高精度有限差分地震波正演方法

三维地震模拟不仅可以更精确地研究地震波的传播规律,而且是三维地震资料处理和解释的工具。本文采用精细积分法用于求解波动方程.对波动方程在空间采用差分格式,时间域采用积分法求解析的方法。文中详细论述了精细积分法的数值方法,并给出了计算公式。理论分析和数值算例的结果表明了用这种混合方法得到的解与精确解十分吻合,比有限差分法具有更高的精度。文中给出的地震波正演模拟算例说明了该方法适用于复杂地表和复杂构造地质体。     

三维波动方程有限差分正演方法

三维地震资料的处理和解释都需要有效的三维正演模型予以验证．本文提出一种在ｘ－ｔ域实现快速、高精度的有限差分正演方法,采用了独特的“平行四边形网格”,并用Ｐ－Ｒ交替差分格式使三维波动方程可以局部地分裂成二维求解方程,从而有效地减少运算量．     

三维波动方程有限差分正演方法

三维地震资料的处理和解释都需要有效的三维正演模型予以验证．本文提出一种在ｘ－ｔ域实现快速、高精度的有限差分正演方法，采用了独特的“平行四边形网格”，并用Ｐ－Ｒ交替差分格式使三维波动方程可以局部地分裂成二维求解方程，从而有效地减少运算量．     

地震正演模拟复杂构造中的地震波传播(英文)

地震正演模拟技术是研究地震波在复杂介质中传播规律的有效途经,尤其在地质构造及其复杂的中国西部地区,其意义更是重大。本文介绍了两种新的正演模拟技术：有限元有限差分方法（FE—FDM）和任意精细积分方法（ADPI）,并结合实例分析来验证FE—FDM和ADPI算法的实际效果,结果证明这两种方法能够有效地适用于复杂介质下的地震波传播性质的研究。     

傅里叶有限差分法三维波动方程正演模拟

傅里叶有限差分(FFD)法兼有相位屏法和隐式有限差分法二者的优势,能够处理复杂地质构造中的波传播问题,但在三维情形下,算子的双向分裂会引起明显的方位各向异性误差.本文用Fourier变换计算双向分裂过程中的高阶交叉项,消除了方位各向异性误差.该方法充分利用了FFD法在双域实现的算法结构,明显减少了由于引入误差校正所带来的计算量.将该方法应用于修改后的三维French模型的地震正演问题,并将得到的叠后记录、单炮记录同全波有限差分法的模拟结果进行对比,结果证实了该方法对一次反射波具有较高的模拟精度,在内存需求和计算效率方面则具有更大的优势.     

基于GPU计算的地震波场高阶有限差分正演研究

本文介绍地震波场高阶有限差分正演及其GPU计算问题,通过数值模拟技术实现地震波正演。对于声波方程,利用泰勒级数展开式得出波动方程的高阶有限差分格式及其离散表达式。运用C++语言和CUDA编写二维和三维GPU正演程序,使用共享存储器提升GPU线程间通信传输速度,并且改善了三维模型情况下共享存储器容量对有限差分阶数的限制问题。建立不同尺度模型针对二维和三维GPU正演程序和CPU正演程序进行计算测试,比较两个程序的计算效率。测试结果表明,无论是在二维和三维的模型下,GPU正演程序的计算耗时都远远小于CPU正演程序的计算耗时,且随着计算数据量的增大,加速效果越来越显著,测试结果可以很好地证明GPU程序相对于单CPU程序计算的高效性。     

地震多级散射波正演模拟方法

地震波在穿越地下散射体群时会产生多级散射波,分析其地震响应特征,可推断散射体的分布情况和性质。本文从二维标量波动方程出发,结合地震散射理论和波恩近似理论,推导了多级散射波方程。在此基础上,采用高阶有限差分法对双点散射体模型和复杂散射体模型进行数值模拟,分析了多级散射波的传播规律和波场特征,并通过抽取多级散射记录和各级散射记录的单道记录与参考单道记录的对比,验证了本文推导散射波方程的准确性。      

井间地震波动方程正演数值模拟及其应用

井间地震正演模拟是在给定地层参数及边界条件的情况下求波动方程数值解的过程.本文详细推导了井间二维声波方程四阶差分方程;根据假设的包含楔形体和丘状体的理论地层模型,对其波场进行了模拟计算分析;据胜利油田垦71区块两口井的实际声波测井资料建立了精细速度模型,对其正演模拟的合成记录波场进行分析,并把合成记录反射波成像与实际的过井三维地震剖面进行了对比,验证了所设计观测系统的合理性.     

