Model Misfit Minimization

Abstract

Abstract In geophysical applications, solutions to ill‐posed inverse problems Ax=b are often obtained by analyzing the trade‐off between data residue ‖Ax−b‖2 and model norm ‖x‖2. In this study, we show that the traditional L‐curve analysis does not lead to solutions closest to the true models because the maximum curvature (or the corner of the L‐curve) depends on the relative scaling between data residue and model norm. A Bayes approach based on empirical risk function minimization using training datasets may be designed to find a statistically optimal solution, but its success depends on the true realization of the model. To overcome this limitation, we construct training models using eigenvectors of matrix ATA as well as spectral coefficients calculated from the correlation between observations and eigenvector projected data. This approach accounts for data noise level but does not require it as a priori knowledge. Using global tomography as an example, we show that the solutions are closest to true models.