Method of Evaluating the Interaction Between a Wavefield and a Solid Body

Abstract

Described is a finite-difference methodology for efficiently computing the response from a model subject to changes within sub-volumes with the sub-volume enclosed with an extrapolation surface within an injection boundary using Green's functions to update the injection boundary and transmitting an updated wavefield from the injection boundary back into the altered sub-volume to include higher order reflections from outside of the altered sub-space.

Description

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a flow chart summarizing important steps of a finite-difference calculation in accordance with the invention; and

FIG. 2 shows a simplified model for an application of a finite-difference calculation as used in accordance with the invention.

Claims

1. A method of evaluating the interaction between a wavefield and a solid body, the method including the steps of using a model including physical and/or geometrical properties representing the body; generating at locations within said model initial waveforms representing an initial interaction between the wavefield and the body,having one or more extrapolation surfaces each enclosing a subspace of the model; andusing Green's function to extrapolate a wavefield from the one or more extrapolation surfaces to a boundary;

2. The method of claim 1 wherein the boundary is defined such that the wavefield propagated from the boundary includes contributions of the wavefield as scattered from inhomogeneities outside the boundary back into the subspace.

3. The method of claim 1 wherein the Green's function used to extrapolate the wavefield to the boundary are Green's functions for an inhomogeneous medium.

4. The method of claim 1 wherein the Green's function used to extrapolate the wavefield to the boundary are Green's functions calculated for the full model including inhomogeneities.

5. The method of claim 1 wherein boundary is updated to included wavefield emitted from a location on the extrapolation surface at past and future times.

6. The method of claim 1, wherein the boundary is an injection boundary fully located inside the model space.

7. The method of claim 6, wherein extrapolation boundary is inside the injection boundary.

8. The method of claim 6, wherein the injection boundary has a greater distance from the boundary of the model space than from the extrapolation surface.

9. The method of claim 1, further comprising the step of computing Green's functions between the location of a simulated source and points on the boundary.

10. The method of claim 1, further comprising the step of computing Green's functions between points on the extrapolation boundary and the location of a simulated receiver.

11. The method of claim 1, further comprising the step of computing Green's functions between one or more source locations and the boundary.

12. The method of claim 1, used iteratively to adapt the response of the model to a measured response of the wavefield.

13. The method of claim 1, used iteratively to adapt the response of an Earth model to a measured response of a seismic wavefield.