SEISMOGRAM SYNTHESIS AND RECOMPRESSION OF DISPERSIVE IN-SEAM SEISMIC MULTIMODE DATA USING A NORMAL-MODE SUPERPOSITION APPROACH

In spite of a geometrical rotation into radial and transverse parts, two- or three-component in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards. A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single- and multi-mode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two-sided recursive filters. To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finite-difference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one- and two-mode recompression filters to the finite-difference data results in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source. Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one- and multi-mode synthetic seismograms and to apply one- and multimode recompression filters to the field data. The comparison of the one- and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show that, probably due to band-limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high-frequency range. Additional techniques which overcome the problem of band-limitation by modelling all of the enclosed single-mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications.     

理论地震图计算方法

近二十多年来,随着理论地震学和计算技术的发展,理论地震图的计算技术有了飞速发展.目前已能对不同的介质模型和震源计算各种体波、面波、地球自由震荡和静态位移场.它们在研究天然地震震源过程、地球内部结构、近场强地面运动、核爆作监测以及地震勘探等领域中发挥了越来越大的作用. 目前常用的理论地震图计算方法主要包括积分变换法、离散数值方法和射线方法几大类.本文对这些方法分类进行了简单介绍,并评论了各种方法的特点和各自的适用范围.     

Influence of focal mechanism on shape of isoseismals: Irpinia earthquake of November 23, 1980

With the use of complete synthetic seismograms for the SH component of motion we have constructed theoretical isoseismals. We have assumed a double-couple point source as determined from first arrivals of P waves. Lateral heterogeneities around the source were also considered. In fact, the crustal part of the model used to compute synthetic seismograms to the west of the Bradano foretrough was significantly different from the one used to synthesize seismograms to the east of the foretrough. Even with such a simple approach, the comparison between theoretical and experimental data is surprisingly good, indicating that the isoseismals' elongation, parallel to the Apennines, depends mainly upon the fault orientation, while the effect of local structures introduces relatively small perturbations in the radiation pattern.Publication n. 198 Istituto di Geodesia e Geofisica-Trieste.     

Determining the focal mechanisms and depths of relatively small earthquakes using a few stations by full‐waveform modelling

Determining the focal mechanism of earthquakes helps us to better define faults and understand the stress regime. This technique can be helpful in the oil and gas industry where it can be applied to microseismic events. The objective of this paper is to find double couple focal mechanisms, excluding scalar seismic moments, and the depths of small earthquakes using data from relatively few local stations. This objective is met by generating three‐component synthetic seismograms to match the observed normalized velocity seismograms. We first calculate Green's functions given an initial estimate of the earthquake's hypocentre, the locations of the seismic recording stations and a 1D velocity model of the region for a series of depths. Then, we calculate the moment tensor for different combinations of strikes, dips and rakes for each depth. These moment tensors are combined with the Green's functions and then convolved with a source time function to produce synthetic seismograms. We use a grid search to find the synthetic seismogram with the largest objective function that best fits all three components of the observed velocity seismogram. These parameters define the focal mechanism solution of an earthquake. We tested the method using three earthquakes in Southern California with moment magnitudes of 5.0, 5.1 and 4.4 using the frequency range 0.1–2.0 Hz. The source mechanisms of the events were determined independently using data from a multitude of stations. Our results obtained, from as few as three stations, generally match those obtained by the Southern California Earthquake Data Center. The main advantage of this method is that we use relatively high‐frequency full‐waveforms, including those from short‐period instruments, which makes it possible to find the focal mechanism and depth of earthquakes using as few as three stations when the velocity structure is known.     

Inversion of seismograms to determine simultaneously the moment tensor components and source time function for a point source buried in a horizontally layered medium

Summary A method of determining simultaneously the moment tensor and source time function in the point source approximation is presented. For trial values of the moment tensor components and of the source time function, parametrized by the sum of overlapping triangles delayed in time, theoretical seismograms can be synthetized and compared with the recorded ones. The iterative procedure determines the adjustment of source parameters until a good correlation of both synthetic and observed records is reached. The Green functions in a horizontally stratified medium are constructed with the use of a modal summation method.The limits of applicability of the algorithm are illustrated by the inversion of four synthetic seismograms constructed for two horizontally stratified models of the structure in Friuli area, Italy. The records constructed for the same structural model as for which the Green functions were computed can be inverted even in the high-frequency range. In the opposite case, when the records and Green functions used corresponded to different structural models, a good correlation of the input records with the final synthetics was obtained for low - pass filtered data only.Additional tests performed with input seismograms contaminated with random noise yielded good resolution of the moment tensor and the duration of the source time function even for a high noise to signal ratio.     

