Three-dimensional inversion of static-shifted magnetotelluric data

A practical method for inverting static-shifted magnetotelluric (MT) data to produce a 3-D resistivity model is presented. Static-shift parameters are incorporated into an iterative, linearized inversion method, with a constraint added on the assumption that static shifts are due to a zero-mean, Gaussian process. A staggered finite-difference scheme is used to evaluate both the forward problem and the 'pseudo-forward' problem needed to construct the full sensitivity matrix. The linear system of equations is efficiently solved by alternating the incomplete Cholesky biconjugate gradient (ICBCG) solver with the static divergence correction procedure. Even with this efficiency in the forward modeling, generating the full sensitivity matrix at every iteration is still impractical on modern PCs. To reduce the computer time to a reasonable level, an efficient procedure for updating the sensitivities is implemented: (1) in the first few iterations, the sensitivities for the starting homogeneous half-space are used, (2) the full sensitivity matrix is computed only once (e.g. at the third iteration), and (3) for the subsequent iterations it is updated using Broyden's algorithm. The synthetic and real data examples show that the method is robust in the presence of static shifts and can be used for 3-D problems of realistic size.