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匹配Z变换完全匹配层在孔隙介质弹性波数值模拟中的应用

石油物探

2019年 58卷第No. 5期

阅读：71

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Title

Application of matched Z-transform perfectly matched layers in the numerical modeling of elastic waves in porous media

单位

中国石油天然气股份有限公司辽河油田分公司勘探开发研究院,辽宁盘锦 124010

Organization

Research Institute of Petroleum Exploration and Development,Liaohe Oilfield Company,PetroChina,Panjin 124010,China

摘要

卷积完全匹配层(CPML)虽能有效吸收各个方向入射的地震波,但其卷积算子在时间域的处理相对复杂。相较于CPML基于匹配Z变换完全匹配层(MZT-PML)能更直接地实现复频移拉伸算子。详细推导了MZT-PML在Biot方程中实现复频移拉伸算子的一般过程,并采用时域交错网格有限差分法进行离散求解,得到了更简单的复频移拉伸算子的实现算法。数值模拟结果表明,MZT-PML可有效吸收固相和流相各分量产生的虚假反射,消除大角度入射波边界反射效果甚佳。长时间能量衰减计算结果证明了MZT-PML具有长时间数值模拟稳定性。

Abstract

Convolutional perfectly matched layers (CPMLs) can effectively absorb seismic waves from numerous angles.However,the convolution operator of CPMLs is challenging to handle in time-domain modeling,and implementing the complex frequency-shifted (CFS) operator using a Z-transform perfectly matched layer (MZT-PML) is more straightforward.Here,MZT-PML is applied to model poroelastic wave propagation and a detailed derivation for implementing the CFS operator using it is given.Further,Biots equations are solved by using a time-domain staggered-grid finite-difference method,thereby allowing the proposal of an easier algorithm with which to perform CFS.Finally,numerical experiments show that MZT-PML can eliminate false reflections originating from large-angle incident waves,and calculations of long-time energy decay verified the stability of the MZT-PML in numerical simulations.

关键词：

完全匹配层; 匹配Z变换; 孔隙介质; 波动方程; 时域有限差分;

Keywords:

perfectly matched layer;; matched Z-transform;; porous media;; wave equations;; time-domain finite-difference;

基金项目

中国石油物探技术攻关项目(2016-03-02)和辽河油田千万吨稳产关键技术研究与应用项目(2017E-1602)共同资助。

DOI

10.3969/j.issn.1000-1441.2019.05.004