合成理论地震图方法综述

合成理论地震图对震源和地下结构的研究而言是一项重要的基础工作.一直以来,诸多地震学领域的先驱们都致力于合成理论地震图的方法发展与改进,是一个愈久弥新的研究课题.同时,经过很多非常有影响力的地震学家的发展,合成理论地震图的方法种类变得多种多样.本文全面而深入地总结合成理论地震图的不同理论、不同方法所具有的优势与不足,并讨论各种理论地震图计算方法的研究进展.以期为理论地震图计算方法的发展以及在实际应用中选择合适的方法提供有价值的参考.经过对比研究,我们得到以下三点认识:(1)在解析类方法中,波数积分法在使用上不区分局部或全球尺度、计算精确且为全波形模拟,因此适用性更为广泛;(2)在数值类方法中,谱元法在适用性和计算效率上是一种最受欢迎且最精确的计算方法;(3)根据不同的需求采用不同方法相结合的混合计算方法是较好的选择.     

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.     

一种近场理论地震图的Haskell矩阵算法

本文提出一种适于层状介质内点源模型的近场理论地震图算法,采用的位移表达式由Has kell矩阵的分解形式和离散波数积分组成。文中还出一起计算若干不同深度震源的近场理论地震图时的简便算法。这样,由本文的点源模型模拟复杂地震震源过程时可免去大量的审复计算。为检验算法功能,文中还给出了与文献[12]的数值计算的对比结果。     

用广义射线和有限差分计算近场理论地震图的混合方法

本文提出一种结合广义射线和有限差分理论而形成的混合方法（以下简称混合方法）．在介质均匀区（包括平行介质分层区）应用广义射线理论，在介质不均匀区应用有限差分理论．在这种结合过程中，把均匀区广义射线的结果作为不均匀区有限差分区波场连续的输入．对于均匀介质模型，混合方法理论地震图和广义射线理论地震图、广义反射透射系数矩阵及离散波数法地震图的对比，取得了满意的结果，在数值上证明了该方法的正确性．计算了１９９０年８月５日Ｈａｋｏｎｅ地震前震在日本Ａｓｈｉｇａｒａ山谷盲测点的响应，理论地震图和实际资料的比较同样取得好的结果．这种方法可用于地震勘探、工程地震、强地面运动的研究．     

地震破裂产生的动态应变场的模拟计算研究

设地震破裂为一个以有限速度扩展的双侧破裂走滑断层,在1°×1°的研究范围内,通过离散波数法合成理论位移地震图,计算研究区域中144个场点的位移时程,在此基础上得到了应变时程和动态应变场,并讨论了应变时程的动态特征和动态应变场的分布特征。地震破裂动态应变场的计算为将来实现地震动态库仑破裂应力场的计算奠定了基础。     

使用CDSN资料确定澜沧地震震源参数

本文使用中国ＣＤＳＮ长周期数字资料，采用理论地震图试错法，确定了１９８８年云南澜沧７．６级强震的震源机制参数，改进Ｋｉｋｕｃｈｉ方法，计算出震源破裂时间过程函数，讨论了该地区发展地质构造。     

火山地震的理论地震图计算方法

本文首先分析了不同类型火山地震的波形,提出了相应的震源模型.然后发展了计算层状介质理论地震图的部分分离变量—有限差分方法,其最重要的环节是引用了吸收边界条件,使计算工作得以简化.这种方法特别适用于火山地震的理论地震图计算.最后,本文给出了计算实例.     

时间域内有限地震断层的反演问题

为了解决有限地震断层破裂过程研究中的正演和反演问题，本文提出：（1）用广义反射、透射系数矩阵和广义射线理论计算上地幔及远场范围体波理论地震图的混合方法．同时采用格林函数的一种新的组合方式，可节约1／3计算机内存．（2）采用基于模拟退火的热浴算法进行全局搜索反演，不仅提高了在计算过程中新模型被接收的可能性，而且使得在时间域内目标函数的计算速度提高了近二个数量级．对1994年台湾海峡地震震源破裂过程的研究结果表明，这次地震的破裂过程相对比较简单．在前4．0s内地震断层的破裂相当剧烈，错动距离的平均值随着破裂时间增加而迅速减少．开始时破裂速度较高，前4．0s的平均值为3．1km／s，之后逐渐降至2．2km／s．错动方向随破裂的变化不大．     

