提高规则网格最短路径方法反射波走时计算精度的走时校正技术

最短路径射线追踪方法是计算地震波走时的主要方法之一,该方法基于惠更斯原理和费玛原理,具有稳健、适于复杂介质模型的优点.为处理方便,最短路径方法中的介质模型通常以规则网格进行剖分,界面节点(界面与网格的交点)以其邻近的模型单元节点(即边界单元节点)近似表示.界面近似将导致计算误差,对于反射波尤为严重.反射波的走时精度可通过减小网格的尺寸提高,但这样会大大增加计算时间,为高精度和高效率地计算地震反射波走时,我们提出了一种基于规则网格的走时校正技术.地震波传播至或起始于边界单元节点的走时校正为地震波传播至或起始于该边界单元节点所对应的界面节点的走时.数值模型计算结果表明,走时校正方法可使反射波的走时精度提高约1～2个数量级,而其计算时间则和常规算法基本上在相同量级.     

隧道工程勘察中的超前预报成像方法研究

针对地下工程领域隧道超前预报地震波波场传播与成像中存在的问题,通过数值模拟,构建二维含低速异常的隧道介质模型,研究隧道弹性波场传播规律和异常体边界成像准确性.首先,利用一阶速度-应力波动方程和高阶交错网格有限差分计算方法,导出隧道超前预报数值模拟的稳定性条件和边界条件,对上述隧道模型进行数值模拟,识别波场特征;其次,利用叠前逆时偏移成像方法,对压制噪音干扰后的波场在互相关成像条件下,对隧道模型中的异常体边界进行逆时偏移成像.研究结果表明：采用高阶交错网格有限差分正演获得异常体边界清晰的反射波和角点产生的散射波;逆时偏移算法获得隧道内异常体准确成像结果,从而大大提高隧道超前预报的分辨率与准确性;靠近掌子面单一震源、多道接收观测系统对异常体成像效果最佳,为隧道内高效数据采集提供理论依据.     

多分量联合逆时偏移最佳匹配层吸收边界

有限空间内的波动方程逆时偏移需要利用有效的边界处理技术用以消除人工截断对偏移结果产生的影响。本文以横向各向同性介质弹性波速度-应力方程为基础,依据传统分裂式最佳匹配层（Perfect Matched Layer,PML）吸收边界技术的思想,推导了应用于逆时偏移的完全匹配层波动方程,并给出了其高阶交错网格有限差分格式。针对由边界处向计算区域内传播的＂反射波＂,以及地震记录排列两端地震同相轴突变对计算区域的影响这两方面问题,本文给出了逆时偏移中吸收层的布设方式。模型和实际资料的弹性波叠前多分量联合逆时深度偏移结果表明本文的边界处理方法取得了较好的吸收效果,获得了好的联合偏移成像结果。     

黏弹性介质VSP记录模拟及在估算Q值研究中应用

采用标准线性固体模型,本文建立了黏弹性介质完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并对黏弹性介质中的地震波传播进行了数值模拟.基于黏弹性波动方程正演模拟提供的零偏VSP全波场数据,本文进行了质心频移法计算Q值的反演分析.结果表明,反射波、转换波及短程多次波对频谱的影响较大,对Q值反演造成一定误差.本文的...     

复杂介质地震波传播模拟中边界元法与有限差分法的比较研究

地震波场数值模拟是理论地球物理学和勘探地球物理学的重要研究手段.在众多数值模拟方法中边界元法和有限差分法是两种典型的地震波传播模拟计算方法.边界元法是一种半解析-半数值的边界型方法,它显式地利用边界连续条件,沿着地层边界进行离散,具有降维、高精度和自动满足远场辐射条件的优点;有限差分法是一种典型的基于微分的区域型方法,它隐式地使用边界连续条件,以空间网格形式进行离散和数值逼近,具有高效、实用和容易数值实现的优点.本文以一个半圆形均匀Valley模型和两个非均匀断裂/断层模型为例,从计算精度、计算效率、频散特性以及适用性等方面对这两种方法进行了比较研究.数值计算结果表明:边界元法可以精确地几何描述有内部断点、断面的复杂构造,能够精确地模拟内部不规则界面之间波的反射/传播;有限差分法不能以足够的精度描述几何断点和内部不规则边界.边界元法在高频时计算量大于有限差分法,有限差分法则需要更小的网格间距以压制数值频散.因此,在处理内部非均质和高频计算时,有限差分法更有效;在处理内部不规则边界、断点、大尺度等问题时,边界元法比有限差分法更有优势.     

