2.5维地震波数值模拟评述:声波模型
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摘要
本文的目的是对基于声波模型的2.5维地震波数值模拟工作进行评述,以便能够找出其存在的问题和解决这些问题的可能途径.根据定义,2.5维问题是三维问题中的一种特殊情况,其特点是:(1)介质参数沿走向保持为常数;(2)场源具有球对称性;(3)场源和接收点均位于垂直于走向的直线上.与三维数值模拟问题不同,2.5维数值模拟问题分为两部分:(1)在垂直于走向的平面内用数值方法解相应的微分方程,这在实质上是二维问题;(2)采用积分变换或其他方法处理来自于计算平面外的影响,这实际上是将一个特殊的三维问题转化成为了无限多个(在离散情况下是有限多个)二维问题的叠加.与二维模型相比,2.5维模型能得到计算平面内的精确地震波振幅信息.鉴于声波模型是反射地震偏移成像理论和应用研究中的基本数据模型,所以对2.5维声波数值模拟的研究具有重要的意义.根据对计算平面外传播效应的处理方式可以将到目前为止提出的2.5维声波数值模拟方法分为四类:(1)几何射线法;(2)滤波校正法;(3)Fourier变换法;(4)近似波动方程法.其中,几何射线法具有直观、快速的特点,但是在焦散区内失效.滤波校正法只在均匀介质条件下严格成立,在一般条件下只是一种精度难以估计的近似.Fourier变换法是一种经典方法,其研究程度已经相当深入.该方法的基本思想是通过沿走向的Fourier变换将2.5维问题转化为有限多个二维问题.从而,对反变换的数值实现直接影响到该方法的精度和效率.近似波动方程法的宗旨是针对2.5维波动问题建立专门的波动方程.与Fourier变换法相比,近似波动方程法等同于一个二维数值模拟,因此可以大大地降低计算量.但是,根据笔者所掌握的资料,到目前为止提出的几个近似波动方程不是具有很大的振幅误差,就是难以进行数值计算.因此,有必要对近似波动方程的形式进行进一步的研究.
The purpose of this paper is to review the published work related to acoustic modeling of seismic waves,with the aims of finding unsolved problems and of giving possible ways for treating the problems.By definition,2.5D modeling problem is a special case in 3D modeling problems and has the following features:(1) the physical parameters remain unchanged along the strike direction;(2) the source possesses a spherical symmetry;and(3) both the sources and the receivers are located along a line perpendicular to the strike.Different from 3D modeling,a 2.5D modeling consists of two parts:(1) numerical analysis of the corresponding partial differential equation in the plane perpendicular to the strike(computation plane),this is in principle a 2D problem;and(2) including the influence of the out-of-plane direction on the wavefield by using integral transform or by using other methods,this actually transforms a special 3D problem into the superposition of infinitely many(for continuous cases) or finitely many(for discrete cases) of 2D problems.In comparison to 2D models,2.5D models can give accurate amplitude information of seismic waves in the computation plane.Since the acoustic model is used as the basic data model in reflection seismic imaging,it is of importance to investigate 2.5D acoustic modeling methods.According to the method used for treating the propagation in the out-of-plane direction,the 2.5D acoustic modeling methods appeared in the literature so far can be classified into four types,namely(1) geometrical ray method;(2) filter factor correction method;(3) Fourier transform method;and(4) approximate wave equation method.Among these methods,the geometrical ray method is fast and straightforward.However,it breaks down in the focal region.The filter correction method is exact only in homogeneous media.Thus,under general conditions the method gives only an approximation with an unknown accuracy.The Fourier transform method is a classical method for treating 2.5D problems and has been investigated quite thoroughly.The basic idea of the method is to transform a 2.5D problem into multiple 2D problems by using Fourier transform along the strike.As a result,the accuracy and efficiency of the method depend strongly on the implementation method of the inverse Fourier transform.The purpose of the approximate wave equation method is to derive a wave equation solely for 2.5D case.In comparison to the Fourier transform method,the approximate wave equation method is equivalent to a single 2D modeling.Consequently,the method needs much less computation time than the method based on the Fourier transform.However,to the author's knowledge,some of the 2.5D wave equations published in the literature cannot model the amplitude correctly under general conditions,and the others have a form not favorable for numerical analysis.Therefore,it is necessarily to study the 2.5D wave equation method in the future work.
The purpose of this paper is to review the published work related to acoustic modeling of seismic waves,with the aims of finding unsolved problems and of giving possible ways for treating the problems.By definition,2.5D modeling problem is a special case in 3D modeling problems and has the following features:(1) the physical parameters remain unchanged along the strike direction;(2) the source possesses a spherical symmetry;and(3) both the sources and the receivers are located along a line perpendicular to the strike.Different from 3D modeling,a 2.5D modeling consists of two parts:(1) numerical analysis of the corresponding partial differential equation in the plane perpendicular to the strike(computation plane),this is in principle a 2D problem;and(2) including the influence of the out-of-plane direction on the wavefield by using integral transform or by using other methods,this actually transforms a special 3D problem into the superposition of infinitely many(for continuous cases) or finitely many(for discrete cases) of 2D problems.In comparison to 2D models,2.5D models can give accurate amplitude information of seismic waves in the computation plane.Since the acoustic model is used as the basic data model in reflection seismic imaging,it is of importance to investigate 2.5D acoustic modeling methods.According to the method used for treating the propagation in the out-of-plane direction,the 2.5D acoustic modeling methods appeared in the literature so far can be classified into four types,namely(1) geometrical ray method;(2) filter factor correction method;(3) Fourier transform method;and(4) approximate wave equation method.Among these methods,the geometrical ray method is fast and straightforward.However,it breaks down in the focal region.The filter correction method is exact only in homogeneous media.Thus,under general conditions the method gives only an approximation with an unknown accuracy.The Fourier transform method is a classical method for treating 2.5D problems and has been investigated quite thoroughly.The basic idea of the method is to transform a 2.5D problem into multiple 2D problems by using Fourier transform along the strike.As a result,the accuracy and efficiency of the method depend strongly on the implementation method of the inverse Fourier transform.The purpose of the approximate wave equation method is to derive a wave equation solely for 2.5D case.In comparison to the Fourier transform method,the approximate wave equation method is equivalent to a single 2D modeling.Consequently,the method needs much less computation time than the method based on the Fourier transform.However,to the author's knowledge,some of the 2.5D wave equations published in the literature cannot model the amplitude correctly under general conditions,and the others have a form not favorable for numerical analysis.Therefore,it is necessarily to study the 2.5D wave equation method in the future work.
引文
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