Error propagation in non-linear delay-time tomography

Abstract

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-noise 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.