A robust methodology for time picking and error analysis of ultrasonic waveforms and rock densities in the laboratory

Abstract

The relationships between elastic wave speeds and rock physical properties are commonly studied through laboratory experiments. However, the estimation of elastic wave arrival times and the associated errors are not reported consistently. Changes in experimental conditions such as pressures or fluid substitution vary the arrival time and shape of the recorded ultrasonic signals. Crosscorrelation techniques are a simple way of estimating time differences between waveforms for a range of experimental conditions. However, in the presence of elastic wave attenuation, which results in the change of waveform shape (frequency content), this technique can be unstable. We design a methodology based on dynamic time warping functions for consistently picking arrival times between different ultrasonic waveforms. This methodology is robust to small changes in ultrasonic waveform shape due to variation in the experimental conditions. Here, we estimate and correlate P- and S-wave time picks for variations in (1) fluid type or saturation and (2) confining or fluid pressures. We also develop a semiautomated error analysis that uses Monte Carlo simulations to propagate uncertainty in time picks into wave speed and elastic moduli errors. We test the methodology on a set of volcaniclastic and intrusive rocks from a geothermal field in New Zealand at atmospheric conditions and confining stresses. The Python code for this analysis is freely available to the community.