A sandwich resonant bar method with transfer matrices for measuring the elastic parameters of rock at low frequency

Rocks and other geological materials have appreciable dispersion in their elastic properties. Rock elastic parameters within the same frequency range as the logging frequency band (1-20 kHz) should be determined to facilitate reservoir prediction and interpretation of logging data. This study suggests a technique for determining the elastic characteristics of rock cores at low frequencies using a sandwich resonant bar by integrating transfer matrices into the one-dimensional transmission model. The frequency response expression of the sandwich resonant bar is derived analytically and then the response is simulated accurately based on this expression. Numerical results show that the first two-order longitudinal resonance frequencies are approximately linearly related to the inverse of the sample's Young's modulus and the density, respectively. In addition, an inversion algorithm based on Gauss-Newton iteration, which converges faster and more efficiently, is proposed in this paper. The residuals between the model's first two resonant frequencies and the simulated results are used as the error function, and the elasticity parameters that minimize the error function are the best estimate for creating the model. This research is valuable for measuring rock elastic parameters accurately in the kilohertz range, which is of practical significance in dispersion-related studies relating to rock cores.