An improved inversion process for measuring the elastic parameters of TI samples via resonant ultrasound spectroscopy

Abstract Accurately measuring the elastic parameters of shale rock samples is highly significant for evaluating shale reservoirs. Resonant ultrasound spectroscopy (RUS) is a non-destructive measurement technique that is increasingly applied to anisotropic materials for elastic parameter estimation and iteratively determines the optimal elastic parameters by fitting the calculated resonance spectrum to the measured spectrum via optimization methods. Traditional measurement methods typically involve manually extracting resonance frequencies for mode matching and applying the Levenberg–Marquardt (LM) algorithm, which heavily relies on initial values for inversion. However, these methods often result in incorrect inversion, particularly when multiple elastic parameters are simultaneously inverted, as the increased complexity hinders the attainment of accurate results. A novel inversion framework, termed hybrid optimization RUS, has been proposed for optimizing the inversion process by integrating the particle swarm optimization algorithm with the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm for inversion (RUS-HL). This approach circumvents mode matching and reduces the dependence on prior knowledge of sample elastic parameters. The RUS-HL misfit function uses resonance peak frequency and Q value information to fit a resonance spectrum with a Lorentzian function, defining the difference between the theoretical and calculated resonance spectra as the misfit function. Compared with conventional misfit functions such as the root mean square error, the proposed inversion calculation can be conducted without mode recognition and without relying on the initial values. The resonance spectra of isotropic and transversely isotropic samples were inverted separately to test the method, resulting in a more efficient and accurate determination of the elastic parameters.