Sonic Attenuations of qP and qSV Waves in Fractured Rock

Abstract

In situ rocks often contain fractures/joints aligned in certain directions. When sonic waves propagate in such anisotropic rocks, fluid can squirt between fractures and the contiguous matrix. In this article, matrix pores are referred to as the primary porosity, whereas fractures are referred to as the secondary porosity. A new model of quasi-P (qP) and quasi-SV (qSV) waves in the band of sonic frequency is constructed, with the full consideration of mechanical anisotropy arising from orientated fractures. Because the mathematical problem involves seven partial differential equations, the method of matrices yielding from plane waves is used for solving the problem. The model is capable of predicting not only sonic qP-wave attenuation but also sonic qSV-wave attenuation. The sonic log of a sandstone reservoir in Saudi Arabia is used as an application example. The modelling successfully reproduces the measured velocities of qP and qSV waves at 10 kHz, as well as the measured quality factors of qP wave (100) and qSV wave (21). Remarkably, the modelling yields a dip angle of 63° at depths of 2.4–2.5 km, which is consistent with the tensional stress, the deep basement and the sandstone nature of the reservoir. It is demonstrated that the new model is capable of well regenerating sonic attenuations of qP and qSV waves in porous rock containing tensional fractures.