FINITE-DIFFERENCE MODELING IN TRANSVERSELY ISOTROPIC MEDIA

We developed a modeling algorithm for transversely isotropic media that uses finite-difference operators in a staggered grid. Staggered grid schemes are more stable than the conventional finite-difference methods because the differences are actually based on half the grid spacing. This modeling algorithm uses the full elastic wave equation that makes possible the modeling of all kinds of waves propagating in transversely isotropic media. The spatial derivatives are represented by fourth-order, finite-difference operators while the time derivative is represented by a second-order, finite-difference operator. The algorithm has no limitation on the acquisition geometry or on the heterogeneity of the media. The program is currently formulated to work in a 2-D transversely isotropic medium but can readily be extended to 3-D. Snapshots can be obtained at any time with no additional computational cost. A four-layer model is used to show the usefulness of the method. Horizontal and vertical component seismograms are modeled in transversely isotropic media and compared with seismograms modeled in the corresponding isotropic media.