Nonlinear Conjugate Gradients Algorithm For 2-D Magnetotelluric Inversion

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 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

3-D resistivity forward modeling and inversion using conjugate gradients

We have developed rapid 3-D dc resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARC‐station 2 for 50 × 50 × 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources. For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix [tilde under A] or its transpose [tilde under A][superscript T] multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of [tilde under A][superscript T] [tilde under A], thus greatly decreasing the time needed to do 3-D inversions. We demonstrate 3-D resistivity tomographic imaging using pole‐pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.United States. Environmental Protection Agency (grant #CR-821516

Electrical structure beneath the northern MELT line on the East Pacific Rise at 15°45′S

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 33 (2006): L22301, doi:10.1029/2006GL027528.The electrical structure of the upper mantle beneath the East Pacific Rise (EPR) at 15°45′S is imaged by inverting seafloor magnetotelluric data obtained during the Mantle ELectromagnetic and Tomography (MELT) experiment. The electrical conductivity model shows no evidence for a conductive region immediately beneath the ridge, in contrast to the model previously obtained beneath the EPR at 17°S. This observation can be explained by differences in current melt production along the ridge, consistent with other observations. The mantle to the east of the ridge at 60 –100 km depth is anisotropic, with higher conductivity in the spreading direction compared to the along-strike direction, similar to the 17°S region. The high conductivity in the spreading direction can be explained by a hydrated mantle with strain-induced lattice preferred orientation of olivine or by partial melt preferentially connected in the spreading direction.This work was supported by NSF grant OCE0118254

Mantle dynamics beneath the East Pacific Rise at 17°S : insights from the Mantle Electromagnetic and Tomography (MELT) experiment

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 111 (2006): B02101, doi:10.1029/2004JB003598.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.This work was supported by NSF grant OCE0118254 and the Research Program on Mantle Core Dynamics, Institute for Research on Earth Evolution (IFREE), Japan Agency for Marine-Earth Science and Technology (JAMSTEC)

Compositional controls on oceanic plates : geophysical evidence from the MELT area

Author Posting. © The Authors, 2005. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature 437 (2005): 249-252, doi:10.1038/nature04014.Magnetotelluric (MT) and seismic data, collected during the MELT experiment at the Southern East Pacific Rise (SEPR) 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 controlled by a decrease in water content above 60 km induced by the melting process beneath the spreading center.US participation in the MELT experiment and subsequent analysis was funded by NSF grants through the Marine Geology and Geophysics Program, Ocean Sciences Division