粘弹各向异性反射体模型方位地震AVO模拟及分析（英文）

基于岩石物理模型和广义各向异性Zoeppritz方法在频率域计算裂缝型反射体模型反射波方位地震AVO响应。反射体模型为粘弹各向异性、有限厚度的地质体,其地震反射波形序列包含如下动力学信息,即分界面处介质的波阻抗和非弹性差异、反射体内部波的各向异性传播、在传播路径上的频散与衰减,以及来自顶底界面的反射波的调谐与干涉等。计算表明,速度频散和衰减增顶界面反射波大入射角反射时的振幅,而减弱底界面反射振幅。对于固定入射角的方位地震方位地震响应,PP波反射特征表现为随方位角的增加反射波形序列延续时间变长,而PSV和PSH转换类型反射波的方位各向异性变化特征稳定且受储层厚度影响较小,表现为PSV波反射振幅随方位角增加而增加,PSH波在0°和90°方位无反射能量,在45°方位反射振幅最强。     

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.     

基于自适应优化有限差分方法的全波VSP逆时偏移

与地面地震资料相比,VSP资料具有分辨率高、环境噪声小及能更好地反映井旁信息等优点.常规VSP偏移主要对上行反射波进行成像,存在照明度低、成像范围受限等问题.为了增加照明度、拓宽成像范围、提高成像精度,本文采用直达波除外的所有声波波场数据(全波),包括一次反射波、多次反射波等进行叠前逆时偏移成像.针对逆时偏移中的四个关键问题,即波场延拓、吸收边界条件、成像条件及低频噪声的压制,本文分别采用自适应变空间差分算子长度的优化有限差分方法(自适应优化有限差分方法)求解二维声波波动方程以实现高精度、高效率的波场延拓,采用混合吸收边界条件压制因计算区域有限所引起的人工边界反射,采用震源归一化零延迟互相关成像条件进行成像,采用拉普拉斯滤波方法压制逆时偏移中产生的低频噪声.本文对VSP模型数据的逆时偏移成像进行了分析,结果表明:自适应优化有限差分方法比传统有限差分方法具有更高的模拟精度与计算效率,适用于VSP逆时偏移成像;全波场VSP逆时偏移成像比上行波VSP逆时偏移的成像范围大、成像效果好;相对于反褶积成像条件,震源归一化零延迟互相关成像条件具有稳定性好、计算效率高等优点.将本文方法应用于某实际VSP资料的逆时偏移成像,进一步验证了本文方法的正确性和有效性.     

二阶声波方程非分裂式CPML实施新方法

完全匹配层(PML)是处理波动方程数值模拟中模型边界反射问题的常用方法,在时间域有限差分(FD)波场数值模拟中得到了广泛的应用.早期的PML技术存在对于近切入射和低频反射吸收效果较差的问题,由此产生了复频移PML(CFS-PML)模型边界反射压制法,其中基于递归卷积技术的复频移PML(CPML),由于其算法在时间域的高效性,被广泛应用于时间域一阶方程的数值模拟.一阶波动方程CPML边界条件是非常成熟的方法,但是二阶方程, CPML方法还需要进一步发展研究.目前,二阶方程的CPML处理方法需要引入辅助方程或者辅助变量,导致计算量增加,从而对数值模拟效率产生一定的影响.本文提出了一种分区域两步法CPML实施策略,简称为TS-CPML. TS-CPML通过对二阶CPML控制方程进行两步有限差分进行数值模拟,从而避免计算引入辅助变量的新二阶偏微分方程或其他辅助方程,具有计算效率高、编程易于实现等特点.我们将该方法应用于二阶声波方程和TTI介质二阶拟声波方程组,数值模拟显示,在相同参数下,由模型边界产生的反射波振幅约为传统二阶方程CPML方法的50%以上,验证了TSCMPL技术的优越性.     

