Open AccessOn the equivalence of two methods for computing partial derivatives of seismic waveforms—II. Laterally homogeneous initial model
Author(s) -
Geller Robert J.,
Hara Tatsuhiko,
Tsuboi Seiji
Publication year - 1990
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.1990.tb04482.x
Subject(s) - eigenfunction , homogeneous , partial derivative , eigenvalues and eigenvectors , perturbation (astronomy) , mathematics , mathematical analysis , infinitesimal , equivalence (formal languages) , seismogram , geology , physics , seismology , pure mathematics , combinatorics , quantum mechanics
SUMMARY The perturbation to the synthetic seismogram (i.e., the partial derivative) due to an infinitesimal laterally heterogeneous perturbation to an initially laterally homogeneous model may be computed by either of the following methods. (1) Solving a (2 l + 1) × (2 l + 1) matrix eigenvalue problem to find the eigenfrequencies and eigenfunctions of the split singlets; summing the split singlets; and then subtracting the original synthetic for the unperturbed model. (2) Using the first‐order term of the Born series. In the present paper we show that the partial derivatives computed by the above two methods are equal.