A Two-and-Half-Dimensional Model-Based Inversion Algorithm for the Controlled-Source Electromagnetic Data

Abstract

Abstract The model-based inversion method for the reconstruction of geometry and conductivity of unknown regions or bodies using marine controlled-source electromagnetic (CSEM) data is presented. The method has the advantage of using a priori information such as the background conductivity distribution, structural information extracted from seismic and/or gravity measurements, and/or inversion results a priorily derived from a pixel-based inversion method. By incorporating this a priori information, the number of unknown parameters to be retrieved becomes significantly reduced. In this paper, we develop the model-based inversion method by adopting the regularized Gauss-Newton minimization scheme. The robustness of the inversion is enhanced by adopting nonlinear constraints and applying a quadratic line search algorithm to the optimization process. We also introduce the adjoint formulation to calculate the Jacobian matrix with respect to the geometrical parameters. We compare the inversion results obtained by the model-based inversion method with those obtained from the pixel-based inversion method. Introduction Electromagnetic inverse scattering methods have been extensively developed and applied to retrieve geometrical and geophysical information in hydrocarbon exploration. Recently, the marine controlled-source electromagnetic (CSEM) technology has attracted much attention for its capability in directly detecting thin hydrocarbon reservoirs, see Constable and Srnka1, Eidesmo et al.2, Ellingrud et al.3, Johansen et al.4, MacGregor and Sinha5 and Tompkins6. The approach is based on comparing the electric field amplitude as a function of the source-receiver offset with a similar measurement for a non-hydrocarbon bearing reservoir, see Eidesmo et al.2. The presence of hydrocarbon raises the amplitude of the measured electric field indicating the existence, and to some degree determining the horizontal location of the hydrocarbon zone. However, with this approach it is difficult to know the reservoir's depth and shape. A more rigorous approach to address this type of application is the full nonlinear inversion approach. In such an approach the investigation domain is usually subdivided into pixels, and by using an optimization process the location, the shape and the conductivity of the reservoir are reconstructed. The optimization process usually adopts the Gauss-Newton minimization method and various types of regularization to obtain good conductivity images. The weighted L2-norm regularization, see Abubakar et al.7 has shown to be able to retrieve reasonably good conductivity images. However, the reconstructed boundaries and conductivity values of the imaged objects are still not sufficiently good. Nevertheless, this pixel-based inversion (PBI) approach can provide some rough information on the location, the shape and the conductivity of the hydrocarbon reservoir. In this paper, we present the so-called model-based inversion method, which uses a priori information on the geometry to reduce the number of unknown parameters and improve the quality of the reconstructed conductivity image. The method adopts the Gauss-Newton minimization method, with nonlinear constraints and regularization for the unknown parameters. It also employs a line search approach to guarantee the reduction of the cost function after each iteration (see Habashy and Abubakar8 for detailed description). The forward modeling simulation is a two-and-half dimensional (2.5D) finite-difference solver as described in Abubakar et al.7 and the parameters that govern the location and the shape of a reservoir include the depth and the location of the user-defined nodes for the boundary of the region. The unknown parameter that describes the physical property of the region is the electrical conductivity. In the numerical examples, we present inversion results of a hydrocarbon body using multiple transmitters and receivers in a marine CSEM setting.