APPLICATION OF THE MULTIPLICATIVE-REGULARIZED GAUSS-NEWTON INVERSION FOR INVERTING3D MARINE CSEM DATA A. Abubakar, J. Liu, G. Pan, T. M. Habashy, M. Zaslavsky, V. Druskin, G. Cairns, C. Nalepa Schlumberger, USA 1. INTRODUCTION The marine controlled-source electromagnetic (CSEM) method has the potential of providing useful information in applica- tions such as off-shore oil exploration. With a horizontal electric dipole as a transmitter towed by a ship and multi-component electromagnetic receivers on the seafloor, this method has been applied in several field surveys. The high contrast in resistivity between saline-filled rocks and hydrocarbons, makes this method well-suited for detecting oil reservoirs ([1, 2]). The approach initially employed 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 [2]. The presence of hydrocarbon raises the amplitude of the mea- sured electric field indicating the existence and, to some degree, determining the horizontal extent 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 (see [3, 4, 5]). In such an approach the investigation domain is subdivided into pixels and through inversion, the location, the shape and the conductivity of the reservoir are reconstructed. In this paper we applied the method developed in [5] for inverting three-dimensional (3D) field data. Unlike the methods in [3, 4], where the minimization approaches are based on non-linear conjugate gradient (CG) or quasi-Newton techniques, our method employed a Gauss-Newton minimization approach. The Gauss-Newton approach is known to have higher convergence rates than non-linear CG or quasi-Newton methods. The method is also equipped with the multiplicative regularization technique so that we do not need to determine the so-called regularization parameter in the optimization process. Further, the algorithm accomodates two different regularization schemes to produce either a smooth (using a standard L 2 -norm function) or a blocky (using a weighted L 2 -norm function) conductivity distribution ([6]). Moreover, to enhance the robustness of the algorithm, we incorporated a non-linear transformation for constraining the minimum and maximum values of the conductivity distribution. A line-search procedure for enforcing error reduction in the cost function in the minimization process is also employed. Since we are dealing with a large-scale computational problem, we will also touch upon an efficient parallel MPI (Message Passing Interface) implementation of our method. 2. THEORY We consider a non-linear inverse problem described by the following equation: d obs = s(m), where d obs =[d obs (r S i , r R j ,ω k ),i = 1, 2, ··· ,I ; j =1, 2, ··· ,J ; k =1, 2, ··· ,K] T is the vector of measured data and r S i , r R j , and ω k are the source position vector, the receiver position vector and the frequency of operation, respectively. The superscript T denotes the transpose of a vector. The vector s(m) represents simulated data computed by solving Maxwell equations: ∇× σ -1 (r)∇× H(r) − iωμH(r)= ∇× σ -1 (r)J(r S ) , (1)