We have developed a method for implementing source wavefields in finite-difference (FD) schemes for marine seismic modeling, migration, and inversion. By using the wavefield injection technique, it is possible to inject arbitrary source wavefields into an FD grid. We have assumed that the notional source signatures from each gun in an air-gun array and their positions are known. The source wavefield is extrapolated to a specified surface below the true source positions using analytical Green’s functions. On this surface, the pressure and its vertical derivative are inserted into the FD grid. The wavefield propagating from this surface will then propagate downward and appear as if it came from the true source position. The source positions do not need to coincide with the FD grid points, and the free-surface reflection coefficient for the source ghost can be specified; i.e., it can deviate from 1, and it can be frequency dependent. These features are possible because of the analytical extrapolation step. The presented method allows modeling of any kind of marine seismic source as long as the notional source signature and radiation pattern from each individual source element is known. A simple full-waveform inversion example shows that it is important to honor the source geometry in forward modeling of seismic data.

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