An efficient tomographic inversion method based on the stochastic approximation

Abstract

Near-surface solutions often play a significant role in imaging subsurface structures for land or shallow marine environments. Unfortunately, the standard approach to first-arrival traveltime tomography may involve the inversion of a large number of traveltime picks and require a considerable computational effort. We have improved the efficiency of traveltime tomography by adopting a method inspired by the field of stochastic optimization. First, we verify that traveltime tomography is solvable by two methods in the field of stochastic optimization: the sample average approximation (SAA) and the stochastic approximation (SA). In SAA, random subsets of the whole data are inverted via nonlinear optimization. The final result is the average of all the inverted models. SA is similar to the SAA method. However, in the SA method, new random data subsets are used in each iteration of the nonlinear iterative inversion. The final result is also the average of multiple inversions. We found that SA performs better than the SAA method for traveltime tomography. However, these two methods do not yield substantial improvements in computational turnaround time in comparison with the classic iterative tomographic inversion that uses all data. Therefore, we adopt one realization of the SA method, and we analyze its feasibility via synthetic tests. We call this technique fast SA tomography (FSAT). We design numerical tests to understand the amount of data reduction that one can tolerate before the solution degrades. We also carry out a detailed statistical analysis to understand the impact of FSAT on the solution of the near-surface imaging problem. We apply FSAT to 2D and 3D field data sets, and the results show that FSAT method only requires a small percentage of the total traveltimes to yield a result nearly identical to the model obtained by using all the picks.