Dix inversion constrained by L1-norm optimization

Abstract:

To accurately invert for velocity in a model with a blocky interval velocity inversion using Dix inversion, we set up our optimization objective function using $L1$ criterion. In this study, we analyze and test an improved version of the Iterative Reweighted Least Squares (IRLS) solver, a hybrid $L1/L2$ solver and a conjugate direction $L1$ solver. We use a 1-D synthetic velocity data set and a 1-D field RMS velocity data set as test cases. The results of the inversion are promising for applications on realistic geophysical problems.