Modular implementation of magnetotelluric 2D forward modeling with general anisotropy

We present a general framework for two-dimensional finite difference modeling of magnetotelluric data in the presence of general anisotropy. Our approach is modular, allowing differential operators for a range of formulations of the governing equations, defined on several possible discrete grids, to be constructed from a basic set of first difference and averaging operators. We specifically consider two formulations of the two-dimensional anisotropic problem, one with Maxwell's equations reduced to a second order system in terms of three coupled electric components, and one in terms of coupled electric and magnetic x-components. Both formulations are discretized on a staggered grid; the second (coupled electric and magnetic) system is also implemented on a grid with fixed nodes (i.e., not staggered). The three implementations are validated and compared using a range of test models, including a half-space with general anisotropy, an infinite fault with axial anisotropy and a simple dyke model. Comparisons to analytic results (for half-space and fault models), and to results from other anisotropic codes, combined with grid-refinement convergence tests, demonstrate that our algorithms are accurate and capable of routine modeling of two-dimensional general anisotropy. These finite difference codes, demonstrating the flexibility of our numerical discretization approach, can be readily applied to other problems

3D magnetotelluric modeling using high-order tetrahedral Nédélec elements on massively parallel computing platforms

We present a routine for 3D magnetotelluric (MT) modeling based upon high-order edge finite element method (HEFEM), tailored and unstructured tetrahedral meshes, and high-performance computing (HPC). This implementation extends the PETGEM modeller capabilities, initially developed for active-source electromagnetic methods in frequency-domain. We assess the accuracy, robustness, and performance of the code using a set of reference models developed by the MT community in well-known reported workshops. The scale and geological properties of these 3D MT setups are challenging, making them ideal for addressing a rigorous validation. Our numerical assessment proves that this new algorithm can produce the expected solutions for arbitrarily 3D MT models. Also, our extensive experimental results reveal four main insights: (1) high-order discretizations in conjunction with tailored meshes can offer excellent accuracy; (2) a rigorous mesh design based on the skin-depth principle can be beneficial for the solution of the 3D MT problem in terms of numerical accuracy and run-time; (3) high-order polynomial basis functions achieve better speed-up and parallel efficiency ratios than low-order polynomial basis functions on cutting-edge HPC platforms; (4) a triple helix approach based on HEFEM, tailored meshes, and HPC can be extremely competitive for the solution of realistic and complex 3D MT models and geophysical electromagnetics in general

3D Magnetotelluric Modeling Using High-Order Tetrahedral Nédélec Elements on Massively Parallel Computing Platforms

We present a routine for 3D magnetotelluric (MT) modeling based upon high-order edge finite element method (HEFEM), tailored and unstructured tetrahedral meshes, and high-performance computing (HPC). This implementation extends the PETGEM modeller capabilities, initially developed for active-source electromagnetic methods in frequency-domain. We assess the accuracy, robustness, and performance of the code using a set of reference models developed by the MT community in well-known reported workshops. The scale and geological properties of these 3D MT setups are challenging, making them ideal for addressing a rigorous validation. Our numerical assessment proves that this new algorithm can produce the expected solutions for arbitrarily 3D MT models. Also, our extensive experimental results reveal four main insights: (1) high-order discretizations in conjunction with tailored meshes can offer excellent accuracy; (2) a rigorous mesh design based on the skin-depth principle can be beneficial for the solution of the 3D MT problem in terms of numerical accuracy and run-time; (3) high-order polynomial basis functions achieve better speed-up and parallel efficiency ratios than low-order polynomial basis functions on cutting-edge HPC platforms; (4) a triple helix approach based on HEFEM, tailored meshes, and HPC can be extremely competitive for the solution of realistic and complex 3D MT models and geophysical electromagnetics in general.This project has been 65% cofinanced by the European Regional Development Fund (ERDF) through the Interreg V-A Spain–France– Andorra program (POCTEFA2014-2020). POCTEFA aims to reinforce the economic and social integration of the French–Spanish–Andorran border. Its support is focused on developing economic, social and environmental cross-border activities through joint strategies favoring sustainable territorial development. BSC authors received funding from the European Union’s Horizon 2020 programme, grant agreement N◦828947 and N◦777778, and from the Mexican Department of Energy, CONACYT-SENER Hidrocarburos grant agreement N◦B-S-69926

Lithospheric structure of an Archean craton and adjacent mobile belt revealed from 2-D and 3-D inversion of magnetotelluric data : example from southern Congo craton in northern Namibia

