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Staggered grid for 2D elastic finite-difference modeling

Images - Appendix C The staggered grid for 2D elastic finite-difference modeling.

In the staggered-grid technique, not all quantities in the differential equations are gridded at the points of the reference grid. Some quantities are defined as half a grid point off the reference grid, say, x = (i ? 1/2) Δx instead of x = i Δx. This figure shows an example of staggered gridding of the quantities entering in the differential equations. The shear stresses is defined at the points on the reference grid, whereas, the normal stresses, the three components of the particle velocity, the mass density, and the Lam? parameters are defined as the points half a grid off the reference grid. Notice that normal stresses, mass density, and the Lam? parameters are located at the same points.

Staggered grid for 3D elastic finite-difference modeling

Images - Appendix C The staggered grid for 3D elastic finite-difference modeling.

Output of the Fortran code

Images - Appendix C (a) The output of the Fortran code for a half-space model (with free surface), (b) the output of the Fortan code for an infinite medium (no free surface). The star indicates the source position, and the dotted lines indicate the boundaries of the geological model.