An efficient least-squares reverse time migration in image domain

The results of least-squares migration have higher fidelity and spatial resolution than that of conventional migration. In this paper, an efficient method for least-squares reverse time migration in imaging domain (IDLSRTM) is proposed by using spatial de-convolution. Given a smooth velocity model with accurate kinematics of seismic wave used for migration (only the migration based on scalar wave equation is considered), the conventional reverse time migration (RTM) can be viewed as one kind of rough solution to the linear inversion problem of subsurface reflectivity. In image domain, the conventional reverse time migration results are a spatial-variant integral of the least-squares reverse time migration results and Hessian matrix. Different column vectors in the Hessian matrix can be regarded as the point spread functions of different imaging points in imaging domain. Because of the smoothness of migration velocity model and the multifold of seismic data acquisition system, the point spread functions of imaging points in a certain local region have well similarity. Therefore, the conventional reverse time migration results can be approximately represented as a spatial-invariant convolution between the least-square reverse time migration results and the Hessian matrix in the local region, and then a least-square reverse time migration method in image domain based on the local region spatial-invariant de-convolution is proposed. The spatial-invariant de-convolution can be efficiently and stably realized by using the pseudo-generalized inverse approach to spatial-invariant de-convolution in wavenumber domain. The size of local region is a trade-off between the efficiency and the effect of the least-square reverse time migration. The method proposed in this paper is applied to synthetic and field seismic data, ideal results are obtained.