f Practical Approaches to Uncertainty Estimation in Geophysical Inversion

Geophysical inversion is essentially a two-step procedure: the first is to find at least one model that fits the data and the second step is to find all possible models that explain the data. The latter is caused by the fact that most geophysical inverse problems have nonunique solutions. An optimization approach that searches for a minimum of a suitably defined error function (that measures the misfit between observed and synthetic data) is often applied to select a candidate solution. A global optimization method such as simulated annealing (SA) or a genetic algorithm (GA) can be used to address the first part of the problem since these methods are often independent of the starting solution. However, at this stage, the solution to our inverse problem is far from being complete. To address the nonuniqueness aspect of the problem we require some measures of the uncertainty in our solution.