Finite-Element Analysis of Noise Preceding the Arrival of S-Wave in Ultrasonic Measurements of Rock Velocities

For oil and gas seismic exploration, rock velocities are essential parameters to tease out reservoir properties from seismic data. The ultrasonic pulse transmission (UPT) method has been a gold standard to estimate reservoir rock velocities in the laboratory. Regarding the UPT method, accurate determination of the travel time of waves plays a significant role in robustly measuring rock velocities. One of the most conventional ways to obtain the travel time is through the arrival picking. However, unclear noise virtually exists preceding the arrival of S-wave interfering with this arrival picking, which, sometimes, can cause enormous errors to measured S-wave velocity. Herein, we develop a 2-D, three-component (2D-3C) finite-element modeling (FEM) algorithm aiming to interpret the noise by combining with UPT measurements. The proposed 2D-3C FEM not only can efficiently compute ultrasonic wavefield radiated by circular P- or S-wave transducers but also able to obtain synthetic waveforms in the testing of S-wave velocity where polarization directions of S-wave transducers are arranged as nonparallel. To analyze the simulated ultrasonic waveforms, we introduce frequently-used concepts of edge and direct plane waves to build elastodynamic models of the ultrasonic wavefield. Then, we compare numerical results with experimental measurements. Our 2D-3C FEM results show good agreement with experimental waveforms both in P- and S-wave velocity testings. Whereafter, we pinpoint constitutions of the noise preceding the arrival of S-wave. Comparison of numerical and experimental waveforms suggests that the edge P-wave with its reflected and converted modes partially contributes to this noise, while the rest part of the noise may stem from the effects of the compressional dipole, the couplant smeared between a transducer and a sample, and inherently parasitic longitudinal vibrations of S-wave transducers. The interpretations on this noise have the potential to benefit future design of more effective S-wave transducers.