Simulations of S-waves from the piezoelectric source to the receiver to assist in laboratory measurements of rock properties

Abstract

The accurate determination of the emitted S-wave arrival time at the piezoelectric receiver of laboratory triaxial cells is challenging due to the complex preceding P and S wave pattern. To analyze this pattern and decipher the true arrival time of the emitted S-wave, we simulate wave propagation from the actuator to the receiver. The piezoelectric response is accounted for, and the electromechanical coupling is solved, using the spectral finite-element method, or approximated using a linear spatial variation of the electric potential over the actuator to capture the same field over the receiver. The fully-coupled algorithms are validated with 1-D simulations and compared with an exact solution constructed with the method of characteristics. Simulations for a 2D simplified experimental system show the validity of the linear simplification. The comparison of simulated results through a section of the triaxial cell with laboratory calibration data for a steel specimen validates our choice of damping material proxy within the actuator. A final series of simulations for two orthotropic shales with different anisotropy axis orientations with respect to the cell, and two Fontainebleau sandstones having very contrasted vP- vS ratios, is presented. These differences in physical properties have little impact on the wave pattern at, and just after the arrival of the main S-wave. The pattern is influenced more by the experimental setup geometry and the actuator’s internal structure than by the nature of the specimen.