Application of the edge wave superposition method

Numerical examples of high-frequency synthetic seismograms of body waves in a 2-D layered medium with complex interfaces (faults, wedges, curvilinear, corrugated) are presented. The wave field modeling algorithm combines the possibilities of the ray method and the edge wave superposition method. This approach preserves all advantages of the ray method and eliminates restrictions related to diffraction by boundary edges and to caustic effects in singular regions. The method does not require two-point ray tracing (source-to-receiver), and the position of the source, as well as the type of source, and the position of receivers can be chosen arbitrarily. The memory and the time required for synthetic seismogram computation are similar to ray synthetic seismograms. The computation of the volume of the medium (the Fresnel volume or Fresnel zones), which gives the essential contribution to the wave field, is included in the modeling program package. In the case of complicated irregular interface (or a layered medium with a regular ray field at the last interface), the method displays a high accuracy of wave field computation. Otherwise, the method can be considered a modification of the ray method with regularization by the superposition of edge waves.     

较复杂介质波场计算中的一种透射边界

传统的人工边界是在声波或弹性波分解为内行和外行分量的基础上设计的.对于较复杂的介质模型（如粘弹介质、弹塑介质、塑性介质模型等）,地震波不能简单地分解为各自满足其运动方程的纵波、横波等成分,且地震波在传播过程中还有衰减现象,因此传统的人工边界已不能有效地用于非弹性的较复杂介质的波场模拟.本文提出了一种适合于更一般的地震模型的波场计算的透射边界条件,并以粘弹介质的一个较简单的二维几何模型为例,通过有限元数值求解这种透射边界和刚性边界下粘弹波的激发和传播,得到地面合成地震记录,证明了这种透射边界用于较复杂介质波场计算是可行的.     

Grid dispersion in generating finite-differences synthetic seismograms

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Site response estimation and ground motion spectrum scenario in the Catania area

A realistic definition of seismic input for the Catania area is obtained using advanced modeling techniques that allow us the computation of synthetic seismograms, containing body and surface waves. With the modal summation technique, extended to laterally heterogeneous anelastic structural models, we create a database of synthetic signals which can be used for the study of the local response in a set of selected sites located within the Catania area. We propose a ground shaking scenario corresponding to a source spectrum of an earthquake that mimics the destructive event that occurred on 11 January 1693. Making use of the simplified geotechnical map for the Catania area, we produce maps which illustrate the spatial variability of the SH waveforms over the entire area. Using the detailed geological and geotechnical information along a selected cross section, we study the site response to the SH and P-SV motion in a very realistic case, adopting and comparing different estimation techniques.     

Spectral element analysis on the characteristics of seismic wave propagation triggered by Wenchuan <Emphasis Type="Italic">M</Emphasis><Subscript>s</Subscript>8.0 earthquake

The 2008 Wenchuan earthquake occurred in an active earthquake zone, i.e., Longmenshan tectonic zone. Seismic waves triggered by this earthquake can be used to explore the characteristics of the fault rupture process and the hierarchical structure of the Earth’s interior. We employ spectral element method incorporated with large-scale parallel computing technology, to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. The AK135 model is employed as a prototype of our numerical global Earth model. The Earth’s ellipticity, Earth’s medium attenuation, and topography data are taken into consideration. These wave propagation processes are simulated by solving three-dimensional elastic wave governing equations. Three-dimensional visualization of our numerical results displays the profile of the seismic wave propagation. The three-point source, which is proposed from the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture process than the one-point source. We take comparison of synthetic seismograms with observational data recorded at 16 observatory stations. Primary results show that the synthetic seismograms calculated from three-point source agree well with the observations. This can further reveal that the source rupture process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. Supported by National Basic Research Program of China (Grant No. 2004CB418406), National Natural Science Foundation of China (Grant Nos. 40774049 and 40474038), and Computer Network Information Center, Chinese Academy of Sciences (Grant No. INF105-SCE-02-12)     

Waveform inversion of weak vrancea (Romania) earthquakes

Summary The inversion of high-frequency seismograms is performed to retrieve source mechanisms, hypocentral depths and source time functions of two weak Vrancea earthquakes (M_L=3.3), one that occurred in the crust, the other in the lithospheric part of the mantle. The digital waveforms recorded by the local Romanian network are used. Synthetic seismograms are computed by the modal summation method, using the point source approximation, for horizontally layered anelastic media. For each source-to-station path a different structural model is adopted which represents the best 1-D approximation of the medium in this azimuth. Thus, lateral inhomogeneities are taken into account in a simplified way. The source is described by the full moment tensor, allowing both deviatoric and volumetric components to be resolved.Although the structural models are simplified for the range of epicentral distances (15<<<170 km) considered, we find that the fit between the synthetic and observed seismograms is satisfactory for frequencies less than a few Hz. The few P-wave polarities available are not sufficient to determine a reliable source mechanism by standard methods, while the waveform inversion allows us to retrieve source mechanisms that are stable with respect to different boundary conditions and in good agreement with the observed polarities. The source time function is the less stable inverted parameter, being the most influenced by the simplification of the structural models.     

