Fast 2D Forward and Inversion Algorithms for Interpreting Marine CSEM Data (2006)

Abstract We present two-dimensional forward and inversion algorithms for the interpretation of marine controlled-source electromagnetic data. The forward algorithm employs a staggered-grid finite difference solution to the total-electricfield Helmholtz equation. Quick solution times are achieved through a) an optimal grid technique that extends the boundaries of the mesh outward from the region of interest using a minimal number of nodes, and b) a direct matrix solution technique that allows for the simultaneous solution for all sources. In addition an anisotropic conductivity averaging formula is employed to upscale models with very fine details to a coarser computational mesh. Simulation of simple models show the accuracy to be within one percent for amplitude and one degree phase as long as there are at least six to ten finite-difference-node-points between the source and receiver. The inversion is accomplished via a constrained Gauss-Newton technique where the model parameters are forced to lie within upper and lower bounds via a nonlinear transformation procedure. The Jacobian is computed using an adjoint method where all of the forward solutions required for computation of both the data misfit as well as the Jacobian matrix are achieved through one run of the forward solution. Employing a line search method enforces reduction of the cost function at each iteration. To improve the conditioning of the inversion problem, we use one of two different modelstructural constraints. The first is a traditional L2-norm regularization scheme, which provides for a smooth solution. The second is the so-called weighted L2-norm constraint (or L1-like norm) that can provide a sharp reconstructed image. The trade-off parameter which provides the relative weighting between the data and the model-constraint part of the cost function is determined automatically to enhance the robustness of the method. The performance of the algorithm is demonstrated using two different models; a simple 2D model with an 8km wide, 100m thick reservoir unit, and a more complicated 3D example simulating complex channelstructures at depth. These examples are further employed to demonstrate the degradation caused by increasing data noise, and the image enhancement that results by using multiple electromagnetic field components. Introduction Marine controlled source electromagnetic (CSEM) methods have recently received increased attention as a hydrocarbonexploration tool [1,2,3,4,5]. The interest results from the technique's ability to directly detect the presence of thin hydrocarbon bearing layers at depth. Initially, data were analyzed by plotting electric field amplitude versus sourcereceiver offset, and then normalizing the data that were acquired over a possible hydrocarbon prospect by data measured over a similar non-hydrocarbon bearing area [1,2]. Because the presence of hydrocarbons at depth increases the amplitude of the measured electric field, the normalized value will be greater than unity for areas containing resistive anomalies at depth, and unity or less for non-hydrocarbon bearing areas.