COUPLAGE SOL-GEOPHONE*

The seismometer-ground system is represented by a damped oscillatory system. Relatively simple approximation formulas are derived to express the coupling between ground and seismometer. These expressions are applicable in seismic exploration. The coupling is that of a mass, suspended by a spring, to the surface that the ground would have in absence of the seismometer. It results in a low-pass filtering of the ground motion, which is due to the presence of the seismometer. This effect is expressed in a unit-impulse response. It appears that, over a sufficiently homogeneous ground and for low frequencies, one has a true coupling between ground and seismometer. To obtain a sufficiently large pass-band, a low seismometer housing-mass together with a not too small housing radius are necessary.     

台湾费丛峡谷对强地面运动的影响研究──利用单台资料及2．5维SH混合方法

本文通过格林函数反褶积方法，由台湾峡谷附近的记录资料预测峡谷区的强地面运动的时程曲线．峡谷区的理论格林函数应用２．５维ＳＨ混合方法求解．通过格林函数反褶积方法得到的峡谷区费丛１及费丛２台的位移、速度、加速度和实际资料对比，取得了满意结果．计算结果表明，峡谷底部的峰值加速度相对峡谷边缘为最小；在靠近震中的一侧，峡谷的加速度的最大振幅相对比另一侧大．还给出了其余３个台的预测结果，研究了它们的加速度傅里叶谱和反应谱．     

台湾费丛峡谷对强地面运动的影响研究──利用单台资料及2．5维SH混合方法

本文通过格林函数反褶积方法，由台湾峡谷附近的记录资料预测峡谷区的强地面运动的时程曲线．峡谷区的理论格林函数应用２．５维ＳＨ混合方法求解．通过格林函数反褶积方法得到的峡谷区费丛１及费丛２台的位移、速度、加速度和实际资料对比，取得了满意结果．计算结果表明，峡谷底部的峰值加速度相对峡谷边缘为最小；在靠近震中的一侧，峡谷的加速度的最大振幅相对比另一侧大．还给出了其余３个台的预测结果，研究了它们的加速度傅里叶谱和反应谱．     

DEBUBBLING: A GENERALIZED LINEAR INVERSE APPROACH*

On seismograms recorded at sea bubble pulse oscillations can present a serious problem to an interpreter. We propose a new approach, based on generalized linear inverse theory, to the solution of the debubbling problem. Under the usual assumption that a seismogram can be modelled as the convolution of the earth's impulse response and a source wavelet we show that estimation of either the wavelet or the impulse response can be formulated as a generalized linear inverse problem. This parametric approach involves solution of a system of equations by minimizing the error vector (ΔX = X^obs– X^cal) in a least squares sense. One of the most significant results is that the method enables us to control the accuracy of the solution so that it is consistent with the observational errors and/or known noise levels. The complete debubbling procedure can be described in four steps: (1) apply minimum entropy deconvolution to the observed data to obtain a deconvolved spike trace, a first approximation to the earth's response function; (2) use this trace and the observed data as input for the generalized linear inverse procedure to compute an estimated basic bubble pulse wavelet; (3) use the results of steps 1 and 2 to construct the compound source signature consisting of the primary pulse plus appropriate bubble oscillations; and (4) use the compound source signature and the observed data as input for the generalized linear inverse method to determine the estimated earth impulse response—a debubbled, deconvolved seismogram. We illustrate the applicability of the new approach with a set of synthetic seismic traces and with a set of field seismograms. A disadvantage of the procedure is that it is computationally expensive. Thus it may be more appropriate to apply the technique in cases where standard analysis techniques do not give acceptable results. In such cases the inherent advantages of the method may be exploited to provide better quality seismograms.     

Realistic Modeling of Seismic Wave Ground Motion in Beijing City

— Algorithms for the calculation of synthetic seismograms in laterally heterogeneous anelastic media have been applied to model the ground motion in Beijing City. The synthetic signals are compared with the few available seismic recordings (1998, Zhangbei earthquake) and with the distribution of observed macroseismic intensity (1976, Tangshan earthquake). The synthetic three-component seismograms have been computed for the Xiji area and Beijing City. The numerical results show that the thick Tertiary and Quaternary sediments are responsible for the severe amplification of the seismic ground motion. Such a result is well correlated with the abnormally high macroseismic intensity zone in the Xiji area associated with the 1976 Tangshan earthquake as well as with the ground motion recorded in Beijing city in the wake of the 1998 Zhangbei earthquake.     

