Least-Squares Reverse Time Migration in Pseudodepth Domain and Its Application

Abstract

The Cartesian-based least squares reverse time migration (LSRTM) aims to obtain a relatively high-resolution amplitude preserving imaging by calculating and solving the Hessian matrix. In addition, conjugate gradient algorithm is proved to be an efficient iterative method, which makes the traditional LSRTM feasible in practical data processing applications. Each iteration process of LSRTM includes two main parts; The first part is the forward simulation of wavefield, and the second part is the back propagation of wavefield. However, the calculation of these two parts takes a lot of time, and oversampling effects will occur in the calculation process. The thesis develops a smooth understanding of the LSRTM scheme in pseudodepth domain and gives information about this type of wavefield extrapolation method to achieve amplitude-preserved image with low computational costs in terms of memory and time. The underground media faced by seismic exploration usually include low velocity bodies, high steep structures and pore fracture units. When simulating the seismic wavefield in these media, in order to ensure the simulation accuracy and computational stability by finite difference methods, the grid spacing needs to be very small, which leads to the oversampling problem of the traditional finite difference forward simulation method in Cartesian coordinate system. In order to overcome this problem, the pseudo depth domain algorithm is applied to the least-squares reverse time migration to improve its computational efficiency. The problem of stabilizing this Pseudodepth wavefield arises from the introduction of the mapping function and velocity and also the vertical axis operator that converts the finite difference solution partially from time into frequency domains. Stability and convergence analysis suggests that the spatial derivatives of Riemannian axis should be approximated by a mixed Fourier pseudo-spectral and ordinary finite-difference schemes methods using a special Gaussian-like impulse function to generate the vector-matrix of the complex source term within the finite-difference operator, in addition to the mapping velocity, which is a differential form of the initial input velocity model, manifestly controls the CFL conditions of the associated Riemannian-finite difference operator. Numerical and synthetic examples indicated that this approach is more stable and efficient in extrapolating a smooth Riemannian wavefield while maintaining Claerbout’s principle for locating subsurface reflectors also choosing an appropriate sampling rate for the new vertical axis is related inversely by the maximum frequency of the impulse wavelet and directly with minimum velocity value in the given model. The LSRTM wavefield extrapolation usually uses the two-dimensional constant density acoustic wave equation, by considering the change of velocity field distribution, and converts it to the corresponding pseudodepth domain, so as to solve the oversampling problem in the true depth domain. For each point in the Cartesian coordinate system, there is a corresponding point in the pseudo depth domain. Therefore, we can interpolate and remodel the reconstructed finite difference modelled wavefield in the new coordinate system through the Cartesian-to-pseudodepth mapping function. Regardless of the applied finite difference algorithm and boundary conditions, wavefield extrapolation in pseudodepth domain can ensure high accuracy and efficiency. Through the test of synthetic and actual data, compared with the traditional LSRTM results, pseudodepth domain LSRTM shows great potentiality in amplitude preserving imaging. On the other hand, pseudodepth domain LSRTM has great advantages in computational efficiency and ensures computational accuracy.