Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method  

基于时间辛格式的傅里叶有限差分地震波场正演（英文）

作　　者：Fang Gang Ba Jing Liu Xin-xin Zhu Kun Liu Guo-Chang 方刚;巴晶;刘欣欣;祝堃;刘国昌(国土资源部天然气水合物重点实验室青岛海洋地质研究所,青岛266071;海洋国家实验室海洋矿产资源评价与探测技术功能实验室,青岛266071;河海大学地球科学与工程学院,南京211100;中国石油大学(华东)地球科学与技术学院,青岛266580;中国石油大学(北京)油气资源与探测国家重点实验室,北京昌平102249)

机构地区：[1]The Key Laboratory of Gas Hydrate, Ministry of Land and Resources, Qingdao Institute of Marine Geology, Qingdao 266071, China [2]Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China [3]School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China [4]School of Geosciences, China University of Petroleum （East China）, Qingdao 266580, China [5]State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum-Beijing, Beijing 102249, China.

出　　处：《Applied Geophysics》2017年第2期258-269,323,共13页应用地球物理（英文版）

基　　金：supported by National Natural Science Foundation of China(41504109,41404099);the Natural Science Foundation of Shandong Province(BS2015HZ008);the project of "Distinguished Professor of Jiangsu Province"

摘　　要：Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference （symplectic FFD） method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.地震波场正演模拟是地震资料处理、解释中最为重要的技术之一。地震波场正演模拟在大时间步长、长时程的波场延拓中,存在计算不稳定的问题。本文基于声波方程的Hamilton表述,在波动方程求解中用辛差分格式进行时间网格离散,用傅里叶有限差分进行空间网格离散,提出一种新的保结构地震波场正演模拟方法一辛格式傅里叶有限差分法,在保证计算精度的同时提高计算的稳定性。利用声学近似处理空间-波数混合域的积分算子,将该方法推广至各向异性介质。给出各向同性和各向异性条件下的地震正演模拟的计算流程,并将本文方法用于BP盐丘、BP TTI等模型的波场正演模拟。数值算例表明本文开发的方法适用于速度变化剧烈的复杂介质地震波场正演模拟,计算精度高,数值频散小,在各向异性介质正演中能够有效避免qSV波残余,在大时间步长的迭代计算中稳定性好。本文为在辛算法的框架下实现高精度地震正演模拟提供了一种新的选择。

关 键 词：symplectic algorithm Fourier finite-difference Hamiltonian system seismic modeling ANISOTROPIC 

分 类 号：P631.4[天文地球—地质矿产勘探]