[雙語翻譯]--外文翻譯--一種模擬導(dǎo)電介質(zhì)電磁響應(yīng)的新方法（英文）

1、GEOPHYSICS, VOL. 54, NO.9 (SEPTEMBER 1989);P. 1180-1192. to FIGS.A new approach to modeling the electromagnetic response of conductive mediaK. H. Lee*, G. Liut, and H. F. MorrisontABSTRACTWe introduce a new and potential

2、ly useful method for computing electromagnetic (EM) responses of ar- bitrary conductivity distributions in the earth. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave

3、 field that satisfies a wave equation. We show that this integral transform can be extended to include vector fields. Our algorithm takes advantage of this relationship between the wave field and the actual EM field. Spe

4、cifically, numerical computation is carried out for the wave field, and the result is transformed back to the EM field in the time domain. The proposed approach has been successfully dem- onstrated using two-dimensional

5、(2-D) models. The appropriate TE-mode diffusion equation in the time domain for the electric field is initially transformedINTRODUCTIONElectromagnetic (EM) methods in geophysics have been used for many years to determine

6、 the electrical conductivity of the subsurface. The major application in Western coun- tries has been in the search for mineral deposits, with lesser applications in groundwater, petroleum exploration, and crustal studie

7、s. In the Soviet Union, EM methods have played a major role both in petroleum exploration and in mineral exploration. In all these applications, the depth of interest requires low frequencies, usually less than 30 kHz; a

8、nd for typical earth conductivities, the conduction current is orders of magnitude greater than the displacement cur- rents. The resulting second-order partial differential equa- tion describing the behavior of the field

9、s is, in fact, ainto a scalar wave equation in an imaginary q domain, where q is a time-like variable. The corresponding scalar wave field is computed numerically using an explicit q-stepping technique. Standard finite-d

10、if- ference methods are used to approximate the fields, and absorbing boundary conditions are implemented. The computed wave field is then transformed back to the time domain. The result agrees fairly well with the solut

11、ion computed directly in the time domain. We also present an approach for general three- dimensional (3-D) EM problems for future studies. In this approach, Maxwell's equations in the time domain are first transforme

12、d into a system of coupled first- order wave equations in the q domain. These coupled equations are slightly modified and then cast into a “symmetric“ and “divergence-free“ form. We show that it is to this particular for

13、m of equations that numerical schemes developed for solving wave equa- tions can be applied efficiently.diffusion equation for which the solutions are quite different from those of the more familar wave equation encounte

14、red in seismic wave propagation or radar. Concepts of pulse or wavelet propagation or of pulse traveltime and the construc- tion of reflectivity images of subsurface structure are not possible for solutions that do not a

15、llow well defined group velocity. The difficulty of depicting the solutions for the diffusion equation in all but simple, elementary situations is one practical reason for the slow acceptance of EM conduc- tivity mapping

16、 in new applications. There are also numerical and computational complications in using EM methods. Whereas perfectly useful model realizations can be obtained with simple ray-tracing algo- rithms in seismic studies, the

17、 EM responses for the same models require a complete solution to a formal boundaryManuscript received by the Editor October II, 1988; revised manuscript received March 6, 1989. *Lawrence Berkeley Laboratory, Bldg. 50 E,

18、University of California, I Cyclotron Road, Berkeley, CA 94720. :j:Department of Materials Science and Mineral Engineering, 414 Hearst Mining Bldg., University of California, Berkeley, CA 94720. This paper was prepared b

19、y an agency of the U.S. government.1180Downloaded 11/18/15 to 134.148.5.68. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/1182 Lee et al.we find thatV x V x D(r, p) + 11 0

20、,-~ O. Ulr = U(rb' q);After we make the connection between equations (4) and (5), it is clear that the independent variable q has the dimension of square root of time. The function U(r, q) would behave as if it were

21、a propagating wave with a velocity of (11(v) = ±7r/4 in the complex w plane. In this connection, the function B(x) in the MT inverse study by Weidelt (1972) is similar in nature to the wave field U(q). This similari