A three-dimensional multiplicative-regularized non-linear inversion algorithm for cross-well electro- magnetic and controlled-source electromagnetic applications

We present three-dimensional inversion algorithms for inversion of cross-well electromagnetic and controlled-source electromagnetic (CSEM) data. The inversion is accomplished with a Gauss-Newton technique where the model parameters are forced to lie within their upper and lower bounds by means of a non-linear transformation procedure. The Jacobian is computed using an adjoint method. A line search method is employed to enforce a reduction of the cost function at each iteration. To improve the conditioning of the inversion problem, we use one of two different regularization schemes. The first is an L2-norm regularization scheme, which provides for a smooth solution. The second is the weighted L2-norm regularization scheme that can provide a sharp reconstructed image. The trade-off parameter that provides a relative weighting between the data and the model-constraint part of the cost function is determined automatically using the multiplicative regularized cost function to enhance the robustness of the method.