Comparison of 1- and 2-D Regularized MT Inversions

We measure the success of a general numerical optimization scheme for solving the nonlinear inverse problem of electromagnetic induction (MT) in two dimensions by comparison with a one-dimensional analytic solution. The general, large-scale method treats the differential equations as constraints and the observations together with the 2-norm of the (positive) conductivity as a penalty function. The one-dimensional comparison problem is solved by means of the Euler-Lagrange equations with a positivity condition for a single frequency observation, but the solution can then be easily extended to many frequencies. Having exact analytic solutions for a simple system provides a valuable check on complex general-purpose codes.