Application of Fractal Model of Electrical and Elastic Properties of Porous Rock to Hirabayashi Borehole Data

To investigate microstructure of fault core and damaged zones, a fractal model for elastic and electrical properties of porous rock was applied to logging data of the Hirabayashi borehole, a 746 m deep borehole penetrating the Nojima fault, the main fault responsible for the Kobe earthquake at 1995. The main advantage of the present model against other theoretical models is possibility to describe both elastic and electrical properties of rock with a single model for a wide range of microstructures including 3D grains and pore anisotropy and various degrees of pore interconnection. Dependencies of the conductivity and the seismic velocities against the porosity were successfully simulated for all zones detected by core analysis: from the outside fault zone (152-426 m) to the upper and lower damaged zones (426-611 m and 641-746 m respectively) and the fault core zone (611-641 m). An interesting feature is that while the number of fractures observed by Fullbore Formation MicroImager (FMI) in the outside fault zone (4.2 fracture/meter) is 2-5% more than in the upper damaged and core zones (3.99 and 4.08) and only 12.5% less than in the outside fault zone (4.8 fracture/meter), the resistivity and seismic velocities in the fault zone are remarkably lower. This seeming discrepancy was explained by increasing number of microcracks that might be not detected by FMI. The seismic velocities and resistivity measured by logging at the depth 152-426 m were successfully simulated under assumption, that porosity of microcracks does not exceed 0.73%, the lowest porosity throughout the depths. At upper and lower damaged zones the experimental data were effectively simulated with porosity of microcrackes of 2.28%. These results are in a good agreement with the porosity measurements of core analysis, namely, 0.67% for the samples taken from the outside fault zone and 2.29% for the samples from the upper and lower damaged zones. The application of the fractal model of electrical and elastic properties of porous rock is demonstrated to be useful for recognizing a rock microstructure using porosity, resistivity and seismic velocities, which are measured in boreholes.