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

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 s k and s j , 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 eastwest 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 northsouth 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 offpath 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.