Fractal Model of Elastic and Electrical Properties of Porous Rock
Abstract
A theoretical model of elastic and electrical properties of porous rock was developed for quantitative joint analysis of collocated seismic velocity tomography and magnetotelluric (MT) experiments. A fractal model applied to elastic properties of rock by Spangengerg (1998) was extended to describe electrical properties of porous rock with the same microstructure for a percolation case. An inverted geometrical model of pore spaces and matrix was also developed to consider isolated pores and a system staying near percolation. The simulation results of electrical properties were compared with the empirical Archie_fs law and former theoretical models of electrical properties of porous rock for special cases of ellipsoidal isolated pores and for interconnected pore geometries, such as a system of tubes along cubic grain edges or films surrounding cubic grains. This comparison shows that the present model is consistent with the former models for special cases. 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. It provides us a simple way to obtain the dependency of a resistivity against a seismic velocity for an arbitrary microstructure. Obtained theoretical dependencies of seismic velocity vs. resistivity allow us to estimate a liquid fraction in a structure from explored seicmic velocity and resistivity distribution. Based on the developed model, an attempt have been successfully made to elaborate a quantitative method for solving the problem whether the variation of resistivity and seismic velocities in a region can be attributed to presence of liquid only or whether other causes should be considered. The developed model can be used for parameterization of a joint MT and seismic inverse problem in a variety of geological settings.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2003
- Bibcode:
- 2003AGUFM.S11F0356P
- Keywords:
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- 0925 Magnetic and electrical methods;
- 3210 Modeling;
- 5112 Microstructure;
- 7203 Body wave propagation;
- 8010 Fractures and faults