Open AccessThe discrete wavenumber/finite element method for synthetic seismograms
Author(s) -
Olson Allen H.,
Orcutt John A.,
Frazier Gerald A.
Publication year - 1984
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1984.tb01942.x
Subject(s) - wavenumber , mathematical analysis , bessel function , finite element method , mathematics , seismogram , spectral element method , finite difference , mixed finite element method , physics , optics , geology , seismology , thermodynamics
Summary. A new method is presented for computing the complete elastic response of a vertically heterogeneous half‐space. The method utilizes a discrete wavenumber decomposition for the horizontal dependence of the wave motion in terms of a Fourier‐Bessel series. The series representation is exact if summed to infinity and consequently eliminates the need to integrate a continuous Bessel transform numerically. In practice, a band‐limited solution is obtained by truncating the series at large wavenumbers. The vertical and time dependence of the wave motion is obtained as the solution to a system of partial differential equations. These equations are solved numerically by a combination of finite element and finite difference methods which accommodate arbitrary vertical heterogeneities. By using a reciprocity relation, the wave motion is computed simultaneously for all source‐observer combinations of interest so that the differential equations need only be solved once. A comparison is made, for layered media, between the solutions obtained by discrete wavenumber/finite element, wavenumber integration, axisymmetric finite element, and generalized rays.