地震数据的反射波动方程最小二乘偏移

Least squares migration of seismic data with reflection wave equation

基于反射波动方程,本文提出了一种估计地下反射率分布的地震数据最小二乘偏移方法.高频近似下,非齐次的一次反射波动方程的源项是由反射率与入射波场的时间一阶导数相互作用产生的.根据反射波动方程,利用线性最小二乘反演方法由地震反射数据重建出地下产生反射波的反射源,再结合波场正演计算出的地下入射波场,得到地下反射率分布的估计.在地下反射源的线性最小二乘反演重建中,我们采用迭代求解方法,并以地震波的检波器单向地下照明强度作为最小二乘优化问题中Hessian矩阵的近似.

We proposed a least squares migration method of seismic data for the estimation of subsurface reflectivity distribution based on reflection wave equation.Under high frequency approximation,the source term of inhomogeneous primary reflection wave equation is generated by the interaction between the reflectivity and the first order derivative of incident wavefield with respect to time.According to the reflection wave equation,we used the linear least squares inversion to recover the subsurface reflection source generating reflection wave from seismic reflection data,then to obtain the estimation of subsurface reflectivity distribution from the recovered reflection source by combining the subsurface incident wavefield calculated by forward modeling.In the reconstruction of the subsurface reflection source with the linear least squares inversion,we adopted the iterative manner for the solution,and used the seismic wave illumination intensity of the receiver direction as the approximation of Hessian matrix of the least squares optimization problem.