1. n. [Formation Evaluation]
A theory developed by M.A. Biot for acoustic propagation in a porous and elastic medium. Compressional and shear velocities can be calculated by standard elastic theory from the composite density, shear, and bulk modulus of the total rock. The problem is how to determine these from the properties of the constituent parts. Biot showed that the composite properties could be determined from the porosity and the elastic properties (density and moduli) of the fluid, the solid material, and the empty rock skeleton, or framework. To account for different frequencies of propagation, it is also necessary to know the frequency, the permeability of the rock, the viscosity of the fluid, and a coefficient for the inertial drag between skeleton and fluid.
Unlike the Gassmann model, the Biot theory takes into account frequency variations and allows for relative motion between fluid and rock framework. As a result, it predicts some of the observed changes in velocity with frequency as well as the critical frequency below which the Gassmann model is valid. It also predicts the existence of a so-called slow wave in addition to the shear wave and the compressional, or fast wave. The slow wave arises when the fluid and the skeleton move 180° out-of-phase with each other. Its velocity is related to fluid mobility, but unfortunately has been observed only in the laboratory, not on logs. At logging frequencies, it degenerates into a diffusion phenomenon rather than a wave, and is apparently too highly attenuated to be observed in real rocks. However, in permeable formations, the Stoneley wave couples into the slow wave, causing the attenuation and dispersion that allow the measurement of Stoneley permeability. The full Biot theory is used mainly to analyze laboratory data. For practical log interpretation, it is more common to use the simpler Gassmann model.
Reference:
See: sonic log
