Three‐dimensional mise‐à‐la‐masse modeling applied to mapping fracture zones

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Abstract
A numerical scheme applying the method of volume integral equations has been developed for borehole‐to‐borehole and borehole‐to‐surface modeling of the apparent resistivity response of a thin conductive body in a half‐space; the inhomogeneity simulates a fracture zone in a geothermal system. The algorithm is applicable for the direct‐current case when the buried electrode is either inside (mise‐à‐la‐masse) or outside (near‐miss) the body. In implementing the scheme, the integral equation is transformed into a matrix equation as a result of discretizing the inhomogeneity into rectangular cells. All physical properties are assumed constant within each cell. The rectangular cells are used through‐out execution of the algorithm. The computed surface and subsurface apparent resistivity responses are examined for bodies of similar shape and size but with different orientations: (1) vertical, (2) horizontal, (3) dipping at 60 degrees, and (4) dipping at 30 degrees. The four bodies produce apparent resistivity cross‐section plots which differ little from each other except in orientation. Varying the depth to the top of a body does not significantly alter the subsurface apparent resistivity response in the vicinity of the body. In both section and plan views, estimates of orientation, areal extent, and dip can often be made. The maximum depth at which a body can be located and still produce a detectable surface anomaly is dependent upon the position of the buried electrode and upon the contrast in conductivity. Locating the buried electrode just outside the body does not significantly alter the results from those when the electrode is embedded in the inhomogeneity. However, the similarity between the results of these two cases decreases as the distance between the electrode and the body is increased.

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