Print Email Facebook Twitter A simple finite-difference scheme for handling topography with the first-order wave equation Title A simple finite-difference scheme for handling topography with the first-order wave equation Author Mulder, W.A. (TU Delft Applied Geophysics and Petrophysics; Shell Global Solutions International B.V.) Huiskes, M.J. (Shell Global Solutions International B.V.) Date 2017 Abstract One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results To reference this document use: http://resolver.tudelft.nl/uuid:f6eecfeb-0059-4a5b-8563-f7c610f65947 DOI https://doi.org/10.1093/gji/ggx178 ISSN 0956-540X Source Geophysical Journal International, 210 (1), 482-499 Part of collection Institutional Repository Document type journal article Rights © 2017 W.A. Mulder, M.J. Huiskes Files PDF ggx178_1_.pdf 4.12 MB Close viewer /islandora/object/uuid:f6eecfeb-0059-4a5b-8563-f7c610f65947/datastream/OBJ/view