Improved adaptive regularization for simulated annealing inversion of transient electromagnetic

Geophysical inversion usually involves ill-posed problem. Regularization is the most commonly used method to mitigate this problem. There are many regularization parameter selection methods, among which the adaptive regularization method can automatically update parameters during iteration, reducing the difficulty of parameter selection. Therefore, it is widely used in linear inversion. However, there are very few studies on the use of adaptive regularization methods in stochastic optimization algorithms. The biggest difficulty is that in stochastic optimization algorithms, the search direction of any iteration is completely random. Data fitting term and stabilizing term vary in a wide range, making it difficult for traditional methods to work. In this paper, we consider the contributions of the data fitting term and the stabilizing term in the objective function and give an improved adaptive regularization method for very fast simulated annealing (VFSA) inversion for transient electromagnetic (TEM) data. The optimized method adjusts the two terms dynamically to make them in balance. We have designed several numerical experiments, and the experimental results demonstrate that the method in this paper not only accelerates the convergence, but also the inversion results are very little affected by the initial regularization parameter. Finally, we apply this method to field data, and the inversion results show very good agreements with nearby borehole data.