Publications

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2012
Ribaudo, JT, Constable CG, Parker RL.  2012.  Scripted finite element tools for global electromagnetic induction studies. Geophysical Journal International. 188:435-446.   10.1111/j.1365-246X.2011.05255.x   AbstractWebsite

Numerical solution of global geomagnetic induction problems in two and three spatial dimensions can be conducted with commercially available, general-purpose, scripted, finite-element software. We show that FlexPDE is capable of solving a variety of global geomagnetic induction problems. The models treated can include arbitrary electrical conductivity of the core and mantle, arbitrary spatial structure and time behaviour of the primary magnetic field. A thin surface layer of laterally heterogeneous conductivity, representing the oceans and crust, may be represented by a boundary condition at the Earthspace interface. We describe a numerical test, or validation, of the program by comparing its output to analytic and semi-analytic solutions for several electromagnetic induction problems: (1) concentric spherical shells representing a layered Earth in a time-varying, uniform, external magnetic field, (2) eccentrically nested conductive spheres in the same field and (3) homogeneous spheres or cylinders, initially at rest, then rotating at a steady rate in a constant, uniform, external field. Calculations are performed in both the time and frequency domains, and in both 2-D and 3-D computational meshes, with adaptive mesh refinement. Root-mean-square accuracies of better than 1 per cent are achieved in all cases. A unique advantage of our technique is the ability to model Earth rotation in both the time and the frequency domain, which is especially useful for simulating satellite data.

Parker, RL, Wheelock B.  2012.  Fourier domain calculation of terrain effects in marine MT. Geophysical Journal International. 189:240-250.   10.1111/j.1365-246X.2011.05350.x   AbstractWebsite

Magnetotelluric surveys on the seafloor have become an important part of marine geophysics in recent years. The distorting effects of topographic relief on the electromagnetic fields can be far-reaching, but local terrain is also important. Thus, computational techniques that can treat a large area containing fine-scale topography could find widespread application. We describe a new solution to the problem based on a well-established theory of electromagnetic induction in thin sheets. The procedure requires taking the Fourier transform of the integral equations derived by Dawson and Weaver in 1979, and by McKirdy, Weaver and Dawson in 1985. The equations in the transformed electric field are solved iteratively by a new technique. We prove the new iterative procedure is always convergent, whereas the original scheme diverges when the grid spacing of the discretization is small. We also give a means of correcting for distant features that need not be specified in as great detail. Preliminary tests confirm the new process is very efficient and that topographic data sets of several million points will be handled with ease.

2011
Van Beusekom, AE, Parker RL, Bank RE, Gill PE, Constable S.  2011.  The 2-D magnetotelluric inverse problem solved with optimization. Geophysical Journal International. 184:639-650.   10.1111/j.1365-246X.2010.04895.x   AbstractWebsite

P>The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.