286 Geophysics in Geothermal Exploration Figure 10.7 Time series of the current emitted by the source (TX), the signal recorded by the surface sensor (RX1), and the signal recorded at the borehole bottom (RX2). To validate the measurement taken at the borehole bottom, we use a 1D subsurface model, with depth-dependent resistivity variations described in Figure 10.9. We employ the EM3DS software developed by the University of Utah (Wannamaker et al., 1984) to simulate the signal recorded by the probe at the borehole bottom. This software uses a volume integral equation formulation (solved using the method of moments) to compute secondary currents in 3D bounded heterogeneities localized within a 1D stratified structure (infinite horizontal, homogeneous, and isotropic layers). The effect of the casing present in the borehole is not modeled in our case. The signal frequency used for modeling is 0.5 Hz. The spatial discretization is limited to 3D bodies, while the response of the horizontal stratification is calculated semi-analytically using Hankel transforms. Thanks to this approach, the number of cells in the models remains moderate, generally fewer than 1000 (compared to the typical values of around 100000 in finite-difference or finite-element methods, where the entire 3D space must be meshed), enabling relatively fast computation. The results of this modeling provide a theoretical response at 0.5 Hz of 7.4 × 10–³ nT/(A·m), compared to the recorded signal of 1.3 × 10–³ nT/(A·m). The orders of magnitude are similar, further validating the recorded signal. The observed differences between the modeling and the recorded signal are attributed to the imperfections of the 1D model and the fact that the probe is within the casing.
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