Open AccessOn the equivalence between stratified media and oscillators
Author(s) -
Urquizú Mercè,
Correig Antoni M.
Publication year - 2004
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2004.02167.x
Subject(s) - equivalence (formal languages) , geology , geophysics , statistical physics , mathematics , physics , pure mathematics
SUMMARY A new method of modelling scattered seismic pulses is developed, based on the deformation that suffers an initial pulse due to scattering and on a reinterpretation of the product of convolution of a Green function with a source time function. In this new interpretation, the convolution product is equivalent to the solution of an ordinary differential equation, in which the source term corresponds to the solution of the homogeneous differential equation. The medium response (identified with the Green function) corresponds to the inhomogeneous term of the differential equation. Numerical solutions show the equivalence between the proposed method and the classical one based on convolution. This method can easily be generalized to any kind of complex medium and source time function.