Efficient depth extrapolation of waves in elastic isotropic media

Conclusions and Discussion

The method presented in this paper can be used in seismic migration algorithms in order to achieve a substantial reduction of run time in comparison with reverse time migration. More specifically, stability of the time-domain modeling typically utilized in the reverse-time migration requires time steps significantly smaller than the time resolution of seismic data (see (Biondi, 2005)). Depth extrapolation of wave fields using one-way equations 10 and 12 can be performed for an arbitrary frequency range. Extrapolating wave fields in the frequency domain using two-way system 3 would require solving a large sparse system of equations using e.g. a finite element method, still posing significant computational challenges for inhomogeneous media. However, the one-way extrapolation method, while limited in dip and less accurate in terms of amplitudes, lends itself to efficient implementation using e.g. PSPI or finite differencing. Furthermore, the approach of this paper can be expected to apply to more complex elastic anisotropic models (see (Grechka, 2009)) and may be developed into a computationally efficient alternative to the existing pseudo-acoustic anisotropic modeling methods while allowing easy separation of pressure and shear waves.

Efficient depth extrapolation of waves in elastic isotropic media