Study Of Finite-element's Centred Mass Matrix And Parallel Algorithm On Simulation Of Seismic Wave

Seismic numerical simulation is one of the most significant subjects in the seismic exploration, and the results affect the qualities of the seismic processing and interpretation. There are some methods, and finite-element is the more important one. Finite-element has some advantages, the arbitrary forms of the finite element, numerical approximation on the irregular interfaces and so on. When seismic simulation is carried out via finite-element method,using Sarma damping boundary condition will cause the spurious reflections on the interfaces between the medium region and the damping region. The spurious reflections were induced by the abrupt change between the two regions. In order to avoiding the spurious reflections, a proportion coefficient was introduced and its value is increasing from zero to a constant in the transition region which is located in the damping region. By this mean we weaken the abruptness on the interfaces, meanwhile the wave in damping region is absorbed perfectly without expanding the damping region.The computational formula of consistent mass matrix derived from the variational principles is the same as the stiffness matrix's, therefore the consistent mass matrix can describe the mass distributing of the finite element. But the consistent mass matrix is a sparse matrix, so there is too much data and volume calculation. When the mass matrix and the stiffness matrix are regard as the three block-tridiagonal matrixes, finite-element equation can be solved by the parallel algorithm for block-tridiagonal linear systems. The numerical simulation results prove that the parallel algorithm is correct and feasible.When the finite element is so small that the nodes of the same finite element can seem as to have the same accelerations, the centred mass matrix was used to substitute for the consistent mass matrix, and the precision isn't below the consistent mass matrix's. The centred mass matrix is a diagonal-matrix, and the stiffness matrix can be compressed, thus the data quantity and the calculation amount are saved. 3D seismic numerical simulation can truly simulate the actual seisimic wave and provide 3D characteristics of the wave field. Finite-element equation using the centred mass matrix is solved in the 3D. The numerical simulation by the parallel algorithm expands the simulation space.