Synthetics and Green's functions for PREM in the Generalized Spherical Harmonic expansion
Author
Gregorian, P.
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Realistic laterally heterogeneous Earth models can be obtained by comparing synthetics to measured seismograms and by minimizing their misfit through iteratively optimizing the model parameters until a satisfactory match between synthetics and data is obtained. The derivative of the misfit with respect to the Earth model parameters can be obtained by a simultaneous calculation of a synthetic seismogram for the model and an `adjoint' wavefield originating from a fictitious source at the receiver position of the time-reversed misfit. The adjoint wavefield is given by a convolution of the misfit with the Green's function. This study provides Green's functions and synthetic seismograms for the Preliminary Reference Earth Model (PREM) using normal mode summation. The synthetics of a point source are calculated using eigenfunctions and eigenfrequencies for PREM provided by the software package \texttt{MINEOS}. The point source includes force terms which allows the calculation of Green's functions, a functionality absent in \texttt{MINEOS}. Synthetics and Green's functions for PREM could be used in the future to perform the first iteration in the optimization procedure of finding a realistic heterogeneous Earth model. To effectively solve the inverse problem of finding a realistic laterally heterogeneous Earth model, more iterations of the optimization procedure are needed, for which synthetic seismograms and Green's functions for laterally heterogeneous Earth models will be required.