Author Posting. © American Geophysical Union, 2013. 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: Solid Earth 118 (2013): 4378–4397, doi:10.1002/jgrb.50258.Archean cratons, and the stitching Proterozoic orogenic belts on their flanks, form an integral part of the Southern Africa tectonic landscape. Of these, virtually nothing is known of the position and thickness of the southern boundary of the composite Congo craton and the Neoproterozoic Pan-African orogenic belt due to thick sedimentary cover. We present the first lithospheric-scale geophysical study of that cryptic boundary and define its geometry at depth. Our results are derived from two-dimensional (2-D) and three-dimensional (3-D) inversion of magnetotelluric data acquired along four semiparallel profiles crossing the Kalahari craton across the Damara-Ghanzi-Chobe belts (DGC) and extending into the Congo craton. Two-dimensional and three-dimensional electrical resistivity models show significant lateral variation in the crust and upper mantle across strike from the younger DGC orogen to the older adjacent cratons. We find Damara belt lithosphere to be more conductive and significantly thinner than that of the adjacent Congo craton. The Congo craton is characterized by very thick (to depths of  250 km) and resistive (i.e., cold) lithosphere. Resistive upper crustal features are interpreted as caused by igneous intrusions emplaced during Pan-African magmatism. Graphite-bearing calcite marbles and sulfides are widespread in the Damara belt and account for the high crustal conductivity in the Central Zone. The resistivity models provide new constraints on the southern extent of the greater Congo craton and suggest that the current boundary drawn on geological maps needs revision and that the craton should be extended further south.The SAMTEX consortiummembers (Dublin Institute for Advanced Studies, Woods Hole Oceanographic Institution, Council for Geoscience (South Africa), De Beers Group Services, The University of the Witwatersrand, Geological Survey of Namibia, Geological Survey of Botswana, Rio Tinto Mining and Exploration, BHP Billiton, Council for Scientific and Industrial Research (South Africa), and ABB Sweden) are thanked for their funding and logistical support during the four phases of data acquisition. This work is also supported by research grants from the National Science Foundation (EAR-0309584 and EAR-0455242 through the Continental Dynamics Program to R. L. Evans), the Department of Science and Technology, South Africa, and Science Foundation of Ireland (grant 05/RFP/ GEO001to A. G. Jones).2014-02-0

Probing the Southern African Lithosphere With Magnetotellurics-Part I: Model Construction

The Southern African Magnetotelluric Experiment (SAMTEX) involved the collection of data at over 700 sites in Archean to Proterozoic southern Africa, spanning features including the Kalahari Craton, Bushveld Complex, and voluminous kimberlites. Here, we present the first 3D inversions of the full SAMTEX data set. In this paper, we focus on assessing the robustness of the 3D models by comparing two different inversion codes, jif3D and ModEM, and two different subsets of the data, one containing all acceptable data and the other containing a smaller selection of undistorted, high-quality data. Results show that the main conductive and resistive features are imaged by all inversions, including deep resistive features in the central Kaapvaal Craton and southern Congo Craton and a lithospheric-scale conductor beneath the Bushveld Complex. Despite this, differences exist between the jif3D and ModEM inverse models that derive mainly from the differences in regularization between the models, with jif3D producing models that are very smooth laterally and with depth, while ModEM produces models with more discrete conductive and resistive features. Analysis of the differences between these two inversions can provide a good indication of the model resolution. More minor differences are apparent between models run with different subsets of data, with the models containing all acceptable data featuring higher wavelength conductivity variations than those run with fewer stations but also demonstrating poorer data fit

custEM: Customizable finite-element simulation of complex controlled-source electromagnetic data

We have developed the open-source toolbox custEM (customizable electromagnetic modeling) for the simulation of complex 3D controlled-source electromagnetic (CSEM) problems. It is based on the open-source finite-element library FEniCS, which supports tetrahedral meshes, multiprocessing, higher order polynomials, and anisotropy. We use multiple finite-element approaches to solve the time-harmonic Maxwell equations, which are based on total or secondary electric field and gauged potential formulations. In addition, we develop a secondary magnetic field formulation, showing superior performance if only magnetic fields are required. Using Nédélec basis functions, we robustly incorporate the current density on the edges of the mesh for the total field formulations. The latter enable modeling of CSEM problems taking topography into account. We evaluate semianalytical 1D layered-earth solutions with the pyhed library, supporting arbitrary configurations of dipole or loop sources for secondary field calculations. All system matrices have been modified to be symmetric and solved in parallel with the direct solver MUMPS. Aside from the finite-element kernel, mesh generation, interpolation, and visualization modules have been implemented to simplify and automate the modeling workflow. We prove the capability of custEM, including validation against analytic-solutions, crossvalidation of all implemented approaches, and results for a model with 3D topography with four examples. The object-oriented implementation allows for customizable modifications and additions or to use only submodules designed for special tasks, such as mesh generation or matrix assembly. Therefore, the toolbox is suitable for crossvalidation with other codes and as the basis for developing 3D inversion routines

Efficient Inversion of Multi-frequency and Multi-source Electromagnetic Data: Final report

BES grant DE-FG02-06ER15819 supported efforts at Oregon State University (OSU) to develop improved inversion methods for 3D subsurface electromagnetic (EM) imaging. Three interrelated activities have been supported by this grant, and its predecessor (DE-FG02-06ER15818): (1) collaboration with a former student of the PI, Dr. Weerachai Siripunvaraporn (now Professor at Mahidol University in Bangkok, Thailand) on developing and refining inversion methods for 3D Magnetotelluric (MT) data . (2) Development at Oregon State University of a new modular system of computer codes for EM inversion, and initial testing and application of this inversion on several large field data sets. (3) Research on more efficient approaches to multi-transmitter EM inverse problems, to optimize use of expensive data sensitivity calculations needed for gradient based inversion schemes. The last of these activities was the main motivation for this research project, but the first two activities were important enabling steps that produced useful products and results in their own right, including freely avaialable software for 3D inversion of EM geophysical data

INTEGRATED APPROACHES FOR SCALABLE AQUIFER NUMERICAL MODELING, INVERSION, AND UPSCALING

Ph.D