FAST CALCULATION OF NORMAL INCIDENCE SEISMOGRAMS

Seismograms can be represented by a convolution of the source with the Green's function associated to the medium. Hence, having calculated t he Green's function the seismic response to different sources can be o btained without repeating the entire numerical procedure. A new method for the determination of the Green's function of a heterogenous mediu m is presented. It is based on the numerical solution of the Lippmann- Schwinger perturbation equation. This integral equation is derived fro m an interpretation of the spatially varying propagation speed as a pe rturbation of a constant reference velocity. It can be solved by a sim ple quadrature method. By utilizing some symmetry properties of the Gr een's function the scheme can be reduced to a tridiagonal linear syste m which can be solved in O(N) operations. Thus the approach leads to a method which is fast and easy to implement. Because the method is for mulated in the frequency domain an easy and elegant implementation of attenuation mechanisms is possible by introducing a complex valued Fre quency dependent perturbation of the reference velocity. Numerical sol utions for some standard examples are presented. A good agreement with results obtained by the reflectivity method can be observed. A simple FORTRAN code for calculating normal incidence seismograms is appended .