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ON THE BREMMER SERIES DECOMPOSITION: EQUIVALENCE BETWEEN TWO DIFFERENT APPROACHES *
Author(s) -
AMINZADEH F.,
MENDEL J.M.
Publication year - 1980
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1980.tb01212.x
Subject(s) - lossless compression , decomposition , equivalence (formal languages) , series (stratigraphy) , integral equation , mathematics , homogeneous , mathematical analysis , pure mathematics , chemistry , algorithm , combinatorics , data compression , geology , paleontology , organic chemistry
A bstract A Bremmer Series decomposition of the solution y ( t ) to the lossless wave equation in layered media iswhere the y j ( t ) are physically meaningful constituents (i.e., y 1 ( t ) are primaries, y 2 ( t ) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.