基于高铁震源简化桥墩模型激发地震波的数值模拟

高铁列车运行过程中绝大部分时间都是行驶在高架桥上的,高铁列车经过桥梁时,通过与大地耦合的桥墩激发地震波发震过程和平地不完全一样.本文探索高铁列车行驶经过高架桥桥墩,通过桥墩对地下介质激发地震波的机理及过程.为了便于理论分析,文中将高铁列车简化为在高架桥上沿一个方向运动的移动线源,通过每节车厢前后组轮对,对每一个桥墩施加力的作用,而桥墩插入地面几十米深至围岩,与表层土壤和深层围岩双重耦合,由此给出高铁列车通过桥墩激发地震波的震源时间函数.同时,基于广义连续介质力学框架下的修正偶应力理论,推导包含介质特征尺度的弹性波动方程,并应用此弹性波动方程以及构建的高铁震源时间函数,采用优化的交错网格有限差分算法,实现数值模拟,将合成的地震记录与实际地震记录对比分析,其结论将为进一步的基于高铁震源的成像和反演研究提供理论依据.     

SYNTHETIC SEISMOGRAMS AT NON-VERTICAL INCIDENCE*

Synthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P- to S-wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non-vertical incidence on synthetic seismograms is examined in this paper. Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source. Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.     

DOWNHOLE SYNTHETIC SEISMIC PROFILES IN ELASTIC MEDIA1

A multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time-domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving-Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms. A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo-Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave-mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles. Synthetic seismograms generated using a different source-receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave-mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo-Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of the field section.     

地震波在垂向不均匀介质中传播问题的某些探讨

本文计算了含有高速夹层介质中首波的理论地震图。通过分析得到,当高速夹层薄到一定程度时,就会产生干涉型首波,从而从一个侧面证明了射线理论的局限性。通过对地震波反射—折射系数能量守恒关系的分析,探讨了反射—折射系数大于1的可能性。最后,介绍了一种计算垂向不均匀介质中拉梅问题理论地震图的数值方法——有限差分法。     

IDA和CDSN资料的长周期面波研究

１９８０年和１９９２年分别在昆明和北京白家疃台架设了ＩＤＡ观测仪器，１９８５年开始又陆续在北京，兰州，海拉尔等地布设和完善了ＣＤＳＮ数字化地震观测台网，为开展长周期面波研究提供了方便。本文结合国内外研究现状，论述了超长周期地震观测在地球自由振荡，震源物理面波理论地震图合成及非均匀地球介质结构研究中的应用。同时结合１９８９年５月６日发生在秘鲁的Ｍｓ７．０地震，介绍了利用简正振型资料开发地震矩张量反演     

WAVELET DECONVOLUTION USING A SOURCE SCALING LAW*

We present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source-receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase. We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non-minimum-phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.     

Rapid directivity detection by azimuthal amplitude spectra inversion

An early detection of the presence of rupture directivity plays a major role in the correct estimation of ground motions and risks associated to the earthquake occurrence. We present here a simple method for a fast detection of rupture directivity, which may be additionally used to discriminate fault and auxiliary planes and have first estimations of important kinematic source parameters, such as rupture length and rupture time. Our method is based on the inversion of amplitude spectra from P-wave seismograms to derive the apparent duration at each station and on the successive modelling of its azimuthal behaviour. Synthetic waveforms are built assuming a spatial point source approximation, and the finite apparent duration of the spatial point source is interpreted in terms of rupture directivity. Since synthetic seismograms for a point source are calculated very quickly, the presence of directivity may be detected within few seconds, once a focal mechanism has been derived. The method is here first tested using synthetic datasets, both for linear and planar sources, and then successfully applied to recent Mw 6.2–6.8 shallow earthquakes in Peloponnese, Greece. The method is suitable for automated application and may be used to improve kinematic waveform modelling approaches.     

Site amplifications in the city of Benevento (Italy): comparison of observed and estimated ground motion from explosive sources

A hybrid approach is applied to construct 2-D synthetic seismograms for explosive sources. The computation of the signals has been performed with a hybrid technique, that couples the modal summation method, describing the P-SV propagation from the source to a target area, to the finite difference method, allowing the computation of the 2-D response of the target area. We use this technique to study the site response in the city of Benevento (Southern Italy). The results are compared both with those obtained for the same model, but considering an extended double-couple source and SH wave propagation and with those derived from a direct analysis of experimental data obtained during the Benevento Seismic Risk Project, funded by the Commission of European Communities. The type and depth of the source and the source-receiver distance can provide different excitations, but the response of the target area, in terms of ratios of response spectra, remains in general stable in the high frequency range (>2 Hz). The explosive source does not excite lower frequencies and is therefore unable to provide estimates of site effects in this frequency range. We also show that it is important to consider both P-SV and SH waves when assessing site effects. Finally, a very good definition of a structural model from geological data is fundamental in order to explain the observed data in the time domain. The observed data validate our synthetic modelling for evaluating the site effects and for a tentative seismic microzonation of the city of Benevento.     

利用区域地震台网、振幅比资料测定小震震源参数

本文提出一种利用区域地震台网垂直向位移记录中和最大振幅的比值,由计算层状介质中点源位错的、综合地震图测定小震震源参数的方法。用人工数据检验该测定方法的可行性;并用此方法测定了海城地震（1975年2月4日,M_s=7.3）前震序列震源参数,与其他方法得到的结果作了对比分析。结果表明,本文提出的方法具有需用记录资料少的优点。