Journal Article

The Complex-Step-Finite-Difference method

Rafael Abreu, Daniel Stich and Jose Morales

in Geophysical Journal International

Volume 202, issue 1, pages 72-93
ISSN: 0956-540X
Published online April 2015 | e-ISSN: 1365-246X | DOI:
The Complex-Step-Finite-Difference method

Show Summary Details


We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion–dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

Keywords: Numerical solutions; Wave propagation

Journal Article.  12198 words.  Illustrated.

Subjects: Volcanology and Seismology

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.