STABILIZATION OF NORMAL-INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE-INDUCED BIAS*

A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well-known inversion schemes for normal-incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half-spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two-stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson-recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large). In the non-linear terms of dynamic deconvolution and Levinson-recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson-recursion, which are set to zero if they are not significantly different from noise. The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.     

Checking the quality of restoration in the frequency domain of CDSN broad-band seismograms using modern control engineering

Incorrect results including false low frequency components may appear during the recovery of ground motion in the frequency domain. In order to check the quality of restoration in the frequency domain of CDSN broad-band seismograms, a digital model of the seismograph systems, based on modern control engineering, is presented and improvement of the method of restoration in the frequency domain is described. Examples shown in this paper demonstrate the effectiveness of the proposed approach in improving the restoration of true ground motion. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 90–99, 1992. The work is supported by the Chinese Joint Seismological Science Foundation.     

SEISMIC INVERSION BY A RMS BORN APPROXIMATION IN THE SPACE-TIME DOMAIN1

A new approximate method to calculate the space-time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. A distorted-wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root-mean-square acoustic wave speed. A closed-form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.     

Relative source time functions of seismic events at the Rudna copper mine, Poland: estimation of inversion uncertainties

The relative source time function (RSTF) inversion uncertainty assessment was performed for two small, mining-induced seismic events (M _W =2.9 and 3.0) that occurred at Rudna copper mine in Poland. The seismograms of selected events were recorded by the seismic net work composed of over 60, short-period, vertical seismometers, recording ground velocity, located in the distance ranging from 400 m up to 8 km from their hypocenters. The RSTFs were calculated for each seismic station independently, using the empirical Green’s function technique. The pseudospectral approximation of the sought RSTF by a finite sum of Gaussian kernel functions was used and the inverse problem was solved with the adaptive simulated annealing algorithm. Both methods improved the stability of the deconvolution procedure and physical correctness of the final solution in comparison to the classical deconvolution methods. To estimate the inversion uncertainties, classical Markov-chain Monte-Carlo techniques were used. The uncertainty analysis allows for improved selection of a priori data to the following inversion for kinematic rupture process.     

The Wilson–Burg method of spectral factorization with application to helical filtering

Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging of the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform. To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behaviour in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and we introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.     

弱各向异性介质弹性波的准各向同性近似正演模拟

准各向同性(QI)近似可用于弱各向异性介质的正演模拟.本文通过运用QI方法的零阶和一阶近似,计算了VTI介质模型的地震记录.得出的地震记录与标准各向同性射线理论(IRT)和基于伪谱法的三维地震正演模拟得出的地震记录作了比较,可以认为是精确的合成地震记录.     

On the Effects of Non-planar Geometry for Blind Thrust Faults on Strong Ground Motion

— We quantify the effects of complex fault geometry on low-frequency (<1 Hz) strong ground motion using numerical modeling of dynamic rupture. Our tests include the computation of synthetic seismograms for several simple rupture scenarios with planar and curved fault approximations of the 1994 Northridge earthquake. We use the boundary integral equation method (BIEM) to compute the dynamic rupture process, which includes the normal stress effects along the curved fault geometries. The wave propagation and computation of synthetic seismograms are modeled using a fourth-order finite-difference method (FDM). The near-field ground motion is significantly affected by the acceleration, deceleration and arrest of rupture due to the curvature of the faults, as well as the variation in directivity of the rupture. For example, a 6-km-long hanging-wall or footwall splay with a maximum offset of 1 km can change 1-Hz peak velocities by up to a factor of 2-3 near the fault. Our tests suggest that the differences in waveform are larger on the hanging wall compared to those on the footwall, although the differences in amplitude are larger in the forward rupture direction (footwall). The results imply that kinematic ground motion estimates may be biased by the omission of dynamic rupture effects and even relatively gentle variation in fault geometry, and even for long-period waves.     

