Improving efficiency of traveltime tomography by stochastic optimization

The first-arrival traveltime tomography is an important approach for solving the near-surface imaging problem, from which results are needed to calculate statics. The method involves inverting massive traveltime picks and therefore may require heavy computation. We apply mathematics methods of Sample Average Approximation (SAA) and Stochastic Approximation (SA) to improve the efficiency of traveltime tomography. SAA and SA are the two approaches to enhance the computational efficiency theoretically, which are realized by selecting a small portion of data randomly to perform the inversion as opposed to all data and that leads to a consequence of saving the computational memory or the computational time cost at the same time. We adapt the SAA and the SA methods in the first-arrival traveltime tomography and compare the inverted results and the computational cost with the standard approach. Both SAA and SA give satisfying approximated solutions, and save computational cost in different aspects. To obtain the same imaging results as the one inverted by the standard approach, one just need run 3-5 iterations of full data inversion. We evaluate the performance of this method by synthetic and real data tests. As our tests, the advantage of the SAA method is main reflected in the view of computational memory, which can save about 95% cost. However, by applying the SA method, the cost of both computational memory and time can be saved at about 95% and 75%, respectively.