Elastic Corrections to Acoustic Finite-difference Simulations – Plane-wave Analysis and Examples

Acoustic finite-difference modelling is playing an increasingly important role in seismic imaging (e.g. in reverse time migration) but the additional cost of elastic finite-difference modelling restricts its use in commercial imaging technology. The cost of full elastic finite-difference modelling can exceed the cost of acoustic modelling in the same velocity model by two orders of magnitude or more. A technique is discussed that corrects an acoustic finite-difference simulation for elastic effects. It is based on estimating the error incurred when using the acoustic wave equation as an approximate solution to the elastic wave equation. The errors are used to generate an effective source field for an additional acoustic simulation that calculates a correction to the wavefield produced in the original acoustic simulation. The cost of this approach is roughly twice that of an acoustic simulation and therefore much less than that of a full elastic simulation. Plane wave theory is used to examine the properties of the method and results from finite-difference simulations are presented to illustrate its accuracy.