Multi-scale Seismic Wave Modeling Strategy and Its Realization

The modeling operator used most frequently in reverse time migration (RTM) and full-waveform inversion (FWI) is finite-difference (FD) operator. FD is not an ideal modeling operator for RTM and FWI. An ideal modeling operator should not only get the characteristics of model and wave-field, describe them in a sparse way, but build the relationship between the velocity model and wave-field. A new modeling strategy is presented here: seismic modeling should find an ideal framework or basis to represent the velocity model sparsely and the cost of seismic wave modeling should increase with the complexity of velocity model. The modeling strategy is realized by a modeling operator which models the seismic wave in TK (time and wave-number) domain. The new modeling operator can model the wave-field efficiently if the velocity is smooth, as a smooth velocity can be described by Fourier basis sparsely. The numerical examples prove that our modeling strategy is more logical than FD.