A finite-difference, time-domain solution for three-dimensional electromagnetic modeling

Journal Article · Tue Jun 01 04:00:00 EDT 1993 · Geophysics; (United States)

DOI:https://doi.org/10.1190/1.1443465· OSTI ID:5930803

Wang, Tsili ^[1]; Hohmann, G W

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1. Univ. of Utah, Salt City, UT (United States). Dept. of Geology and Geophysics

The authors have developed a finite-difference solution for three-dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell's equations in time using a staggered-grid technique. The time-stepping uses a modified version of the Du Fort-Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic fields responses throughout the earth. Because it solves the coupled, first-order Maxwell's equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence-free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times. An inhomogeneous Dirichlet condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth-order difference method at early times and a second-order method at other times. Numerical checks against analytical, integral-equation, and spectral differential-difference solutions show that the solution provides accurate results. Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10ms. That model contains 100 X 100 X 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 [omega] [center dot] m.

• OSTI ID: 5930803
• Journal Information: Geophysics; (United States), Journal Name: Geophysics; (United States) Vol. 58:6; ISSN GPYSA7; ISSN 0016-8033
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
580000* -- Geosciences
CALCULATION METHODS
COMPUTERIZED SIMULATION
DATA ANALYSIS
ELECTRICAL SURVEYS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC SURVEYS
FINITE DIFFERENCE METHOD
GEOPHYSICAL SURVEYS
IMAGE PROCESSING
ITERATIVE METHODS
MATHEMATICAL MODELS
MATHEMATICS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PROCESSING
SIMULATION
SURVEYS
THREE-DIMENSIONAL CALCULATIONS