Simulated annealing for airborne EM inversion

Abstract

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.