RAPID 2.5-DIMENSIONAL FORWARD MODELING AND INVERSION VIA A NEW NONLINEAR SCATTERING APPROXIMATION

We introduce a novel approximation to numerically simulate the electro magnetic response of point or line sources in the presence of arbitrar ily heterogeneous conductive media. The approximation is nonlinear wit h respect to the spatial variations of electrical conductivity and is implemented with a source-independent scattering tensor. By projecting the background electric field (i.e., the electric field excited in th e absence of conductivity variations) onto the scattering tensor, we o btain an approximation to the electric field internal to the region of anomalous conductivity. It is shown that the scattering tensor adjust s the background electric field by way of amplitude, phase, and cross- polarization corrections that result from frequency-dependent mutual c oupling effects among scatterers. In general, these three corrections are not possible with the more popular first-order Born approximation. Numerical simulations and comparisons with a 2.5-dimensional finite d ifference code show that the new approximation accurately estimates th e scattered fields over a wide range of conductivity contrasts and sca tterer sizes and within the frequency band of a subsurface electromagn etic experiment. Furthermore, the approximation has the efficiency of a linear scheme such as the Born approximation. For inversion, we empl oy a Gauss-Newton search technique to minimize a quadratic cost functi on with penalty on a spatial functional of the sought conductivity mod el. We derive an approximate form of the Jacobian matrix directly from the nonlinear scattering approximation. A conductivity model is rende red by repeated linear inversion steps within range constraints that h elp reduce nonuniqueness in the minimization of the cost function. Syn thetic examples of inversion demonstrate that the nonlinear approximat ion reduces considerably the execution time required to invert a large number of unknowns using a large number of electromagnetic data.