significantly higher than in the neighboring volcanicarea of Mt. Etna.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Seismic fragility of traction elevators

Second‐generation performance‐based earthquake engineering (PBEE‐2) requires a library of component fragility functions to estimate probabilistic damage to a wide variety of building components. The present work draws on a large body of (mostly) post‐earthquake reconnaissance and (some) post‐earthquake survey observations of traction elevators to create fragility functions useful in PBEE‐2. Two surveys provide detailed observations of 115 representative elevators at 12 hospitals shaken in the 1989 Loma Prieta and 1994 Northridge earthquakes and selected without regard to or foreknowledge of damage. Of these, 55 failed and 60 did not. Approximately half were installed after an important code change of 1972, so one can distinguish the performance of pre‐1973 and post‐1973 elevator construction. They experienced a range of strong motion: 22 with peak ground acceleration (PGA) < 0.25 g, 93 with 0.25 g < PGA < 0.85 g. The hospitals had elevator failure rates as low as 0% and as high as 100%. A third survey describes damage qualitatively for six sites with PGA ≤ 0.25 and per‐site failure rates of 0% to perhaps 30%. Fragility functions are offered where the damage state is the loss of functionality of the elevator. The elevators in these surveys exhibit a median capacity of PGA ≈ 0.35 g with a logarithmic standard deviation of 0.40. Capacity is modestly sensitive to whether the elevator was installed before or after 1973. Using building‐specific intensity measures such as S_a(T₁) does not improve the fragility functions. Copyright © 2015 John Wiley & Sons, Ltd.     

抚仙湖秋、冬季光衰减特征及其与有色可溶性有机物的关系

为了研究抚仙湖紫外辐射(UVR)和光合有效辐射(PAR)衰减的时空特征及其与有色可溶性有机物(CDOM)、悬浮物(SS)、浮游植物(叶绿素a表征)等因子的关系,于2014年10月(秋季)、2015年1月(冬季)开展现场调查,结果显示:秋季不同波长(段)的漫射衰减系数Kd(305)、Kd(340)和Kd(PAR)分别为1.27±0.12、0.68±0.11和0.32±0.13 m-1,冬季分别为1.13±0.10、0.63±0.07和0.36±0.07 m-1;秋季CDOM的不同波长吸收系数ag(254)、ag(305)和ag(340)分别为4.09±0.26、1.18±0.09和0.57±0.05 m-1,冬季分别为2.95±0.24、0.61±0.11和0.11±0.07 m-1,秋季ag(254)、ag(305)和ag(340)显著高于冬季;秋季Kd(305)显著大于冬季,这与秋季(雨季)较高的CDOM丰度、浮游植物生物量(及SS浓度)有关.秋季ag(305)/Kd(305)、ag(340)/Kd(340)均显著高于冬季;秋季及秋冬季整体而言,ag(254)与Kd(305)、Kd(340)呈显著正相关,各多元逐步回归方程中均包含ag(254),说明CDOM吸收对UVR的衰减有重要贡献.空间差异方面,秋季北部的ag(254)、Kd(305)和Kd(340)显著高于南部,冬季南北部无明显差异,或与雨旱季北岸河流输入的CDOM和SS的情况有关.此外,浮游植物对UV-B衰减的影响和SS(与CDOM的交互作用)对UV-A衰减的影响更在于季节变化方面,而影响UVR、PAR衰减的各因子的相对贡献有待进一步量化.     

High frequency fall-off of source spectra using Q -free spectra estimation

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅａｒｔｈｑｕａｋｅｓｏｕｒｃｅｓｐｅｃｔｒａｓｔｕｄｉｅｓｍａｙｂｅｔｒａｃｅｄｂａｃｋｔｏｌａｔｅ１９６０ｓ（Ａｋｉ,１９６７;Ｂｒｕｎｅ,１９７０;Ｈａｎｋｓ,１９７９）．Ｆｏｒｉｔｓｉｍｐｏｒｔａｎｃｅｉｎｓｔｒ...     

