Cross-Well Electromagnetic Tomography

We present an efficient approach to cross-well electromagnetic tomography based on a new nonlinear scattering approximation. The approximation uses a source-independent scattering tensor whose projection onto the background electric field (i.e., the electric field excited in the absence of conductivity variations) is an approximaton to the electric field inside the region of anomalous conductivity. The scattering tensor adjusts the background electne field by way of amplitude, phase and cross-polarization corrections that result from frequency-dependent mutual coupling among scatterers. Numerical simulations and comparisons with a 2.5-D finite:differene.e code show that the new approximation accurately describes scattered fields even with large contrasts in electrical conducrivity and large scatterer dimensions within the frequency range qf -a crass-well electromagnetic experiment. In our inversion. we implement a Gauss-Newton search technique to minimize a quadratic cost function with penalty on the spatial derivatives of the sought model. We derive an approximate form of the Jacobian matrix directly from the nonlinear scattering approximation. A conductivity model is found by repeated linear inversion steps within range constraints that help reduce nonuniqueness in the minimization of the cost function. Examples of inversion are shown with both numerically simulated data as well as data from an electromagnetic cross-well field experiment acquired by a university research consortium.