Open AccessError propagation in non‐linear delay‐time tomography
Author(s) -
Dorren H. J. S.,
Snieder R. K.
Publication year - 1997
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.1997.tb05324.x
Subject(s) - linearization , tomography , algorithm , linear model , inversion (geology) , mathematics , perturbation (astronomy) , linear system , propagation of uncertainty , computer science , nonlinear system , mathematical analysis , physics , statistics , optics , quantum mechanics , structural basin , biology , paleontology
SUMMARY Delay‐time tomography can be either linearized or non‐linear. In the case of linearized tomography, an error due to the linearization is introduced. If the tomography is performed in a non‐linear fashion, the theory used is more accurate from the physical point of view, but if the data have a statistical error, a noise bias in the model is introduced due to the non‐linear propagation of errors. We investigate the error propagation of a weakly non‐linear delay‐time tomography example using second‐order perturbation theory. This enables us to compare the linearization error with the noise bias. We show explicitly that the question of whether a non‐linear inversion methods leads to a better estimation of the model parameters than a linearized method is dependent on the signal‐to‐noisc ratio. We also show that, in cases of poor data quality, a linearized inversion method leads to a better estimation of the model parameters than a non‐linear method.