中强地震前山东地下流体地震前兆模糊分维特征研究

采用模糊集理论与分形理论相结合的模糊分维方法，计算山东地下流体在１９８３年菏泽５．９级地震和１９９５年苍山５．２级地震前的变化。分析结果认为，模糊分维值反映了地震前兆时序观测资料的结构变化特征，具有一定的物理意义，为从复杂的地下流体前兆观测值中提取地震异常信息提供了新的方法，但对某些台、测项而言、必须具体分析其模糊分维变化特征及其震前异常变化特征。     

横向不均匀介质中Kirchhoff-Helmholtz积分合成地震图

本文将Kirchhoff-Helmholtz积分方法应用于横向非均匀介质的合成地震图计算.与反射率方法及二维有限差分方法进行了比较.表明KH积分方法能很好的模拟反射波震相,且精度较高.KH 积分方法能够计算复杂界面的反射波,且其计算效率明显大于有限差分.     

邢台地区长周期地震动特征初步分析

沉积平原中存在地表低速沉积层是长周期地震动产生的关键因素,而长周期地震动会对长周期建筑物造成严重威胁和震害。本文基于邢台地震的历史地震震源模型和含地表沉积层的地壳速度模型,采用离散波数有限元法,对邢台地区进行了长周期地震动的计算分析。研究表明,邢台平原地区在大震中会产生长周期地震波,邢台地震中反应谱峰值区域位于宁晋南,与极震区基本重合。震中距小于55km区域内的周期1.5—4s的放大系数谱超过了抗震设计规范谱,反应谱放大系数值在周期2s附近达到峰值。因此,邢台地区因存在地表软弱沉积层,该区抗震设防可能对长周期地震动估计不足,建议应予以特别考虑。     

云南武定M6.5地震动态库仑破裂应力变化的数值模拟及其与余震活动的关系

在离散波数法（DWN）基础上,计算了武定M6.5地震断层破裂在周围介质中产生的位移时程（位移理论地震图）和动态位移场;进行弹性动力学转换后,求得应变时程和动态应变场;最后得到了武定M6.5地震所产生的动态库仑破裂应力变化量和动态库仑破裂应力变化场,进而研究其与后续余震的关系. 结果表明,动态应力最大峰值和静态应力的正区均呈非对称性分布,两者的分布特征与余震的分布特征基本一致. 在动态应力峰值为正的确定区应力值超过了0.1 MPa触发阈值, 在静态应力值为正的确定区应力值超过了0.01 MPa触发阈值. 这说明动态应力和静态应力均有助于余震的发生.      

Synthetic seismograms for finite sources in spherically symmetric Earth using normal-mode summation

Normal-mode summation is the most rapidly used method in calculating synthetic seismograms. However, normal-mode summation is mostly applied to point sources. For earthquakes triggered by faults extending for as long as several 100 km, the seismic waves are usually simulated by point source summation. In this paper, we attempt to follow a different route, i.e., directly calculate the excitation of each mode, and use normal-mode summation to obtain the seismogram. Furthermore, we assume the finite source to be a ‘‘line source' and numerically calculate the transverse component of synthetic seismograms for vertical strike-slip faults. Finally, we analyze the features in the Love waves excited by finite faults.     

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。     

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.     

ZERO MEMORY NON-LINEAR DECONVOLUTION*

A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions.     

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.     

天然地震PS转换波动力学特征的初步研究

本文根据合成理论地震图的广义射线理论,并应用自行编写的FORTRAN计算程序,研究了单一界面、薄层和迭层界面上形成的PS转换波的动力学特征,讨论了沉积盖层及上部地壳介质吸收对转换波的影响。     

利用低纬赤道带垂测站台网测量西移两日行星波的纬向波数

本文介绍一种利用低纬赤道带垂测站台网测量西移两日行星波纬向波数k的新方法.对IGY期间1958年的测量结果分析表明:西移两日行星波纬向波数k=2出现的次数,比k=3出现的次数要多得多.     

宽频带数字地震记录仿真的应用

利用傅里叶分析法，把速度型宽频带数字地震记录变成台站人员所熟悉的长周期，中长周期模拟常规地震记录，分析人员能在仿真后的记录波形图上识别震相和计算震级。为地震台站用宽频带数字地震记录取代模拟记录提供了一种资料处理方法。