精确常Q分数阶黏声波方程的近似与正演模拟  

Approximation and forward simulation of accurate constant Q fractional viscoacoustic equation

作　　者：韦增涛 熊高君[1] 谢明志 WEI Zengtao;XIONG Gaojun;XIE Mingzhi(College of Geophysics,Chengdu University of Technology,Chengdu 610059,China)

机构地区：[1]成都理工大学地球物理学院,成都610059

出　　处：《物探化探计算技术》2025年第2期179-189,共11页Computing Techniques For Geophysical and Geochemical Exploration

摘　　要：相比整数阶波动方程,分数阶黏声波方程能够更准确地表征常Q模型中地震波的传播特点,有效分离波的振幅衰减与相位频散效应,是模拟地震波的衰减特性以及发展稳定的衰减补偿逆时偏移方法的基础。传统黏声波方程采用的近似频散关系降低了方程的精度,笔者根据更为精确的频散关系推导了一个新的分数阶黏声波方程,分别与前人提出方程中的振幅衰减项与相位频散项对比,结果表明在小Q值介质中新方程更精确。该方程含有空间变分数阶拉普拉斯算子,在Q值剧烈变化的介质中需要正确处理该算子,避免在计算时产生周期性干扰。笔者提出了帕德逼近的方法将变分数阶算子近似为常分数阶算子。在层状模型与复杂模型中,对比了传统空间平均值法以及泰勒展开法,帕德逼近法提高了计算效率且保证了良好的近似效果。Compared to the integer-order wave equation,the fractional viscoacoustic wave equation more accurately characterizes the propagation features of seismic waves in the constant-Q model.It effectively separates amplitude attenuation and phase dispersion effects,providing a foundation for simulating seismic wave attenuation and developing stable attenuation compensation reverse-time migration(RTM)methods.Due to approximate dispersion relations,the accuracy of traditional viscoacoustic vibroacoustic wave equations is reduced.This paper derives a new equation based on a more accurate dispersion relation,comparing its amplitude attenuation and phase dispersion terms with previous equations.The results show that the new equation is more precise in low-Q media.The equation involves a spatially varying fractional Laplacian operator,which must be handled carefully in media with significant Q variations to avoid periodic interference during computations.This paper proposes a Padéapproximation method to approximate the varying fractional operator with a constant fractional operator.In model experiments,compared to the averaging method and Taylor expansion,the Padéapproximation improves computational efficiency while ensuring approximation accuracy.

关 键 词：黏声波方程 变分数阶拉普拉斯算子 泰勒展开 帕德逼近 

分 类 号：P631.4[天文地球—地质矿产勘探]