基于OBS的正演模拟与初至识别研究

在深部壳幔结构研究中,采用OBS接收到深部构造的折射、反射信号并通过层析成像反演地下结构是当前最为有效的方法.初至识别则是层析成像处理OBS资料最重要的工作之一,而基于OBS的正演模拟对于初至的正确识别具有重要的指导作用.本文利用二维声波波动方程实现了基于OBS的数值模拟,获得了水平层状、倾斜模型条件下的OBS共接收点道集.通过研究OBS共接收点道集反射波、折射波在不同地质模型下的规律,对OBS初至识别方法进行总结,并在实际资料处理中加以应用.结果表明,利用OBS共接收点道集的多图对比可以较简便地实现初至识别,其中水平层状地质模型初至必然呈现对称性,而倾斜模型的初至则需要综合考虑反射波、折射波的规律进行判断.     

利用GPU技术及分块策略加速地震波场模拟

传统的利用有限差分方法模拟地震波场需要耗费较大的机时.为了提高地震波场的模拟效率,采用GPU并行计算技术是一种非常好的方法.文章基于一阶应力-速度声波方程的交错网格有限差分法,采用分块策略,将一个地质模型分解成多个小规模的地质子块,每个子块交由一个线程块负责,并利用常数存储器、块内共享存储器和寄存器减少对全局存储器的访问,实现了波场模拟的GPU加速.单CPU和GPU/CPU下不同规模网格的波场模拟结果表明:利用GPU加速可以将模拟效率提高数倍.尤其是当模拟大规模网格且炮点个数较多时,可以更加显著的提升模拟效率.     

2D surface topography boundary conditions in seismic wave modelling

New formulations of boundary conditions at an arbitrary two-dimensional (2D) free-surface topography are derived. The top of a curved grid represents the free-surface topography while the grid's interior represents the physical medium. The velocity–stress version of the viscoelastic wave equations is assumed to be valid in this grid. However, the rectangular grid version attained by grid transformation is used to model wave propagation in this work in order to achieve the numerical discretization. We show the detailed solution of the particle velocities at the free surface resulting from discretizing the boundary conditions by second-order finite-differences (FDs). The resulting system of equations is spatially unconditionally stable. The FD order is gradually increased with depth up to eighth order inside the medium. Staggered grids are used in both space and time, and the second-order leap-frog and Crank–Nicholson methods are used for time-stepping. We simulate point sources at the surface of a homogeneous medium with a plane free surface containing a hill and a trench. Applying parameters representing exploration surveys, we present examples with a randomly realized surface topography generated by a 1D von Kármán function of order 1. Viscoelastic simulations are presented using this surface with a homogeneous medium and with a layered, randomized medium realization, all generating significant scattering.     

基于波动方程理论的地震波场数值模拟方法综述

地震波场数值模拟的重要性日益凸显,其在地震勘探、各向异性介质属性研究、强地面振动预测、理论地震图合成等方面的应用日渐增多.基于波动方程理论的模拟方法有很多,如:有限差分法、伪谱法、有限元法、谱元法、边界元法等,而现有的综述性文献仅仅是关注某一种或是几种算法,还未有融入最新的文献后系统论述以上五种方法的综述性文献.鉴于此...     

