118 Geophysics in Geothermal Exploration Faust (1953) has established an empirical relationship between seismic velocity V, depth Z, and electrical resistivity measurements Rt. For a formation of a given lithology, the velocity V can be written as a function of the depth Z and resistivity Rt as follows: V = C·(Z·Rt) 1/b (3.5) with: • V the P-wave velocity of the formation in m/s, • Z the depth in m, • Rt the electrical resistivity in Ω·m, • C and b the coefficients associated with Faust’s equation. At each well where a long normal log has been recorded, an interval velocity log has been extracted from the 3D seismic interval velocity block. The two sets of data (resistivity and seismic velocity) have been combined to calibrate an empirical Faust’s law, which has then been used as a local constraining function to transform the 3D pseudo-velocity block into a 3D pseudo-resistivity block. For each well, the two coefficients, C (constant coefficient) and b (power law exponent), of that empirical law were determined through a least-square minimization of the difference between the 3D-block-extracted seismic velocities and the velocities predicted from Faust’s law using the long normal resistivity log data as input. The previous seismic-derived 3D resistivity block (Rt-seis) was converted into a 3D pseudo-porosity block, by using the Archie-law-derived formula (equation (3.1) with m = 2). The results are shown in Figures 3.2c and 3.2d. Figure 3.2c shows the long normal resistivity log Rt, the resistivity log Rt-seis converted from seismic velocity log using Faust’s law, the estimated seismic porosity log using Archie’s law. Figure 3.2d shows porosity and velocity sections extracted from the 3D blocks, oriented South-East North-West, and passing close to borehole M09. The high porosity layer, observed on the porosity log at 87 m depth (Figure 3.2c) clearly appears on the porosity section in the 45–100 m interval distance (Figure 3.2d). The example shows how long normal resistivity logs can be used as constraints to transform seismic velocity sections into seismic sections in porosity, using petrophysical equations established by Faust and Archie. In addition to conventional logging tools, borehole wall imaging tools, such as formation micro scanner, high resolution acoustic or optical televiewers are currently run. The tools provide high resolution (several cm) oriented images of the borehole walls. They are used to detect dips, discontinuities, features such as fractures, to show diameter changes with open fractures and breakouts. They are also used to identify facies and perform stratigraphic interpretations (Gaillard et al., 2024).
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