基于自适应网格的仿真型有限差分地震波数值模拟

在复杂山地和复杂海底条件下,地表和海底的剧烈起伏对地震波数值模拟提出了更高的要求.常规有限差分法采用矩形网格对模型进行网格剖分,由于矩形网格自身的限制,起伏地表或起伏海底只能由一系列阶梯状折线代替,从而引起人为虚假绕射波.此外,在模拟液-固界面的反射波时,如果界面与网格线不一致,则需要更密的网格才能得到精确的结果.为了解决上述问题,本文将自适应网格生成技术引入到起伏海底速度模型的网格剖分中,采用高阶仿真型有限差分法(MFD)对曲线坐标下的声波方程波进行了数值模拟.利用自适应网格生成技术对速度模型进行网格剖分不仅可以准确地描述模型边界,而且可以有效消除虚假绕射波.高阶仿真型有限差分法可以有效压制频散提高计算精度.模型试算结果表明,本文方法对复杂海底模型具有很好的适应性.     

模拟震源动力学破裂过程的数值方法研究

为模拟震源的动力学破裂过程,本文讨论一种求解剪切裂纹动力学扩展问题的有限差分法。在研究二维反平面破裂的基础上,我们把所用方法推广到三维问题。研究了许多简单震源模型,通过对比同一问题的解析解和其它数值解,对方法的正确性和计算精度进行了检验,结果表明我们的数值方法是可行的。最后,作为初步应用的例子,我们研究了非均匀断层的自发破裂问题。     

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

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Finite element analysis of water flow in variably saturated soil

A two-dimensional Galerkin finite element model for water flow in variably saturated soil is presented. A fourth-order Runge-Kutta time integration method is employed which allows use of time steps at least 2 times greater than for a traditional finite difference approximation of time derivatives. For short total simulation times computer execution costs for the Runge-Kutta method are greater than for the finite difference approximation due to the start up cost of the Runge-Kutta method, but for longer simulation times the Runge-Kutta method requires considerably less computational effort even when automatic time-step adjustment is used with the finite difference procedure. A comparison of the method of influence coefficients and 2 × 2 Gaussian integration to compute element matrices indicates that the influence coefficient method reduces total execution time to 60% of that required for numerical quadrature. Computed pressure heads using the influence coefficient method and numerical integration are found to be in close agreement with each other even under conditions of highly non-linear soil properties in a heterogeneous domain. Fluxes computed by the two methods are also generally in close agreement except under extremely non-linear conditions when some deviations were observed at short simulation times.     

徐淮地区煤矿井筒破裂原因初探

本用震源力学理论和方法研究了徐淮地区从１９７０年以来构造应力场的方向和强度的时空变化过程。结果表明：以唐山地震为分界线，本区的应力场Ｐ轴取向由震前平均６１．８°变为震后平均７７．７°。如果将本区以宿北断裂为界分为南区和北区两个部分，则北区的Ｐ轴取向从６８．１°变７１．２°，而南区的Ｐ轴取向由６２．５°变到８３．６°，南区的变化明显于北区。     

基于高阶双渐近透射边界的大坝-库水动力相互作用直接耦合分析模型

高阶双渐近时域透射边界能够同时模拟行波和快衰波的传播,并且能够在全频范围内迅速逼近准确解,具有优良的收敛性能和计算效率.本文将动水压力波高阶双渐近透射边界直接嵌入到近场有限元方程中,建立了大坝-库水动力相互作用的直接耦合分析模型.该模型的整体控制方程保留了近场有限元方程系数矩阵对称稀疏的优势,可以方便地利用现有的通用有限元求解器求解.基于有限元开源软件框架体系OpenSees（Open System for Earthquake Engineering Simulation）,编程实现了直接耦合分析模型,并将其应用于二维重力坝、三维拱坝与库水动力相互作用分析.数值算例表明,该直接耦合分析模型具有很高的精度和计算效率.     

