The conventional approach of elastic Full Waveform Inversion (FWI) requires a forward modeling and a depth migration. The forward modeling engine, which is usually based on a finite difference solution of the elastic wave equation, computes the data residual that compares the data derived from the current model with the real data from the true model. Migration is an adjoint operator of the forward modeling, which is usually based on Reverse Time Migration (RTM) on the data residual, and finds the gradient function from the current model toward the true model.
Numerically, this scheme suffers from huge computational costs associated with the time stepping of forward modeling and the migration. Assuming multiple free data and smooth lateral variation of subsurface properties, this work serves as an introduction to elastic waveform inversion using Pre-Stack Time Migration (PSTM) and the corresponding forward modeling.
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