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Simulating and imaging wavefield of irregular topography based on spectral element method

For the high-precision seismic imaging of complex structures on irregular topographies, this study proposes a Chebyshev spectral-element reverse time migration (CSE-RTM) method coupled with the implicit Newmark time integral method. The approach is first applied to a numerical example to consider factors affecting numerical accuracy, such as the time step and the pattern of subdivision of the computational domain. The results show that the smaller the time step is, the higher the numerical accuracy is and that numerical accuracy improves when the grid nodes tend to be distributed uniformly in the computational domain. The spectral element method combines the advantages of the stronger boundary-related adaptability of the finite element method with the high accuracy and fast convergence of the spectral method. This method is applied to reverse time migration imaging, and tests of the model show that its accuracy of imaging is higher than that of the conventional finite-difference reverse time migration method in case of complex structures in areas with irregular topography. To improve the efficiency of parallel computing of the CSE-RTM, an iterative algorithm is proposed to solve the hierarchical equilibrium sparse linear equations (HELPs) for it based on the idea of the degrees of cohesion of freedom and local relaxation. This algorithm has the advantage that the efficiency of parallel computation does not decrease with an increasing number of processors while the number of iterations required for convergence is controlled. Owing to the fast convergence of the spectral method on a sparse grid coupled with the parallel computational scheme of HELPs, the efficiency of calculation of the CSE-RTM is significantly improved.