Experience with three-dimensional inversion of controlied, multi-source, electromagnetic data collected in the marine environment suggests that the derived resistivity images can, under appropriate conditions, play a role in hydrocarbon saturation predictions. Significant technical challenges exist in the simulation and inversion of these data.
The Controlled-Source Electromagnetic (CSEM) surveys conducted by ExxonMobil beginning in 2002 provide data for which electromagnetic imaging offers a significant potential due to the relatively high spatial density of electric field recordings, the low level of anticipated noises and the excellent electrical coupling provided by the marine environment. Unfortunately, significant technical issues are presented by the large dynamic range of the recordings, the three-dimensional nature of the anticipated targets, and the logistics of marine recordings. A series of inversion results at three locations offshore of West Africa illustrate the progress made in confronting these technical difficulties.
Electromagnetic soundings in conductive sediments are heavily constrained by the skin-depth phenomena to a very narrow range of frequencies which must both successfully penetrate to maximum target depth and also resolve significant conductivity variations between the sea bottom and the target zone. The implied frequency range for targets of practical interest varies from approximately 1/16 Hz to 2 Hz and the skin depth from 2 km to no less than 0.2 km. On these scales reservoir targets are unquestionably three dimensional objects for which two dimensional approximations are either inappropriate or unnecessarily restrictive. Only three general techniques for simulation and, therefore, inversion of Maxwell''s equations (in the frequency domain) are available: integral equations (IE), finite difference (FD), and finite element (FE). The classic IE approach has a computational cost which is O(N3) where N is a measure of the size of the grid required to represent the inhomogeneous domain (Hohmann, 1987 and Zhdanov, 2002). Recent reported progress (Chew et al., 2004 and Cui et al., 2004) suggests that this estimate can be reduced to methods with computational costs of O(N''Niterlog(N)) where Niter is the number of iterations required for an iterative solution. Unfortunately these techniques are still under development and may or may not ultimately compete with FD and FE methods for realistic earth models. Finite difference and finite element methods have costs which are O(N''Niter) where N now measures the size of the grid for the entire domain. Weak scattering approximations (Zhdanov, 2002) were judged not to be appropriate based upon the anticipated range of conductivity variations and the large domain of unknown subsurface resistivities sought by the inversion process. The availability of a massively parallelized FD approach (Newman and Alumbaugh, 1997) dictated its selection versus a more sophisticated FE approach restricted in scope to a single processor platform. Our particular approach uses the scattered field method based upon a layered background field, reducing the difficulties of the large conductivity contrast implied by the air layer. All inversion results reported here use both amplitude and phase information. The diffusive phenomena typical of low frequency electromagnetic radiation are well known to be susceptible to least-squares inversion approaches, unlike the notorious pre-stack seismic inverse problem.
