Experimental and theoretical enhancement of the inversion accuracy of the Thomsen parameter δ in organic-rich shale

Experimental physical inversion of rock from the diagonal group velocities is an effective method for the determination of Thomsen's delta anisotropy parameter in organic-rich shale. We further enhance the inversion accuracy of d through conducting more reliable experimental measurements and through theoretical expression. First, we assembled two sets of group velocity acquisition methods, a rotational ultrasonic transducer system and a laser ultrasonic system, and then we assessed which of them was more applicable and accurate by comparing the waveforms and observations on the same cylindrical organicrich shale. Second, we combined the delta-based phase velocity approximation and stricter physical constraints of d, which are deduced on a standard VTI medium, to improve the theoretical part of the inversion. As a result of better observations by the optimal test methods and the proposed d inversion methods, the least errors between the best fitted curve to the observations are 3.24% for the traditional method and 2.1% for the proposed method, which verifies the superiority of the proposed method. Based on experimental tests on two cylindrical shale specimens, we find that rotational ultrasonic transducer measurement is more applicable for quick velocity anisotropy measurements, while for observations obtained by the laser technique, system relative error and the necessary scattering effect processing should be conducted. The procedure of the inversion is more robust and accurate when conducted on the proposed d-based inversion.