Intermediate simulation of the inverse seismic problem Page: 4 of 22
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INTERMEDIATE SIMULATION OF THE INVERSE SEISMIC PROBLEM
by
John E. Brolley
ABSTRACT
An introductory study of the inverse seismic problem
is performed. The complex cepstrum of a seismogram generated
by the convolution of three factors 1) the Seggern-Blandford
source function of an explosion, 2) the Futterman mantle
transfer function, and 3) the SRO seismometer transfer func-
tion, is used. For a given Q and yield, a synthetic seismo-
gram is computed. Arbitrary values of Q and yield are intro-
duced and a search is conducted to find that pair of values
which minimized the cepstral difference between the original
and arbitrary seismograms. The original values are accurately
recovered. Spectral and amplitude characteristics of the
various factors are presented. Possible application to the
problem of studying a medium intervening between a source and
receiver is discussed.
I. INTRODUCTION
The inverse seismic problem is defined as the process of tracing a seismic
signal backwards from the seismometer to the source. The goal in this case is
to learn as much as possible about the source. Information concerning the in-
tervening media that conduct the signal is also sought where it is not known.
1 2
This problem I. * * * 5 and its inverse have been studied for some time.
The present study presents a simplified problem wherein the earth is re-
garded as a one-dimensional system with the seismic source and seismometer em-
bedded in a mantle as depicted in Fig. 1. The approach is exegetical and pro-
vides a foundation for more elaborate calculations wherein the effects of the
earth's crust may be considered as well as more complicated mantle models.
A convenient model for the underground nuclear explosion is that of
3 4
Seggern and Blandford. Futterman's descriptor of the single layer mantle is
1
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Brolley, J.E. Intermediate simulation of the inverse seismic problem, report, March 1, 1980; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1069434/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.