Quantum Annealing for Seismic Imaging

Abstract

Recent developments in quantum annealing have shown promising results in logistics, life sciences, machine learning and more. However, in the field of geophysical sciences the applications have been limited. A quantum annealing application was developed for residual statics estimation. Residual statics estimation is a highly non-linear problem in geophysical subsurface imaging. The problem is run on a quantum annealer as well as on a hybrid solver. Quantum annealers solve binary quadratic models, which are a specific type of NP-Hard problem. The hybrid solver uses quantum annealers together with classical computers to solve optimisation problems. Two binary quadratic models were developed for the purpose of residual statics estimation, one based on the one-hot encoding and the other on standard binary encoding. These two models were theoretically analysed and subsequently implemented and tested. Tests with synthetic data were done using the quantum annealer. The solutions found with quantum annealing were often only a few bit-flips away from the global optimum. Therefore, the results were further improved by post-processing of the data with the steepest descent method. It was found that the one-hot encoding with steepest descent performed superior to the other methods. As a final test the hybrid solver was used to solve a business-sized and realistically difficult problem. The hybrid solver outperformed a current industry standard cross-correlation solver.