Incorporating prior information into static and time-lapse inversions using iteratively reweighted least squares

Abstract:

It is well known that incorporating prior information into tomographic inversion problems can reduce non-uniqueness and improve imaging resolution. In many cases, useful information is available that can be used to constrain the inversion beyond the standard forms of Occam’s type regularization constraints. For example, the sign of the change in some estimated property may be known across some physical (e.g. borehole, water table) or temporal boundary (e.g. after a tracer injection). Or, some estimate of the probability that an estimated parameter takes on a particular value in a particular region of the model may be available. In this talk, we present a flexible method of incorporating such information into static and time lapse inversion problems using iteratively reweighted least squares. The approach uses combinations of weighting functions and structural metrics to encourage a particular condition via inequality constraints. Using electrical resistivity tomography, we demonstrate several examples where incorporating relatively simple forms of prior information dramatically alter the inverse solution and significantly improve imaging resolution.