APPROXIMATE SENSITIVITIES FOR THE ELECTROMAGNETIC INVERSE PROBLEM

We present an approximate method for generating the Jacobian matrix of sensitivities required by linearized, iterative procedures for invert ing electromagnetic measurements. The approximation is based on the ad joint-equation method in which the sensitivities are obtained by integ rating, over each cell, the scalar product of an adjoint electric held (the adjoint Green's function) with the electric held produced by the forward modelling at the end of the preceding iteration. Instead of c omputing the adjoint held in the multidimensional conductivity model, we compute an approximate adjoint held, either in a homogeneous or lay ered half-space. Such an approximate adjoint held is significantly fas ter to compute than the true adjoint held. This leads to a considerabl e reduction in computation time over the exact sensitivities. The spee d-up can be one or two orders of magnitude, with the relative differen ce increasing with the size of the problem. Sensitivities calculated u sing the approximate adjoint held appear to be good approximations to the exact sensitivities. This is verified by comparing true and approx imate sensitivities for 2- and 3-D conductivity models, and for source s that are both finite and infinite in extent. The approximation is su fficiently accurate to allow an iterative inversion algorithm to conve rge to the desired result, and we illustrate this by inverting magneto telluric data to recover a 2-D conductivity structure. Our approximate sensitivities should enable larger inverse problems to be solved than is currently feasible using exact sensitivities and present-day compu ting power.