Open AccessA comparison of synthetic seismograms of core phases generated by the full wave theory and by the reflectivity method
Author(s) -
Choy George L.,
Cormier Ver F.,
Kind Rainer,
Müller Gerhard,
Richards Paul G.
Publication year - 1980
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.1980.tb04301.x
Subject(s) - seismogram , synthetic seismogram , caustic (mathematics) , eigenfunction , computation , geology , range (aeronautics) , diffraction , synthetic data , series (stratigraphy) , optics , geometry , mathematical analysis , physics , mathematics , geophysics , algorithm , seismology , paleontology , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material
Summary. Because the computation of synthetic seismograms has become an invaluable tool for the study of the Earth, it is of major interest to know whether two different methods, the reflectivity method and the full wave theory, generate identical record sections when applied to the same body wave problem. The full wave theory employs approximations by assuming de‐coupling of P and SV potentials in arbitrarily thick radially inhomogeneous layers and by representing radial eigenfunctions by the first term in a uniformly asymptotic series. The reflectivity method employs approximations by transforming depth‐dependent variables of a spherically symmetric Earth to those of a plane‐layered medium and by replacing this medium by a stack of homogenous layers. We have compared record sections generated by the two methods using the same Earth model, source parameters, distance ranges and body waves. Specifically, we examined core phases, which should provide a stringent comparison because they contain a wide range of frequency‐dependent phenomena including diffraction and the effects that arise from a cusp and a caustic. It is found that the synthetic record sections of the two techniques are identical when displacements are low‐pass filtered. This is the case for many practical purposes, for displacement generally must be convolved with an instrument response and a source function of several seconds duration before comparison with observed seismograms. However, as the content of the higher frequencies becomes more significant, the waveforms of the reflectivity records become more contaminated by reverberations. These reverberations arise when the smooth velocity or density. profile is approximated by homogeneous layers whose thicknesses are too large for the wavelengths involved. The reflectivity method must choose between using coarser layering (at the expense of accuracy) or finer layering (and greater computation time). The full wave theory can also handle body waves with turning points at or near the centre of the Earth, a region where the earth‐flattening approximation begins to break down.