T-matrix approach to seismic forward modelling in the acoustic approximation

Forward seismic modelling in the acoustic approximation, for variable velocity but constant density, is dealt with. The wave equation and the boundary conditions are represented by a volume integral equation of the Lippmann-Schwinger (LS) or Fredholm type. A T-matrix (or transition operator) approach from quantum mechanical potential scattering theory is used to derive a family of linear and nonlinear approximations (cluster expansions), as well as an exact numerical solution of the LS equation. For models of 4D anomalies involving small or moderate contrasts, the Born approximation gives identical numerical results as the first-order t-matrix approximation, but the predictions of an exact T-matrix solution can be quite different (depending on spatial extention of the perturbations). For models of fluid-saturated cavities involving large or huge contrasts, the first-order t-matrix approximation is much more accurate than the Born approximation, although it does not lead to significantly more time-consuming computations. If the spatial extention of the perturbations is not too large, it is practical to use the exact T-matrix solution which allows for arbitrary contrasts and includes all the effects of multiple scattering.     

线性粘弹体中地震波场伪谱法模拟技术

以积分本构方程为基础,应用对应原理建立线性粘弹体中的波动方程,采用伪谱法进行数值模拟.实际计算结果表明该方法能有效模拟标准线性粘弹体中地震波的传播.     

Homotopy scattering series for seismic forward modelling with variable density and velocity

We have derived a convergent scattering series solution for the frequency-domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann–Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann–Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann–Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like $N^3$, where $N$ is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann–Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so-called homotopy analysis method to derive an iterative solution for the vectorial Lippmann–Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as $N^2$. Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three-layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.     

One-way wave equation seismic prestack forward modeling with irregular surfaces

Mathematical geophone （MG） and equal-time stacking （ETS） principles are used to implement seismic prestack forward modeling with irregular surfaces using the oneway acoustic wave-equation. This method receives seismic primary reflections from the subsurface using a set of virtual MGs. The receivers can be located anywhere on an irregular observing surface. Moreover, the ETS method utilizes the one-way acoustic wave equation to easily and quickly image and extrapolate seismic reflection data. The method is illustrated using high single-noise ratio common shot gathers computed by numerical forward modeling of two simple models, one with a flat surface and one with an irregular surface, and a complex normal fault model. A prestack depth migration method for irregular surface topography was used to reoroduce the normal fault model with high accuracy.     

复杂地表的单程波动方程地震叠前正演

作者基于数学检波器和等时叠加原理,实现了复杂地表的单程波动方程地震叠前正演模拟。该方法采用虚拟的数学检波器接收地下的反射地震信号,灵活地将接收点布置在地表的任何地方,从而满足地表起伏的要求。此外,根据等时叠加原理, 该方法采用单程波动方程进行波场延拓和成像,计算简单快速。通过复杂正断层的数值模拟,得到了高信噪比的共炮集地震记录,并采用适用于起伏地形的深度偏移方法对该共炮集地震记录进行了叠前深度偏移,较好地实现了地震波的偏移归位,从而证明了这里提出的起伏地表的单程波动方程地震叠前正演方法是正确和有效的。     

Fast and accurate calculation of seismic wave travel time in 3D TTI media

The Tilted tilted transversely isotropic(TTI)media,a kind of anisotropic medium,widely exists within the earth.For faster calculation of travel times in the TTI...     

Shear wave velocity modelling in crustal rock for seismic hazard analysis

P-wave velocity data along with the thickness of sedimentary and crystalline layers within bedrock were collected from all global regions and presented in the Global Crustal Model CRUST2.0, published in 2001. This well-organised database provides invaluable potential contributions towards future seismic hazard modelling, particularly for stable continental regions (SCRs), where there is a scarcity of representative strong motion records for conventional modelling purposes. The P-wave velocity information presented in CRUST2.0 has been converted herein to S-wave velocity information. The latter is especially important for purposes of seismic hazard modelling. The value of the CRUST2.0 model has therefore been greatly enhanced by the important findings presented and further developed in this paper. By making the best use of available information on crustal conditions, the amplification behaviour of seismic waves affecting a region, an area or a site for any given earthquake scenario may be predicted. The developed methodology, which is intended for worldwide applications, has been illustrated by case studies in which model S-wave velocity profiles were developed for different geological regions within North America. The model profiles were found to be in excellent agreement with field measurements reported for each respective region.