The 3D acoustic wave equation for a heterogeneous medium is used for the seismic modeling of compressional (P-) wave propagation in complex subsurface structures. A combination of finite difference and finite integral transform methods is employed to obtain a “2.5D” solution to the 3D equation. Such 2.5D approaches are attractive because they result in computational run times that are substantially smaller than those for the 3D finite difference method. The acoustic parameters of the medium are assumed to be constant in one of the three Cartesian spatial dimensions. This assumption is made to reduce the complexity of the problem, but still retain the salient features of the approach. Simple models are used to address the computational issues that arise in the modeling. The conclusions drawn can also be applied to the more general fully inhomogeneous problem. Although similar studies have been carried out by others, the work presented here is new in the sense that (i) it applies to subsurface models that are both vertically and laterally heterogeneous, and (ii) the computational issues that need to be addressed for efficient computations, which are not trivial, are examined in detail, unlike previous works. We find that it is feasible to generate true-amplitude synthetic seismograms using the 2.5D approach, with computational run times, storage requirements, and other factors, being at reduced and acceptable levels.
Practical Quantum Computing