| The mapping from the data space to the model space is known as the inverse problem. Nonlinear inverse problem are in general more difficult and computationally expensive to solve than linear problems. For nonlinear inverse problems when a priori information in the form of a starting model is not available, then a gradient based algorithm may converge to a local solution rather than to the global one. Global optimization methods such as simulated annealing (SA) have been applied recently to several geophysical inverse problems.; SA resembles the thermodynamic process of annealing to form crystals from a melt. The minimum energy state may be viewed as corresponding to the minimum of the cost function. It is well known that determining the 'critical temperature' is one of the most important factors regarding the efficiency of the SA algorithm. Here we determined the 'critical temperature' by executing the SA process for a fixed number of sweeps at a fixed temperature for different temperatures and then calculating the average energy for those sweeps. We constructed the a posteriori probability density function (PPD) and then determined the best model from it.; We performed inversion using the SA method at a fixed temperature on two-offset VSP data, and on cross-borehole data to determine the slowness of the layers between the source well and the receiver well. The results of our inversion suggest that SA has the potential to solve nonlinear inverse problems even when the solution space is large and multimodal.; We also performed inversion to compute bathymetry from shipboard free-air gravity anomaly data. Our results show an error of less than 1% of depth, which is within the acceptable error range for measuring depth according to International Hydrographic Bureau standards. |
