Abstract
We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.
| Original language | English (US) |
|---|---|
| Pages (from-to) | T57-T67 |
| Number of pages | 1 |
| Journal | GEOPHYSICS |
| Volume | 77 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: Stoffa would like to acknowledge the King Abdullah University of Science and Technology (KAUST) for their support of his research. We are grateful for the technical and editorial comments from the anonymous reviewers and associate editor Stig Hestholm. Their suggestions significantly helped to improve the original manuscript. We thank ConocoPhillips for permission to publish this work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.