In this paper, one-way wave equations with true amplitude are established by the decomposition of the wave field operator for wave equation in 3-D heterogeneous media. Moreover, the Split Step Fourier (SSF) and Fourier Finite Difference (FFD) migration operators with true amplitude are derived mathematically and specific steps are given.

Prestack depth migration is an important imaging method for complex geological structures. A generalizsed system for wavefield continuation based on wavefield splitting theory is presented in this paper. The system is coupled by downgoing and upgoing waves, and the commonly used equation for wavefield continuation is a special case of this coupled system. Based on an approximation of the square root operator, a new hybrid migration method with high precision is derived. The method can be implemented numerically through the splitting technique. Two examples of numerical migration are given: one is a poststack depth migration for a model with large lateral velocity contrasts; the other is a prestack depth migration for the Marmousi model with complex strucdtures. Both numerical results demonstrate the effectiveness and high precision of the hybrid method. The MPI parallel computation is adopted in order to increase computational efficiency.

The permeability identification problem for the two‐dimensional porous medium is studied by both the direct method and the optimization method. The formulation is different from the previous work. We determine the permeability from travel‐times of the fluid at every point in the domain, which can be measured in the experiment. This inverse problem can be solved into two steps. So this inverse problem can be divided into two subproblems to research. The numerical algorithm of the inversion of velocity for the two‐dimensional porous medium from the travel‐time of the fluid is studied, followed by the study of the numerical algorithm of the inversion of permeability for the two‐dimensional porous medium from the velocity. Finally the numerical examples are presented. Numerical results indicate the effectiveness and validity of the numerical algorithm used in this work.

3‐D seismic migration for an irregular acquisition geometry usually needs zero trace padding to form a regular area. The benefit of zero padding is easy to do 3‐D migration, but it will reduce the computational efficiency and migration quality. In this paper we use an additional absorbing thin layer surrounding the irregular geometry instead of zero padding. It has greatly decreased computational cost and improved the migration quality. In order to form an absorbing layer, a damping factor is added to one‐way wave equation. Since the wave field value attenuates quickly when the wave penetrates this thin layer, the reflection with the boundary condition that the wave‐field value is zero is very small. Since the migration algorithm with the zero‐boundary condition is easy to be implemented, 3‐D migration for an irregular acquisition geometry can be done directly. The effectivity of this method is illustrated by processing the practical data.