Full Waveform Inversion (FWI) on acoustic seismic data is based on data prediction using an updated velocity model. The key concept in the updating process is calculating the gradient of a miss-fit function, which is the difference between actual data and the predicted data. In each step, the gradient function, in either the time or frequency domain, is estimated by depth migration algorithms.
We have developed a fast full waveform inversion scheme that is based on the Pre-Stack Time Migration (PSTM). We use the forward Kirchhoff operator for prediction of shot records from the reflectivity function. Then, we derive the wavefield perturbation as a result of the velocity perturbation. Then we derive the adjoint operator for velocity perturbation using shot perturbation. This result is similar to a solution of the inverse problem as Prestack Kirchhoff Time Migration (PSTM) and crosscorelation with the source wavelet.
The methodology is fast compared to any PSDM techniques in forward and inverse iterations; however, our forward operator is assumed to be linear with negligible lateral velocity change. Therefore, since we are doing time migration, we are limited to models without complex structures. We have tested the theory on left portion of Marmousi as shown in Figure 1.
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