Open AccessSynthetic seismograms using multifold path integrals ‐ II. Computations
Author(s) -
Sen Mrinal K.,
Frazer L. Neil
Publication year - 1987
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.1987.tb01650.x
Subject(s) - seismogram , helmholtz free energy , mathematical analysis , discontinuity (linguistics) , mathematics , quadrature (astronomy) , computation , helmholtz equation , geometry , physics , algorithm , optics , geology , boundary value problem , seismology , quantum mechanics
Summary Synthetic seismograms for a laterally variable multilayered elastic medium are computed by using multifold Kirchhoff‐Helmholtz path integrals. Multifold path integrals (MFPI) are a generalization of elastic Kirchhoff‐Helmholtz (KH) integrals and were devised to circumvent the failure of the latter at caustics of source/receiver ray‐fields on the surface(s) of integration. MFPI uses geometrical optics, plane wave generalized reflection and transmission coefficients, and an elastodynamic form of the KH integral. Such integrals can be evaluated numerically either in the frequency domain, by using a multidimensional generalized Filon quadrature formula, or directly in the time domain. We discuss two time domain techniques and show some examples of 2‐D synthetics obtained by our algorithm. We also compare some of our results with those obtained by the finite difference technique. Unlike many other asymptotic methods, the MFPI method computes the signals diffracted from corners on any of the surfaces of material discontinuity. Careful examination of the source/receiver ray‐field often enables one to reduce the fold of an MFPI by replacing the integrals over surfaces that do not have corners with their stationary phase point values.