The electromagnetic (EM) inverse problem in geophysics consists of deducing the Earth’s conductivity from measurements of electric or magnetic fields near the surface. It requires fast and accurate forward modeling, a method of solving nonlinear equations, and a method of controlling nonuniqueness. Four modeling methods are considered for simulation of airborne EM data over a 3-D conductivity model: a one-dimensional (1-D) approximation, the 3-D Born approximation, a finite-element (FE) method with approximate boundary conditions, and an FE method with exact boundary conditions. The 1-D and Born approximations are fast, but not very accurate. The two FE methods give similar responses, and the method with approximate boundary conditions requires much less computer resources. Three methods are considered for solving the EM inverse problem by unconstrained nonlinear optimization: conjugate gradient (CG), quasi-Newton, and Gauss-Newton (GN) methods. For the simple models considered, the GN method required the least CPU time; the CG method, the most. An alternative to regularization for controlling nonuniqueness is joint inversion of several different surveys to produce a single model that fits all of the data. An example with airborne EM data and pole-pole dc resistivity data shows that such joint inversion can effectively reduce nonuniqueness in EM inversion.
Figures & Tables
In 1975 Jerry Hohmann published a paper1 that described his numerical implementation of an integral-equation method for three-dimensional electromagnetic (3-D EM2) modeling. The matrix equation for the simple model that he studied—a half-space containing a rectangular body discretized into 100 cubic cells—barely fit into the computer (a UNIVAC 1108 at the University of Utah). Coaxing interesting and correct results from the model and method clearly comprised much of the art and fun of the paper. And winding through the paper’s 50 or so equations and nearly 20 figures was a clear message: 3-D EM is different!
Three-dimensional electromagnetics is qualitatively different with new phenomena3 and new challenges to our understanding of how electromagnetic fields interact with Earth and other conductive bodies (including our own). In subsequent years, Jerry with his students and colleagues pursued these challenges across many fields—mining geophysics, geothermal exploration, magnetotelluric crustal studies, environmental geophysics, oil and gas exploration—in both the time and frequency domains. Of his 51 articles4 in journals and monographs, more than half dealt with three-dimensional electromagnetics.
In 1995, 20 years after Jerry’s classic paper (and three years after his death from cancer in May, 1992), nearly 200 scientists from around the world gathered at Schlumberger–Doll Research in Ridgefield, Connecticut, for a symposium in his memory, the (first) International Symposium on Three-Dimensional Electromagnetics. More than 70 papers were presented in oral and poster sessions during three days organized around the themes: Modeling, Inversion, and Practice. The quality of the work presented, the liveliness of the discussions, and the demand for the symposium proceedings were the impetus for this new volume. We invited the authors to submit longer, more tutorial versions of their articles for a book to be published by the Society of Exploration Geophysicists (SEG) in the series Geophysical Developments.
As is evident from the size of this volume, we were overwhelmed by the response. We hope that readers will find the contents equally weighty. The 44 articles collected here are the work of 97 authors, representing 55 different institutions (universities, government or industrial research labs) from 13 countries around the world. All have been reviewed and edited according to the strict standards of SEG’s lead journal, Geophysics. They represent the state of the art in 3-D EM at the time final revisions were received (from the fall of 1997 through the spring of 1998).
The lead article addresses one of Jerry’s favorite subjects—the need for independent checks on any numerical calculation; it shows how far we have come since 1975 and how far we still are from routine, confident use of 3-D EM models. We have grouped the remaining articles into nine sections:
3-D EM and parallel computers
Magnetotellurics and global induction
Mining and exploration geophysics
Borehole geophysics and logging
This division into techniques and applications is naturally very rough; many articles could easily appear in two or three different sections. The subjects covered in this volume touch, we believe, on every major technique being used today to compute, analyze, visualize, and understand 3-DEM fields in every major application of electrical geophysics (and in two applications outside geophysics: the interaction of 3-DEM fields with the human body and the non-destructive testing of aircraft). The late 1980’s saw the rapid development of 3-D seismics, which has revolutionized exploration for oil and gas in the 1990’s. The early years of the new millenium may see another revolution brought about by the rapid advances now occurring in 3-D EM.
Ridgefield, Connecticut USA
23 May 1998