Spectral-difference parallel algorithm for the seismic forward modeling in the presence of complex topography

A spectral-difference parallel algorithm for modeling acoustic and elastic wave fields for the 2.5D geometry in the presence of irregular surface topography is considered. The initial boundary-value problem is transformed to a series of boundary-value problems for elliptic equations via the integral Laguerre transform with respect to time. For solving difference equations, it is proposed to use efficient parallel procedures based on the fast Fourier transform and the dichotomy algorithm, the latter was designed for solving systems of linear algebraic equations (SLAEs) with tridiagonal and block-tridiagonal matrices. A modification of the dichotomy algorithm for diagonally dominant matrices, which makes it possible to reduce the time of preparatory computations and increase scalability of the method relative to the number of processors, is considered. The influence of different methods of curved boundary approximation on the quality of solution is investigated; practical evaluation of accuracy is performed. Calculations of the wave field with the use of high-resolution meshes for the Canadian Foothills medium model are presented. Implementation of the complex frequency-shifted PML boundary conditions for a dynamic elasticity problem is considered in the context of the spectral-difference approach.