Optimal Nearly Analytic Discrete Approximation to the Scalar Wave Equation

Research Article| June 01, 2006 Optimal Nearly Analytic Discrete Approximation to the Scalar Wave Equation Dinghui Yang; Dinghui Yang 1Department of Mathematical Sciences Tsinghua University Beijing 100084, People's Republic of China dhyang@math.tsinghua.edu.cn (D.Y., M.L.) Search for other works by this author on: GSW Google Scholar Jiming Peng; Jiming Peng 2Department of Computing and Software McMaster University Hamilton, Ontario, Canada L8S 4L7 pengi@mcmster.ca terlaky@mcmaster.ca (J.P., T.T.) Search for other works by this author on: GSW Google Scholar Ming Lu; Ming Lu 1Department of Mathematical Sciences Tsinghua University Beijing 100084, People's Republic of China dhyang@math.tsinghua.edu.cn (D.Y., M.L.) Search for other works by this author on: GSW Google Scholar Tamas Terlaky Tamas Terlaky 2Department of Computing and Software McMaster University Hamilton, Ontario, Canada L8S 4L7 pengi@mcmster.ca terlaky@mcmaster.ca (J.P., T.T.) Search for other works by this author on: GSW Google Scholar Author and Article Information Dinghui Yang 1Department of Mathematical Sciences Tsinghua University Beijing 100084, People's Republic of China dhyang@math.tsinghua.edu.cn (D.Y., M.L.) Jiming Peng 2Department of Computing and Software McMaster University Hamilton, Ontario, Canada L8S 4L7 pengi@mcmster.ca terlaky@mcmaster.ca (J.P., T.T.) Ming Lu 1Department of Mathematical Sciences Tsinghua University Beijing 100084, People's Republic of China dhyang@math.tsinghua.edu.cn (D.Y., M.L.) Tamas Terlaky 2Department of Computing and Software McMaster University Hamilton, Ontario, Canada L8S 4L7 pengi@mcmster.ca terlaky@mcmaster.ca (J.P., T.T.) Publisher: Seismological Society of America Received: 15 Apr 2005 First Online: 09 Mar 2017 Online ISSN: 1943-3573 Print ISSN: 0037-1106 Copyright © 2006 Bulletin of the Seismological Society of America Bulletin of the Seismological Society of America (2006) 96 (3): 1114–1130. https://doi.org/10.1785/0120050080 Article history Received: 15 Apr 2005 First Online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation Dinghui Yang, Jiming Peng, Ming Lu, Tamas Terlaky; Optimal Nearly Analytic Discrete Approximation to the Scalar Wave Equation. Bulletin of the Seismological Society of America 2006;; 96 (3): 1114–1130. doi: https://doi.org/10.1785/0120050080 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract Recently, we proposed the so-called optimal nearly analytic discrete method (onadm) for computing synthetic seismograms in acoustic and elastic wave problems (Yang et al 2004). In this article, we explore the theoretical properties of the onadm including the stability criteria of the onadm for solving 1D and 2D scalar wave equations, numerical dispersion, theoretical error, and computational efficiency when using the onadm to model the acoustic wave fields. For comparison in the 1D case, we also discuss numerical dispersions and stability criteria of the so- called Lax–Wendroff schemes with accuracy of O(Δt4, Δx8) and O(Δt4, Δx10) and the pseudospectral method (psm). We then apply the onadm to the heterogeneous case in synthetic seismograms. Promising numerical results illustrate that the onadm provides a useful tool for large-scale heterogeneous practical problems because it can effectively suppress numerical dispersions caused by discretizing the wave equations when too-coarse grids are used. Numerical modeling also indicates that simultaneously using both the wave displacement and its gradients to approximate the high-order derivatives is important for decreasing the numerical dispersion and source-generated noise caused by the discretization of wave equations because wave- displacement gradients include important seismic information. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.