线性反演最小二乘叠前偏移的矩阵形式解析

Matrix representation of least square prestack migration based on linearization

最小二乘偏移是一种基于线性化反演理论的保幅成像方法。本文根据最小二乘偏移成像的基本理论,通过对波场传播算子、最小二乘成像以及Hessian算子的矩阵表达形式的详细分析,阐述了最小二乘偏移方法的数学物理含义,进而指出最小二乘偏移与常规偏移之间的关系。最后通过对理论模型的数值试验表明,最小二乘偏移较常规偏移具有更高的分辨率和保幅特性。

Least square migration(LSM)is an amplitude-preserved migration method based on linearized inversion imaging theory.According to the basic theory of LSM,we explain in this paper the mathematical and physical meaning of LSM by analyzing concretely the propagation operator of seismic wave,least square imaging,and matrix representation of Hessian operator.Then we formulate the relationship between LSM and conventional migration.Numerical experiments show that LSM owns better imaging resolution and amplitude preserved property than conventional migration method.