Approximate Sensitivities for Multidimensional Electromagnetic Inversion
Colin G. Farquharson, Douglas W. Oldenburg, 1999. "Approximate Sensitivities for Multidimensional Electromagnetic Inversion", Three-Dimensional Electromagnetics, Michael Oristaglio, Brian Spies
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Linearized, iterative inversion of electromagnetic data requires computation of partial derivatives (sensitivities) with respect to parameters of the model, e.g., the conductivities of cells. Methods based on the adjoint equation compute these sensitivities by integrating, over each cell, the scalar product of an adjoint electric field with the electric field produced by the forward modeling in the preceeding iteration. We approximate the partial derivative by computing the adjoint field in either a homogeneous or a layered half-space. Computation of the approximate adjoint field is significantly faster than that of the true adjoint field, with the relative efficiency increasing with the size of the problem. Approximate sensitivities compare well with exact values for sample controlled-source surveys in 2-D and 3-D models. We demonstrate that approximate sensitivities can be sufficiently accurate to drive an iterative algorithm by inverting synthetic magnetotelluric data. Approximate sensitivities should enable the solution of inverse problems larger than those now practical.