基于反射波动方程的地震反射数据波形成像  

Seismic reflection data waveform imaging based on reflection wave equation

作　　者：陈生昌[1] 

机构地区：[1]浙江大学地球科学学院,浙江杭州310027

出　　处：《石油地球物理勘探》2018年第3期487-501,共15页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(41074133;41374001);国家重大专项(2016ZX05033002);中国石化地球物理重点实验室开放研究基金联合资助

摘　　要：在有关波现象和地下介质物理性质空间变化的高频近似条件下,散射波退化为反射波,相应的散射波动方程退化为基于阻抗相对扰动的反射波动方程;再通过定义反射率为阻抗相对扰动沿入射波传播方向的方向导数,推导出基于反射率变化的反射波动方程。利用推导出的反射波动方程和线性反演理论,建立基于反射波动方程的地震一次反射数据波形成像方法。根据基于阻抗相对扰动的反射波动方程和基于反射率变化的反射波动方程,首先应用反射波传播算子的伴随算子,建立阻抗相对扰动近似反演方法和反射率波形偏移方法;再应用反射波传播算子的最小二乘逆算子,建立阻抗相对扰动最小二乘反演方法和反射率最小二乘波形偏移方法。针对波场传播算子的最小二乘逆算子的巨大计算量和不稳定性,在阻抗相对扰动的最小二乘反演和反射率的最小二乘波形偏移中均采用迭代方式求解。本文提出的波形成像方法,可在波动方程意义下真实地应用地震数据的波形信息,因此是真正的波动方程偏移成像方法。Under the high frequency approximation on wave phenomena and spatial variations of physical parameters of subsurface medium,scattering waves degrade into reflection waves,and the corresponding scattering wave equation degrades into reflection wave equation based on impedance relative perturbation.Reflection wave equations based on the reflectivity is derived through the definition of reflectivity as the directional derivative of the impedance relative perturbation with respect to the propagation direction of incident wave.Using these reflection wave equations and the linear inverse theory,we establish a waveform imaging method based on reflection wave equations for seismic primary reflection data.According to the reflection wave equation based on the impedance relative perturbation and the reflection wave equation based on the reflectivity,we first apply adjoint operators of reflection wave propagator to establish an approximate inversion of impedance relative perturbation and a reflectivity waveform migration,then reapply the least squares inverse operator of refection wave propagator to establish a least squares inversion of impedance relative perturbation and a reflectivity least squares waveform migration.Aiming at the huge amount of calculation and the instability of the least squares inverse operator of reflection wave propagator,we use an iterative solution to the least squares inversion of impedance relative perturbation and the reflectivity least squares waveform migration.The waveform imaging method proposed in this paper can faithfully use the waveform information of seismic data in the sense of wave equation,and it is a real wave equation migration imaging.

关 键 词：地震反射数据 反射波动方程 阻抗相对扰动 反演 反射率 波形偏移 

分 类 号：P631[天文地球—地质矿产勘探]