We investigate a new algorithm for computing regularized solutions of the two-dimensional magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such 'minimum-structure' models: the Gauss-Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie-Madden) are more efficient than the GaussNewton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients-based algorithms avoid two computationally intensive 14-1 Rodi and Mackie tasks that are performed at each step of a Gauss-Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie-Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie-Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

Magnetotelluric (MT) and seismic data, collected during the MELT experiment at the Southern East Pacific Rise (SEPR) 1,2 , constrain the distribution of melt beneath this mid-ocean-ridge spreading center and also the evolution of the oceanic lithosphere during its early cooling history. In this paper, we focus on structure imaged at distances ~100 to 350 km east of the ridge crest, corresponding to seafloor ages of ~1.3 to 4.5 Ma, where the seismic and electrical conductivity structure is nearly constant, independent of age. Beginning at a depth of about 60 km, there is a large increase in electrical conductivity and a change from isotropic to transversely anisotropic electrical structure with higher conductivity in the direction of fast propagation for seismic waves. Because conductive cooling models predict structure that increases in depth with age, extending to about 30 km at 4.5 Ma, we infer that the structure of young oceanic plates is instead

[1] The electromagnetic data from the Mantle Electromagnetic and Tomography (MELT) experiment are inverted for a two-dimensional transversely anisotropic conductivity structure that incorporates a correction for three-dimensional topographic effects on the magnetotelluric responses. The model space allows for different conductivity values in the along-strike, cross-strike, and vertical directions, along with imposed constraints of model smoothness and closeness among the three directions. Anisotropic models provide a slightly better fit to the data for a given level of model smoothness and are more consistent with other geophysical and laboratory data. The preferred anisotropic model displays a resistive uppermost 60-km-thick mantle independent of plate age, except in the vicinity of the ridge crest. In most inversions, a vertically aligned sheet-like conductor at the ridge crest is especially prominent in the vertical conductivity. Its presence suggests that the melt is more highly concentrated and connected in the vertical direction immediately beneath the rise axis. The melt zone is at least 100 km wide and is asymmetric, having a greater extent to the west. Off-axis, and to the east of the ridge, the mantle is more conductive in the direction of plate spreading at depths greater than 60 km. The flat resistive-conductive boundary at 60 km agrees well with the inferred depth of the dry solidus of peridotite, and the deeper conductive region is consistent with the preferred orientation of olivine inferred from seismic observations. This suggests that the uppermost 60 km represents the region of mantle that has undergone melting at the ridge and has been depleted of water (dissolved hydrogen). By contrast, the underlying mantle has retained a significant amount of water.

We have developed a robust and efficient finite difference algorithm for computing the magnetotelluric response of general three‐dimensional (3‐D) models using the minimum residual relaxation method. The difference equations that we solve are second order in H and are derived from the integral forms of Maxwell's equations on a staggered grid. The boundary H field values are obtained from two‐dimensional transverse magnetic mode calculations for the vertical planes in the 3‐D model. An incomplete Cholesky decomposition of the diagonal subblocks of the coefficient matrix is used as a preconditioner, and corrections are made to the H fields every few iterations to ensure there are no H divergences in the solution. For a plane wave source field, this algorithm reduces the errors in the H field for simple 3‐D models to around the 0.01% level compared to their fully converged values in a modest number of iterations, taking only a few minutes of computation time on our desktop workstation. The E fields can then be determined from discretized versions of the curl of H equations.

Abstract. Within the syntaxial bends of the India-Asia collision the Himalaya terminate abruptly in a pair of metamorphic massifs. Nanga Parbat in the west and Namche Barwa in the east are actively deforming antiformal domes which expose Quaternary metamorphic rocks and granites. The massifs are transected by major Himalayan rivers (Indus and Tsangpo) and are loci of deep and rapid exhumation. On the basis of velocity and attenuation tomography and microseismic, magnetotelluric, geochronological, petrological, structural, and geomorphic data we have collected at Nanga Parbat we propose a model in which this intense metamorphic and structural reworking of crustal lithosphere is a consequence of strain focusing caused by significant erosion within deep gorges cut by the Indus and Tsangpo as these rivers turn sharply toward the foreland and exit their host syntaxes. The localization of this phenomenon at the terminations of the Himalayan arc owes its origin to both regional and local feedbacks between erosion and tectonics.