频率多尺度全波形速度反演  

Frequency multiscale full-waveform velocity inversion

作　　者：张文生[1] 罗嘉[1] 滕吉文[2] 

机构地区：[1]中国科学院数学与系统科学研究院、计算数学与科学工程计算研究所、LSEC,北京100190 [2]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学报》2015年第1期216-228,共13页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(11471328);973项目(2010CB731503)资助

摘　　要：以二维声波方程为模型,在时间域深入研究了全波形速度反演.全波形反演要解一个非线性的最小二乘问题,是一个极小化模拟数据与已知数据之间残量的过程.针对全波形反演易陷入局部极值的困难,本文提出了基于不同尺度的频率数据的"逐级反演"策略,即先基于低频尺度的波场信息进行反演,得出一个合理的初始模型,然后再利用其他不同尺度频率的波场进行反演,并且用前一尺度的迭代反演结果作为下一尺度反演的初始模型,这样逐级进行反演.文中详细阐述和推导了理论方法及公式,包括有限差分正演模拟、速度模型修正、梯度计算和算法描述,并以Marmousi复杂构造模型为例,进行了MPI并行全波形反演数值计算,得到了较好的反演结果,验证了方法的有效性和稳健性.Inverse problems arise naturally in oil geophysical exploration.In order to detect the structures of oil/gas objects,one of the most important step in seismic data processing is that we need to know the velocity information of subsurface.This belongs to scope of seismic inversion.There are various seismic inversion methods to achieve the goal,for example the seismic tomography based on ray tracing and the conventional velocity analysis based on CDP stack.Currently,the popular method is the full-waveform inversion（FWI）method based on wave equations.The FWI method uses the prestack data rather than the poststack data as an input and has high accuracy to image complicated velocity structures.The inversion can be implemented in the time domain or in the frequency domain.While there are many works of frequency-domain FWI methods,here we focus on the time-domain FWI method and try to inverse complicated velocity structures.Mathematically,the prestack data can be obtained by the forward modeling of wave equations.The seismic waves generated by a Ricker wavelet source propagate through the underground media.When the waves encounter the interfaces or inhomogeneous objects with different physical parameters,they are reflected back to the surface.These reflected waves are received by the geophones on the surface and used for inversion or other seismic data processing.This process is usually modeled by wave equations such as the acoustic wave equation if we assume the underground media is acoustic.In this paper,we investigate the full-waveform velocity inversion based on the 2-D acoustic wave equation and the corresponding computations are completed in the time domain.The forward problem is to solve the acoustic wave equation numerically and obtain the prestack data.Many numerical methods can be used to solve the forward problem,for example,the finite element method and the finite volume method and so on.In this paper we adopt the finite difference method because of easy programming and its high efficiency.Since the comp

关 键 词：声波方程 频率多尺度 时间域 全波形反演 速度 BFGS MARMOUSI模型 有限差分法 MPI并行 

分 类 号：P315[天文地球—地震学]