Determination of the Acoustic Coupling Factor of Biot's Theory of Elasticity, Using in situ Seismic Measurements

Abstract

Besides other elastic, petrophysical, and hydrophysical parameters, the acoustic coupling factor (coupling factor or structure factor, s ) is a critical micro-geometrical parameter in the Biot's theory of elasticity. The coupling factor exerts a specific influence on the mechanisms of propagation and attenuation of vibrations (seismic waves and acoustic signals) in porous media. It is a measure of the internal structure (geometry and shape of pores and pore tubes) of a porous medium, and thus it is a good indicator of the degree of coupling between pore fluid and solid grains. It is unity for no coupling and infinity for perfect coupling. In this study, the coupling factor is obtained for surface soils and shallow sediments, using compressional wave velocity ( x p ) determined from in situ seismic refraction measurements. The investigated soils and underlying sediments (aeration zone and aquifer) exhibit a general s range of 1.22-3.19 (average = 1.82), corresponding to a general x f range of 134-2060 m/s (average = 1134 m/s). The s values are correlated to the bulk modulus-shear modulus ratio (K/ w ) and the porosity (φ). A direct linear correlation between s and K/ w and an inverse polynomial correlation between s and φ are obtained, with coefficients of correlation of 0.91 and 0.98, respectively. Also, various items related to the coupling factor, Biot's theory, attenuation mechanisms, fast and slow compressional waves (first and second kinds), and shear waves are discussed.