Application of generalised finite differences method to reflection and transmission problems in seismic SH waves propagation. (9th January 2017)

• Record Type: Journal Article
• Authors: Ureña, Miguel; Benito, Juan José; Ureña, Francisco; Salete, Eduardo; Gavete, Luis
• Other Names: Vigo‐Aguiar Jesus guestEditor.; Garcia Rubio Raquel guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 6(2018)
• Page Start: 2328
• Page End: 2339
• Publication Date: 2017-01-09
• Subjects: generalised finite difference method -- seismic waves -- reflection and transmission; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4268
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A matrix formulation of the generalised finite difference method is introduced. A necessary and sufficient condition for the uniqueness of the solution is demonstrated, and important practical consequences are obtained. A generalised finite differences scheme for SH wave is obtained, the stability of the scheme is analysed and the formula for the velocity of the wave due to the scheme is obtained in order to deal with the numerical dispersion. The method is applied to seismic waves propagation problems, specifically to the problem of reflection and transmission of plane waves in heterogeneous media. A heterogeneous approach without nodes at the interface is chosen to solve the problem in heterogeneous media. Copyright © 2017 John Wiley & Sons, Ltd.