Summary

The aim of seismic inversion is to estimate the subsurface elastic properties. Deterministic seismic inversion based on local optimization suffers from getting trapped in a local minimum. Also, the inversion result is generally band limited. Various stochastic inversion algorithms have been introduced to address these issues. Many of them, however, are computationally very expensive or can be trapped in a local minimum if the inversion parameters are not carefully chosen. Quantum Annealing (QA) is a global optimization algorithm that is proven to be faster than the conventional Simulated Annealing (SA) and is less prone to getting trapped in a local minimum. Here, we run this inversion algorithm to resolve Woodford formation in the Cana field, Oklahoma. The results are compared with those obtained by a deterministic inversion. Our results clearly demonstrate superior performance of our stochastic QA inversion over standard SA and deterministic inversion of field data.

Introduction

The aim of seismic inversion is to estimate the subsurface elastic properties. This is accomplished by finding the minimum of a suitably defined error function. Deterministic inversion can be used to find a single solution of this minimization problem; this solution is the closest to the initial model. Seismic inversion is a highly non-linear problem that has multiple minima of different heights. Although deterministic inversion is computationally cheap, it fails in finding the global minimum when the initial model is far from it. Moreover, deterministic inversion is band limited. Thus, global minimization methods are preferred in such problems (Sen and Stoffa, 2013; Menke, 2012).

Because the model space in a typical geophysical inversion problem is very large, the grid search algorithm is not a practical approach. Pure Monte Carlo method, which randomly evaluates the error function at many points, is still very expensive. Simulated Annealing (SA) introduced by Kirkpatrick et al. (1983) is another global optimization method that randomly samples the target distribution but also utilizes Metropolis criterion to accept or reject the next trial solution. Hence, SA converges to the global minimum faster than pure Monte Carlo method. Unfortunately, SA could be trapped in a local minimum if the annealing scheduled is not properly designed. Moreover, it is still a very expensive method in geophysical inversion where we invert for a large number of parameters. Ingber (1989, 1993) introduced Very Fast Simulated Annealing (VFSA) algorithm that is faster than SA but it can also be trapped in a local minimum.

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