To understand the complex damage pattern produced by the interaction between a 3-D sedimentary basin and 3-D spherical wavefronts, scattering of seismic waves by 3-D models due to a local point source is investigated by using the Pseudo-Spectrum method.The 3-D wavefields at different time steps are evaluated n111 nerically for a corner diffraction and a sediment-filled basin model.3-D wavefronts of both models are investigated from snapshots over free surface and vertical cross-sections.Numerical results show that model corners generate strong out-of-plane scattering energy which causes strong seismic energy focusing and defocusing in some specific locations.For an incident wave from a point source below the basin, the sediment-filled basin traps wave energy which propagates inward and focuses near the basin center.This energ)r extends to the basin b• ottom with decreasing amplitude.Besides, part of the incident energy is blocked by this basin, resulting in low amplitudes at the surrounding rock sites.This blocking effect is not predicted by the plane wave incidence.Comparisons are made with the results from 2-D models, and they show that the 3-D wavefronts from a point source or from in-plane scattering can be approximated by 2-D models; however, wavefronts from out-of-plane scattering cannot be reproduced.
Abstract The reduction in spatial variance of strong ground motion with increasing earthquake magnitude has been reported recently. However, we show that the observed dependence of spatial variance on magnitude is its implicit dependence on the frequency content (dominant frequency) of the wave field. Time‐domain cross‐correlations of pairs of accelerograms are used to quantify the spatial variations in this paper. Magnitude is one of the factors contributing to the dominant frequency. We attempt to study separately the effects of magnitude, hypocentral distance, peak ground acceleration and focal depth on the dominant frequency in order to find the most significant one. The data base consists of 1965 records of horizontal acceleration from 148 local earthquakes in Taiwan. The analysis shows the overwhelming effect of the source magnitude on the formation of the dominant frequency with an empirical relationship: No significant effect of hypocentral distance, local acceleration amplitude or depth is detected for all their values available (up to 170 km, 250 cm/s 2 , and 100 km, respectively). The prevailing effect of magnitude on the dominant frequency is a real cause of the consistently observed reduction of spatial variance of ground motion with increasing magnitude of earthquakes.
Source spectra of S waves were determined using records of eighteen earthquakes occurring in the Chia-Yi and Tai-Nan area with local magni tudes of 2.8 � M L �5.8 as obtained fr om a rock-site station.In addition to the correction of geometrical spreading, elimination of the anelastic attenua tion effect fr om the observed spectra was carefully examined to measure the high-frequency spectral levels of seismic sources.As to the source spectra, two types of spectral shapes may be observed.For earthquakes of M L < 5.4, the spectra obey the m-squared model with a single corner frequency.However, this observation cannot provide an ad equate representation for earthquakes of M L �5.4, since they clearly dem onstrate the existence of two corner frequencies on the spectrum.The dif fe rence in spectral shapes may reveal that the rupture of larger earthquakes proceeded as a series of multiple events while a single fault patch results in smaller earthquakes.This explanation is supported by both spectral shapes and waveform characteristics, and may disclose the complexity of earth quake sources of larger magnitude.The seismic moment of M0 measured fr om spectral level at low fre quency range satisfies a r elation with lower corner frequency of lo in M0 oo /0-3• For the set of earthquakes, the average stress drop is 125 bars.Nonetheless, this model is a poor fit to the shapes of source spectra for events of M L � 5.4.The source spectra obtained by the two greater events, the 1991 Chiali (M L = 5. 7) and 1993 Tapu (M L = 5.8) earthquakes, were discussed in this subject.In describing these spectra, a stress drop of about 60 bars was estimated fr om the spectral level in a lower fr equency range, while 600 bars was required to interpret the high-frequency amplitudes.By applying the Sato and Hirasawa (1973) source model, the average scale length of the fault heterogeneities inferred fr om the higher corner frequency of /0 is about 300 meters, and this is almost identical to the source radius of the Brune (1970, 1971) model for small events with a magnitude of around 3. Based on the seismic moments taken from the Harvard centroid-mo-
In this study, we applied the reversibility of elastic wave to a discussion of the reverse time propagation of wave equation.Based on the backward propga tion concept, we evalu�ted the feasibility of reconstructing the image of elastic wave sources and scatterers.The finite element.method was used to calculate elastic wave propagation in the medium.The same computational code was also used to reconstruct the.reverse time image.It was found that after our careful process ing of the absorption boundary for artificial reflectio, n, we could use the time-trace records at the surface to invert the locations of seismic sources or underground scat terer accurately.Our results show that point source, 'finite fault and multi-sources are well reconstructed.Although direct waves are much stronger than scattering wavefields, the imaging of the underground anomaly is still well reconstructed from the reverse time process.The image reconstruction technique based on the finite element method is flexible and easily to use for many applications.1.
Synthetic seismograms for seismic waves penetrating near the inner outer core boundary are implemented using the generalized ray method.The model takes into account the detailed velocity jump near the inner outer core boundary and the possible depth dependent attenuation of the inner core.The source-side surface .-eflections,considered as the later phases of the observed seismograms, are included in the model.The program de veloped in this study is suitable for the rnodeling of shallow.andintermedi-.ate deep events along the major seismic.zones and the.mid�ocean ridges.• These areas provide good glob .al c.o:verage .ofl.".ay .pathsfor .studying the structure of the earth's core in, detail.Numerical ,modeling in this studyshows that the source�side.surfac�, r;�flections, of the 1core phases.make.a significant contribu�ion to, determining� the: core ;v,elocity structure for the.• c:>bservations of the spatial-dens(l ar1 ray, with s:wall aperture.Additionally, the possible depth dependent inner-core attenuation can be resolved from regional array seismograms.The results. of this study show that the newly developed generalized ray -code displays a high poten�ial for further eluci dating the earth's core structure using the available data.
Abstract Non‐linear seismic response of soil is studied by comparing the spectral ratios of surface to downhole horizontal accelerations on weak and strong motion. Data from two boreholes are analysed. One is drilled in the alluvial deposits in the south–west quadrant of the SMART 1 array. The second one penetrates Pleistocene terrace deposits in the northern part of the SMART2 array. Observed weak and strong motion spectral ratios are compared with the theoretical ones predicted by the geotechnical soil model which postulates a hysteretic constitutive law. A significant non‐linear response is found at the first site for the events with surface peak acceleration exceeding roughly 0–15g. Deamplification of the strong motion occurred in the frequency range from approximately 1 to 10 Hz. The maximum observed difference between the average weak and strong motion amplification functions of an 11 m‐thick near‐surface stratum is a factor of 2–3. Nonlinear response characteristics are in qualitative agreement with the model. An additional corollary is that the amplification function calculated from the shear wave coda is equivalent to the average amplification calculated over the ensemble of small earthquakes. No statistically significant non‐linear response is detected on the second array, that is tentatively accounted for by the stiffer soil conditions and weaker accelerations achieved at the SMART2 site. The results indicate that the non‐linear amplification can be detectable at certain soil conditions above a threshold acceleration level.
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