Publications

Export 4 results:
Sort by: Author Title Type [ Year  (Desc)]
2012
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
Parker, RL.  2011.  New analytic solutions for the 2-D TE mode MT problem. Geophysical Journal International. 186:980-986.   10.1111/j.1365-246X.2011.05091.x   AbstractWebsite

A closed-form solution is given for a 2-D, transverse electric mode, magnetotelluric (MT) problem. The model system consists of a finite vertical thin conductor with variable integrated conductivity over a perfectly conducting base. A notable property of the solution is that the frequency response possesses a single pole in the complex plane. Systems with finitely many resonances play a central role in the 1-D MT inverse problem based on finite data sets, but until now, no 2-D system of this kind was known. The particular model is shown to be just one of a large class of thin conductors with same the property, and further examples are given. The solutions of the induction problem for members of this family can often be written in compact closed form, making them the simplest known solutions to the 2-D MT problem.

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.

2010
Parker, RL.  2010.  Can a 2-D MT frequency response always be interpreted as a 1-D response? Geophysical Journal International. 181:269-274.   10.1111/j.1365-246X.2010.04512.x   AbstractWebsite

Weidelt and Kaikkonen showed that in the transverse magnetic (TM) mode of magnetotellurics it is not always possible to match exactly the 2-D response at a single site with a 1-D model, although a good approximation usually seems possible. We give a new elementary example of this failure. We show for the first time that the transverse electric (TE) mode responses can also be impossible to match with a 1-D response, and that the deviations can be very large.