New Methods for Arrival Time Determination in Bender Element Tests for Time-Lapsed $V_s$ Tomography

This paper examines and reports on two new methods, i.e., the Stockwell transform based (ST) method and self-healing cross-correlation (SC) method, in determining the S-wave arrival time for bender element tests, especially for $V_s$ tomographic imaging. In the ST method, the Stockwell transform is first carried out to obtain a high-resolution time-frequency representation of the receiving signal; then, the energy in the frequencies around the resonant frequency is summed, followed calculation of the associated energy gradient. The maximum energy gradient is selected as the objective criterion to determine the arrival of the S-wave, since its arrival leads to a distinct amplitude increase and a notable change in the associated energy. The accuracy of this ST method is validated using both numerical and physical experiments. The ST method requires high computing power for signal processing; hence, the SC method is proposed to tackle this practical problem. Considering two consecutive measurements made by the same pair of bender elements in a time interval, subjected to only small changes in the stress states, both measurements should exhibit a similar waveform but with a minute time-shift. Therefore, the cross-correlation peak of the two consecutive measurements gives the travel time difference between them. The validity of the SC method is verified by a laboratory pile installation test equipped with a bender element sensing layer; and good agreement is found between the results obtained from the ST and SC methods. The strengths of these two methods enable us to objectively and automatically process the tremendous amount of bender element signals produced by the high-resolution time-lapsed $V_s$ tomographic images, as demonstrated by process monitoring of the pile installation.