基于点扩散函数的黏声介质反演成像

从弹性波基本方程出发,分析了地震波吸收与衰减补偿物理机制和黏声介质中应力-应变关系,得到了衰减与补偿统一表达的黏声介质传播方程。采用交错网格有限差分和最佳匹配层吸收边界条件来模拟这一方程,实现了黏声介质地震波场吸收与补偿的格林函数计算。凹陷速度模型测试结果表明,该方法能有效补偿吸收衰减振幅。从Hessian核函数的数学物理特征出发,对比分析了声波点扩散函数(PSF)和黏声波点扩散函数,结果表明,吸收衰减效应显著降低了照明振幅强度,带吸收衰减的PSF明显比声介质PSF能量低,在深层这种能量损耗更为强烈;吸收衰减效应改变了观测系统对地下的照明图样。进行了面向目标体的PSF分解和求逆,并将求得的逆算子直接作用于成像结果。盐丘模型测试结果表明,在盐丘周围,吸收衰减效应显著降低了成像分辨能力,精确的逆PSF能够有效提高反演成像结果的分辨率。

In this study,the physical mechanism of absorption attenuation and compensation for seismic wave are analyzed.Based on the fundamental equations of elastic wave theory,we derived the propagation equation with a uniform expression,which considers the stress-strain relationship in the viscoelastic medium.We used the finite difference with staggered grid and PML absorption boundary conditions to solve this equation,and calculated the Greens function for forward and backward propagation of wavefields in viscoacoustic media.The test results of the sag velocity model showed that the method can effectively compensate the absorption attenuation of wavefields in viscoacoustic media.Based on mathematical physical characteristics of Hessian kernel function,we compared the point spreading function (PSF) with and without Q compensation.Results showed that PSF can represent the resolution ability of the observation system for the target points in different directions.We performed PSF decomposition and inversion for targets,then applied the inverted PSF to the imaging results.The test results of a salt model showed that the effective inversed PSF can improve the resolution of inversion imaging,which was reduced by the absorption attenuation around the salt.

国家自然科学基金项目(41674123,41574098)、中央高校基本科研业务费专项资金项目(2018QNA3013)和中国石化地球物理实验室开放基金项目共同资助。