Ground-roll attenuation using a 2D time-derivative filter

We present a new filtering method for the attenuation of ground-roll. The method is based on the application of a bi-dimensional filter for obtaining the time-derivative of the seismograms. Before convolving the filter with the input data matrix, the normal moveout correction is applied to the seismograms with the purpose of flattening the reflections. The method can locally attenuate the amplitude of data of low frequency (in the ground-roll and stretch normal moveout region) and enhance flat events (reflections). The filtered seismograms can reveal horizontal or sub-horizontal reflections while vertical or sub-vertical events, associated with ground-roll, are attenuated. A regular set of samples around each neighbourhood data sample of the seismogram is used to estimate the time-derivative. A numerical approximation of the derivative is computed by taking the difference between the interpolated values calculated in both the positive and the negative neighbourhood of the desired position. The coefficients of the 2D time-derivative filter are obtained by taking the difference between two filters that interpolate at positive and negative times. Numerical results that use real seismic data show that the proposed method is effective and can reveal reflections masked by the ground-roll. Another benefit of the method is that the stretch mute, normally applied after the normal moveout correction, is unnecessary. The new filtering approach provides results of outstanding quality when compared to results obtained from the conventional FK filtering method.     

柴达木盆地东部地震地面运动放大效应

柴达木盆地是青藏高原东北部大型断陷山间盆地,该地区的流动观测记录了2008年11月10日发生于大柴旦附近的M_W6.3地震。和附近的基岩上的记录相比,盆地内部的记录显示出非常显著的地面运动放大效应,表现为峰值速度的增大、持续时间的延长,其呈现出长持续时间的后续震相。傅里叶频谱分析表明盆地内部显著的后续震相的频率和直达波相比较低,地面质点运动轨迹图显示后续震相为面波运动特征。为了解释地面运动的差异,构建二维模型,通过交错网格高阶有限差分方法计算了地震波在盆地内部的传播过程,结果显示盆地内部低速层的存在造成直达波的放大以及多次反射与转换,盆地边缘结构造成的波的相干叠加产生了强烈的次生面波,其低频、大振幅、长持续时间的特征是盆地内部地面运动放大的主要原因。     

Ground-motion modelling at regional distances for earthquakes in a continental interior,I. Theory and observations

To understand the ground-motion contribution by multiple-mode surface-wave arrivals, the surface-wave theory required for predicting ground-motion time histories is discussed. The adequacy of the theory in accounting for observed earthquake ground motion is tested by comparing theoretically predicted long-period seismograms with real seismograms for two earthquakes in the central United States. The agreement between the predicted and observed maximum vertical component L_g ground velocities and accelerations in the 2- to 3-sec period range is excellent over a distance range of 100 to 2,000 km.     

CalculationoflongperiodresponsespectratoearthquakegroundmotionfromseismogramsofType513seismographs

ＣａｌｃｕｌａｔｉｏｎｏｆｌｏｎｇｐｅｒｉｏｄｒｅｓｐｏｎｓｅｓｐｅｃｔｒａｔｏｅａｒｔｈｑｕａｋｅｇｒｏｕｎｄｍｏｔｉｏｎｆｒｏｍｓｅｉｓｍｏｇｒａｍｓｏｆＴｙｐｅ５１３ｓｅｉｓｍｏｇｒａｐｈｓＹＡＮＸＩＡＮＧＹＵ（俞言祥）ＳＵＹＵＮＷＡＮ...     

The effect of canyon topography on strong ground motion at Feitsui damsite: Quantitative results

The free-field accelerograms along Feitsui Canyon are analysed and modelled by a numerical scheme to study the effect of canyon topography. Six strong-motion accelerometers (SC1–SC6) were deployed along the Feitsui Canyon in 1991. The observations suggest that the amplitude of ground motion at the trough of the canyon is smaller than that on its slopes. The integral equation method is applied to a two-dimensional model of Feitsui Canyon to study the effects of the canyon topography. We choose the ground motion of SC3 station at the trough of the canyon as the input motion to the model, which is then used to predict the ground motion at the other five stations. The simulated and observed seismograms agree well in displacement and velocity, although the simulated acceleration at high frequency is underestimated. The simple model can reproduce the observed accelerations at all frequencies below 4 Hz.     

