An Approximation to the General Galerkin Method of Computing Coupled-Mode Synthetic Seismograms

Abstract

Research Article| February 25, 2014 An Approximation to the General Galerkin Method of Computing Coupled‐Mode Synthetic Seismograms Duayne M. Rieger; Duayne M. Rieger Department of Geology and Geophysics, Yale University, Kline Geology Lab, 210 Whitney Avenue, New Haven, Connecticut 06511 Search for other works by this author on: GSW Google Scholar Jeffrey J. Park Jeffrey J. Park Department of Geology and Geophysics, Yale University, Kline Geology Lab, 210 Whitney Avenue, New Haven, Connecticut 06511 Search for other works by this author on: GSW Google Scholar Author and Article Information Duayne M. Rieger Department of Geology and Geophysics, Yale University, Kline Geology Lab, 210 Whitney Avenue, New Haven, Connecticut 06511 Jeffrey J. Park Department of Geology and Geophysics, Yale University, Kline Geology Lab, 210 Whitney Avenue, New Haven, Connecticut 06511 Publisher: Seismological Society of America First Online: 14 Jul 2017 Online ISSN: 1943-3573 Print ISSN: 0037-1106 Bulletin of the Seismological Society of America (2014) 104 (2): 962–971. https://doi.org/10.1785/0120130114 Article history First Online: 14 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Duayne M. Rieger, Jeffrey J. Park; An Approximation to the General Galerkin Method of Computing Coupled‐Mode Synthetic Seismograms. Bulletin of the Seismological Society of America 2014;; 104 (2): 962–971. doi: https://doi.org/10.1785/0120130114 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 Quasi‐Love (QL) scattered surface waves are the result of lateral gradients of seismic anisotropy in Earth’s upper mantle. These polarization anomalies can be forward modeled in the context of normal‐mode coupling. However, methods for computing coupled‐mode synthetic seismograms, such as the general Galerkin method, are computationally intensive, especially in the case of 3D structure. In this report, we present an approximation of the general Galerkin method of computing coupled‐mode synthetic seismograms. The approximation replaces the formal eigenvector decomposition of the elastic potential energy coupling matrix V in the general Galerkin method with a piecewise approach. The approximation uses the closed‐form eigenvectors of 2×2 coupling matrices V(kj), which represent the interactions between two individual singlets sk and sj, to form the eigenvectors of V. The approximation is benchmarked against the exact general Galerkin method using zonally symmetric anisotropic structure. We find the approximation successfully reproduces the QL waveforms with a slight underestimate of the amplitude. By limiting the east–west extent of the zonally symmetric structure, we extend the approximation to a 3D structure. We find that the sharp lateral gradients in anisotropy created by the north–south running boundaries of the 3D structure contribute to the observed scattering until they are outside the sensitivity zone as defined by Ritzwoller et al. (2002). This demonstrates the sensitivity of QL surface‐wave scattering to off‐path structure. We also explicitly confirm the path‐integral asymptotics that in the limit of smooth off‐path structure, QL surface‐wave scattering can be represented via the path integral along the source–receiver great circle path rather than the volume integral over Earth. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.