Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method

Abstract

S U M M A RYA method for simulating seismic wave propagation in a laterally heterogeneous whole earth model is presented by solving the elastodynamic equations in 2-D cylindrical coordinates using the pseudospectral method (PSM). The PSM is an attractive timedomain technique that uses the fast Fourier transform for an accurate di¡erentiation of ¢eld variables in the equations. Since no dispersion error arises in Fourier di¡er-entiation, even when using a large grid spacing, computer memory and time are reduced by several orders of magnitude compared to traditional ¢nite-di¡erence methods. In order to examine body-wave phases with current computing resources, a slice through the sphere is approximated with a 2-D cylindrical model. An irregular grid spacing is used in the vertical coordinate to improve the treatment of the various structural boundaries appearing in the earth model by matching the heterogeneity in the model. Synthetic seismograms obtained by the PSM calculation are compared with those calculated from an exact simulation method for a spherically homogeneous (1-D) earth model and achieve good agreement.The PSM method is illustrated by constructing the seismic P^SV wave¢eld for strongly heterogeneous earth models including a shield structure near the free surface and velocity perturbations just above the core^mantle boundary. The visualization of the evolution of seismic P and S waves in time and space is tracked using a sequence of snapshots and synthetic seismograms. These displays allow direct insight into the nature of the complex seismic wave behaviour in the Earth's interior.

A multidomain approach of the Fourier pseudospectral method using discontinuous grid for elastic wave modeling

“…If such a uniform grid is used to represent the velocity variation in the very low velocity region, it then causes spatial oversampling in the higher velocity region. Application of the mapping technique in both x and z directions as suggested by Fornberg (1988), Jastram and Tessmer (1994) and Furumura et al (1998b) can re-locate the grids by following the interface and reduce the grid spacing at the very low velocity layers to improve the accuracy of the results. But the total number of grid points remains the same and the spatial oversampling in high-velocity region is not removed.…”

“…The thickness of the first and second layer is 1.8 km and 7.5 km, respectively. The calculation of spatial derivatives with respect to z is performed by using the mapping scheme (Fornberg, 1988;Jastram and Tessmer, 1994;Furumura et al, 1998b) since the z is varying in the z direction.…”

The Spectral-Element Method, Beowulf Computing, and Global Seismology

“…In this differential or "strong" formulation of the wave equation, displacement derivatives are approximated using differences between adjacent grid points, which makes the implementation of accurate boundary conditions difficult. The pseudospectral technique, in which the wave field is expanded in global basis functions (typically sines, cosines, or Chebyshev polynomials) (15,16 ), has similar limitations because it is also based on a strong formulation. Nevertheless, this method has been used to simulate wave propagation in a portion of the mantle (17 ).…”

Optimized viscoelastic wave propagation for weakly dissipative media

“…Other axisymmetric approaches to global and local wave propagation have been presented (Alterman & Karal 1968;Igel & Weber 1995, 1996Chaljub & Tarantola 1997;Furumura et al 1998;Thomas et al 2000;Takenaka et al 2003;Toyokuni et al 2005;Jahnke et al 2008), but only recently Toyokuni & Takenaka (2006, 2012 generalized their method to include moment tensor sources, attenuation and the Earth's centre. These methods are all based on isotropic media and especially the finite-difference methods among them have to deal with large dispersion errors for interface-sensitive waves such as surface waves and diffracted waves (Igel & Weber 1995;.…”