Efficient seismic analysis for nonlinear soil-structure interaction with a thick soil layer

The direct finite element method is a type commonly used for nonlinear seismic soil-structure interaction(SSI) analysis. This method introduces a truncated boundary referred to as an artificial boundary meant to divide the soilstructure system into finite and infinite domains. An artificial boundary condition is used on a truncated boundary to achieve seismic input and simulate the wave radiation effect of infinite domain. When the soil layer is particularly thick, especially for a three-dimensional problem, the computational efficiency of seismic SSI analysis is very low due to the large size of the finite element model, which contains an whole thick soil layer. In this paper, an accurate and efficient scheme is developed to solve the nonlinear seismic SSI problem regarding thick soil layers. The process consists of nonlinear site response and SSI analysis. The nonlinear site response analysis is still performed for the whole thick soil layer. The artificial boundary at the bottom of the SSI analysis model is subsequently relocated upward from the bottom of the soil layer(bedrock surface) to the location nearest to the structure as possible. Finally, three types of typical sites and underground structures are adopted with seismic SSI analysis to evaluate the accuracy and efficiency of the proposed efficient analysis scheme.     

Impedance functions for three-dimensional foundations supported on an infinitely-long canyon of uniform cross-section in a homogeneous half-space

A direct boundary element procedure is presented to determine the impedance matrix for a three-dimensional foundation supported on an infinitely-long canyon of uniform cross-section cut in a homogeneous half-space. The uniform cross-section of the canyon permits analytical integration along the canyon axis leading to a series of two-dimensional boundary problems involving Fourier transforms of the full-space Green's functions. Solution of these two-dimensional boundary problems leads to a dynamic flexibility influence matrix which is inverted to determine the impedance matrix. The accuracy of the procedure is demonstrated by comparison with previous solutions for a surface-supported, square foundation and results obtained by a three-dimensional boundary element method (BEM) for a foundation of finite-width supported on an infinitely-long canyon. Compared with the three-dimensional BEM, the present method requires less computer storage and is more accurate and efficient. The foundation impedance matrix determined by this procedure can be incorporated in a substructure method for earthquake analysis of arch dams.     

Mass lumping models of the linear diffusion equation

The nodal domain integration method is used to develop a numerical model of the linear diffusion equation. The nodal domain integration approach is shown to represent an infinity of finite element mass matrix lumping schemes including the Galerkin and subdomain integration versions of the weighted residual method and an integrated finite difference method. Neumann, Dirichlet and mixed boundary conditions are accommodated analogous to the Galerkin finite element method. In order to reduce the overall integrated approximation relative error, a mass matrix lumping formulation is developed which is based on the Crank-Nicolson time advancement approximation. The optimum mass lumping factors are found to be strongly related to the model timestep size.     

Seismic response of base-isolated liquid storage tanks considering fluid–structure–soil interaction in time domain

The seismic response analysis of a base-isolated liquid storage tank on a half-space was examined using a coupling method that combines the finite elements and boundary elements. The coupled dynamic system that considers the base isolation system and soil–structure interaction effect is formulated in time domain to evaluate accurately the seismic response of a liquid storage tank. Finite elements for a structure and boundary elements for liquid are coupled using equilibrium and compatibility conditions. The base isolation system is modeled using the biaxial hysteretic element. The homogeneous half-space is idealized using the simple spring-dashpot model with frequency-independent coefficients. Some numerical examples are presented to demonstrate accuracy and applicability of the developed method.Consequently, a general numerical algorithm that can analyze the dynamic response of base-isolated liquid storage tanks on homogeneous half-space is developed in three-dimensional coordinates and dynamic response analysis is performed in time domain.     

Scattering of elastic waves in cracked media using a finite difference method

This paper presents a simple, flexible way of introducing stress-free boundary conditions for including cracks and cavities in 2D elastic media by a finite difference method (FDM). The surfaces of cracks and cavities are discretized in a staircase on a rectangular grid scheme. When zero-stress is applied to free surfaces, the resulting finite difference schemes require a set of adjacent fictitious points. These points are classified based on the geometry of the free surface and their displacement is computed as a prior step to later calculation of motion on the crack surface. The use of this extra line of points does not involve a significant drain on computational resources. However, it does provide explicit finite difference schemes and the construction of displacement on the free surfaces by using the correct physical boundary conditions. An accuracy analysis compares the results to an analytical solution. This quantitative analysis uses envelope and phase misfits. It estimates the minimum number of points per wavelength necessary to achieve suitable results. Finally, the method is employed to compute displacement in various models with cavities in the P-SV formulation. The results show suitable construction of the reflected P and S waves from the free surface as well as diffraction produced by these cavities.