Improving ShakeMap performance by integrating real with synthetic data: tests on the 2009 M w?=?6.3 L’Aquila earthquake (Italy)

The ShakeMap software automatically generates maps of the peak ground motion parameters (shakemaps) and of instrumental intensity soon after an earthquake. Recorded data are fundamental to obtaining accurate results. In case observations are not available, ShakeMap relies on ground motion predictive equations, but due to unmodelled site conditions or finite fault effects, large uncertainties may appear, mainly in the near-source area where damage is relevant. In this paper, we aim to account for source effects in ShakeMap by computing synthetics to be used for integrating observations and ground motion predictive equations when near-source data are not available. To be effective, the computation of synthetics, as well as of the finite fault, should be done in near real time. Therefore, we computed rapid synthetic seismograms, by a stochastic approach, including the main fault features that were obtained through inversion of regional and teleseismic data. The rapidity of calculation is linked to a number of assumptions, and simplifications that need testing before the procedure can run in automatic mode. To assess the performance of our procedure, we performed a retrospective validation analysis considered as case study of the M _w = 6.3 earthquake, which occurred in central Italy on April 6, 2009. In that case, the first shakemaps, generated a few minutes after the earthquake, suffered large uncertainties on ground motion estimates in an area closer to the epicenter due to the lack of near-field data. To verify our approach, we recomputed shakemaps for the L’Aquila earthquake, integrating data available soon after the earthquake at different elapse times with synthetics, and we compared our shaking map with the final shakemap, obtained when all the data were available. Our analysis evidences that (1) when near-source data are missing, the integration of real data with synthetics reduces discrepancies between computed and actual ground shaking maps, mainly in the near-field zone where the damage is relevant and (2) the approach that we adopted is promising in trying to reduce such discrepancies and could be easily implemented in ShakeMap, but some a priori calibration is necessary before running in an automatic mode.     

Deterministic Approach for the Seismic Microzonation of Bucharest

— The mapping of the seismic ground motion in Bucharest, due to the strong Vrancea earthquakes is carried out using a complex hybrid waveform modeling method which combines the modal summation technique, valid for laterally homogeneous anelastic media, with finite-differences technique, and optimizes the advantages of both methods. For recent earthquakes, it is possible to validate the modeling by comparing the synthetic seismograms with the records. We consider for our computations the frequency range from 0.05 to 1.0 Hz and control the synthetic signals against the accelerograms of the Magurele station, low-pass filtered with a cut-off frequency of 1.0 Hz of the 3 last major strong (M_w > 6) Vrancea earthquakes. Using the hybrid method with a double-couple seismic source approximation, scaled for the source dimensions and relatively simple regional (bedrock) and local structure models, we succeeded in reproducing the recorded ground motion in Bucharest at a satisfactory level for seismic engineering. Extending the modeling to the entire territory of the Bucharest area, we construct a new seismic microzonation map, where five different zones are identified by their characteristic response spectra.     

Verification of precarious rock methodology using shake table tests of rock models

Precariously balanced rocks in seismically active regions are effectively upper-limit strong motion seismoscopes that have been in place for thousands of years. Thus, estimates of the dynamic toppling acceleration of these rocks (through rigid body rocking) can provide constraints on the peak ground accelerations experienced during past earthquakes. We have developed a methodology that uses a two-dimensional numerical code to calculate the dynamic rocking response of precarious rocks to realistic ground acceleration time histories. Statistical analyses of the dynamic response of these rocks to a range of synthetic seismograms, as well as strong motion records, can provide important information about the ground motion attenuation curves and seismic hazard maps. We use shake table tests to investigate the dynamic rocking response of 13 wooden rectangular blocks of various sizes and aspect ratios subjected to realistic seismograms and compare the results with those of numerical tests. Our results indicate good agreement between the shake table and numerical results.