Seismic anomalies in the aftershock sequence of November 16, 2000, in Papua New Guinea

The study of seismic anomalies, related both to the temporal trend of aftershock sequences and to the temporal series of mainshocks, is important for an understanding of the physical processes relating to the existence and the characteristics of seismic precursors. The purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay of an aftershock sequence. It is realized by means of several parameters. We focused our work on an analysis of the Papua New Guinea seismic sequence that occurred on November 16, 2000. The magnitude of the mainshock is M = 8.2. The observed temporal series of shocks per day can be considered as a sum of a deterministic contribution and a stochastic contribution. If the decay can be modeled as a nonstationary Poisson process where the intensity function is equal to n(t) = K(t + c)^−p + K ₁, the number of aftershocks in a small time interval Δt is the mean value n(t)Δt, with a standard deviation σ = √n(t)Δt. We observe that there are some variations in seismicity that can be considered as seismic anomalies before the occurrence of a large aftershock. The data, checked according to completeness criteria, come from the website of the USGS NEIC data bank (). The text was submitted by the authors in English.     

Variation of lunar and solar geomagnetic tides with sunspot and geomagnetic activity

Summary Solar and lunar geomagnetic tides inH at Alibag have been determined by spectral analysis of discrete Fourier transforms following the method of Black and the well-known Chapman-Miller method. The seasonal variation inL ₂(H) is opposite to that inL ₂(D) with maximum in thed season and minimum in thej season. In bothH andD the enhancement due to sunspot activity is larger in lunar tide than in solar tide. Surprisingly, the enhancement due to magnetic activity is greater inL ₂(H) than inS ₁(H), while the contrary is true for declination. It is inferred that there is a local time component of the storm time variation contrary to the view expressed by Green and Malin. The enhancements in amplitudesL ₂ andS ₁ inH andD, due to sunspot activity and due to magnetic activity, have been separated. The results show that the amplitude at zero sunspot number increases with magnetic activity in all the four parameters, while the enhancement due to sunspot activity at different levels of magnetic activity decreases with increase ofK _p. But if bothK _p andR are increasing, whenK _p increases enhancement due toR decreases and whenR increases enhancement due toK _p decreases.     

The coda attenuation of the Yao’an area in Yunnan Province

An earthquake withM=6.5 happened on January 15, 2000 in Yao’an of Yunnan Province. After the earthquake, a temporary digital network with 6 detectors around the epicenter area was set up. 402 aftershocks were located more precisely. According to coda short recording observed, the coda averaging quality factor has been acquired via Sato’s single scattering model analyses,Q _c(f)=49f ^0.95,f=1.5～20.0 Hz, which has the attenuation characteristics of high structural active region.     

Damage distribution during the 1994 Northridge, California, earthquake relative to generalized categories of surficial geology

The spatial distributions of severely damaged buildings (red-tagged) and of breaks in the water distribution system following the 1994 Northridge, California, earthquake (M_L = 6·4) are investigated relative to the local characteristics of surficial geology. The pipe breaks are used as an indicator of nonlinear soil response, and the red-tagged buildings as indicator of severe shaking. The surficial geology is described by several generalized categories based on age, textural character and thickness of the near surface layer. Two regions are studied: the San Fernando Valley and Los Angeles-Santa Monica. The analysis shows that there is no simple correlation between damage patterns and surficial geology. Single family wood-frame buildings were damaged less when built on fine silt and clay (0–3 m thick) from the late Holocene.     

Attenuation of High Frequency P and S Waves in the Gujarat Region,India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (Q _P) and S (Q _S) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average Q _P and Q _S are: Q _P = (105 ± 2) f ^{0.82 ± 0.01}, Q _S = (74 ± 2) f ^{1.06 ± 0.01} for Kachchh region; Q _P = (148 ± 2) f ^{0.92 ± 0.01}, Q _S = (149 ± 14) f ^{1.43 ± 0.05} for Saurashtra region and Q _P = (163 ± 7) f ^{0.77 ± 0.03}, Q _S = (118 ± 34) f ^{0.65 ± 0.14} for mainland Gujarat region. The low Q (<200) and high exponent of f (>0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between Q _S estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that Q _C > Q _S for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The Q _S/Q _P ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.