a thin body embedded in a conductive half-space-with The time-domain electromagnetic (TEM) modeling or without overburden. The results indicate the conduc method of Oristaglio and Hohmann is reformulated tive half-space will both delay and attenuate the re here in terms of the secondary field. This finite sponse of the body and even obscure it if the conduc dilTerence method gives a direct. explicit time-domain tivity contrast is small. The results also suggest that the solution for a two-dimensional body in a conductive conductive host can alter the decay rate of the response earth by advancing the field in time with DuFort of the body from its free-space counterpart. OUf results Frankel time-differencing. As a result, solving for the for multiple bodies illustrate the importance of early secondary field, defined as the difference between the time measurements to obtain resolution, particularly for total field and field of a half-space, is not only more measurements of the horizontal magnetic field. The ver efficient but is also simpler and eliminates several prob tical magnetic field, however, can be used to infer the lems inherent in the solution for the total field. For dip direction of a dipping body by studying the migra example, because the secondary field varies slowly both tion of the crossover. in space and time, it can be modeled on a coarse grid The results for models which include overburden with large time steps. In addition, for a simple body the show that the effect of a conductive overburden, in addi field is local; therefore, because the field can be assumed tion to the half-space effect, is to delay the response of to satisfy a simple boundary condition in the earth com the body, because the primary current initially tends to putation is greatly simplified. Our tests show that for concentrate and slowly diffuse through the overburden, the same accuracy, the secondary-field solution is and does not reach the body until later time. This effect roughly five times faster than the total-field solution. also complicates the early-times profiles, becoming We compute and analyze the magnetic field impulse more severe as the conductivity of the overburden is response for a suite of models, most of which consist of increased.
We attempted to develop a direct time-domain, finite-difference solution for the electromagnetic response of a 3-D model. The algorithm is an extension of our 2-D modelling technique, which uses the Du Fort-Frankel finite-difference scheme. However, the vector nature of the field makes the 3-D problem much more complicated than its 2-D counterpart, and a supercomputer is required for computations. Unlike the 2-D case, where we solve for the electric field, the solution is formulated in terms of secondary magnetic field to avoid dealing with a discontinuous normal component of electric field. However, that difficulty is replaced with a problem involving the gradient of conductivity, which is discontinuous at interfaces. We experimented with both smoothing the conductivity variation, so that the gradient is well defined; and integrating the gradient terms, which results in a tangential current density contrast. Our limited experiments indicate that the magnetic field step response is computationally more stable than the impulse response, because it is a smoother function with smaller dynamic range. However, the step response takes longer to compute because its source, which involves the primary fields in the earth, requires very accurate numerical integration. Due to computer time and memory limitations on the supercomputer available to us, we were not able to develop an accurate numerical solution. We were able to carry out only a few tests on small models for which results were not in good agreement with values computed using a 3-D integral equation solution.
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