基于地震波方程的地震数据波形偏移与最小二乘波形偏移方法

针对当前岩性油气藏和页岩油气藏勘探对地震数据偏移成像高精度和高分辨的需求,对当前常见的偏移、偏移照明补偿和最小二乘偏移进行了简要回顾和评述。根据地下非均匀体的大小和速度变化与地震波长之间的相对关系,将非均匀体划分为散射体和反射体,相应地产生散射波和反射波。在散射理论的基础上,推导得到了描述散射波传播和散射的散射波方程。利用高频近似,推导得到了两种描述反射波的反射波方程,即基于速度相对扰动的反射波方程和基于反射面上反射率的反射波方程。将得到的散射波方程和反射波方程作为地震散射数据和反射数据的正演方程,利用线性反演方法,分别提出了地震散射数据和反射数据的的波形偏移与最小二乘波形偏移。地震反射数据的波形偏移与最小二乘波形偏移包括了目标分别为速度相对扰动和反射率两种不同形式的波形偏移与最小二乘波形偏移。

In view of the needs for high fidelity and high resolution of seismic migration in the explorations of lithologic reservoirs and shale reservoirs,a brief review is presented on current migration,migration with illumination compensation,and least-squares migration.According to the relative relationship between seismic wavelength with volume and velocity variation of inhomogeneous body,an inhomogeneous body is divided into a scatterer and reflector,which would generate scattered waves and reflected waves,respectively.Based on scattering theory,a scattering wave equation is derived to describe the propagation of scattered waves.Using high frequency approximation,two kinds of reflection wave equations are derived from the scattering wave equation:one is the reflection wave equation based on the relative perturbation of velocity,and the other is the reflection wave equation based on the reflectivity of the reflection interface.Using the scattering wave equation and the reflection wave equations as the forward equations for scattering seismic data and reflection seismic data,respectively,a waveform migration and a least-squares waveform migration for the two kinds of seismic data are proposed using a linear inversion approach.The waveform migration and the least-squares waveform migration for the reflection seismic data are both implemented for two aims,namely,the relative perturbation of velocity and the reflectivity,respectively.

国家自然科学基金项目(41074133,41374001)、国家科技重大专项(2016ZX05033002)和中国石化地球物理重点实验室开放基金项目(WTY-WX-2015-04-01,WTY-WX-2015-04-02,WTY-WX-2015-04-03,WTY-WX-2015-04-04)共同资助。