Two dimensional seismic modelling by finite element legendre polynomial condensation technique

A two dimensional forward modelling algorithm allowing anisotropy in density and wave propagation velocity for any geological model solves the wave equation by using the Finite Element Method. The condensation of global matrices is achieved by introducing hierarchical modes in the form of Legendre Polynomials. This does not only reduce the memory requirements and overall computational time to a great extent but also enables one to develop algorithms which are suitable for either multiple processors or mini- computers. The algorithm was successfully applied to simulate both the normal incidence and shot profile seismograms on several geological models by using an expansion of ten polynomials. Usually the harmonic modes associated with the deformation being simple, the simulation could have been done by using lower order polynomials. But the real earth models posses more complex modes and hence an allowance for higher order polynomials is kept in the program. A convergence test is also carried out both in space and time. The results presented in this paper indicate the efficiency and accuracy achieved by this method and its feasibility in computing synthetic seismograms for complex geological structures.