Comparing approaches to measuring seismic phase variations in the time, frequency, and wavelet domains

Congcong Yuan, Jared Byran, & Marine A. Denolle

Submitted July 1, 2020, SCEC Contribution #10144

Temporal changes in subsurface properties can be monitored by measuring phase shifts in the coda of two seismic waveforms that share a similar source-receiver path but that are recorded at different times. The seismic waveforms at the same receiver are usually obtained either from repeated earthquake sources or from repeated ambient noise cross-correlations. Five algorithms are popular to measure phase shifts in the coda waves, namely the Windowed Cross Correlation (WCC), Trace Stretching (TS), Dynamic Time Warping (DTW), Moving Window Cross Spectrum (MWCS), and Wavelet Cross Spectrum (WCS). The seismic wavespeed perturbation is then obtained from the linear regression of phase shifts on their respective lags under the assumption that the velocity perturbation is homogeneous between (virtual or active) source and receiver. We categorize these methods into the time domain (WCC, TS, DTW), frequency domain (MWCS), and wavelet domain (WCS). In this study, we complement this suite of algorithms with two wavelet-domain methods, which we call Wavelet Transform Stretching (WTS) and Wavelet Transform Dynamic Time Warping (WTDTW) whereby we apply traditional stretching and dynamic time warping techniques to the wavelet transform. This study aims to verify, validate, and test the accuracy and performance of all methods by performing three numerical experiments, in which the elastic wavefields are solved for in various 2D heterogeneous halfspace geometries with an established spectral-element code (SPECFEM2D). Through this work, we validate the assumption of a linear increase in phase shifts with respect to phase lags as a valid argument for homogeneous and laterally homogeneous velocity changes. Additionally, we investigate the sensitivity of seismic frequency of coda waves to the depth of the velocity perturbation. Overall, we conclude that seismic wavefields generated and recorded at the surface lose sensitivity rapidly with the depth of the velocity change for all source-receiver offsets. However, the measurements over a spectrum of seismic frequencies exhibit a pattern such that wavelet methods, and preferably WTS, yield greater opportunity to track the depth of the velocity changes.

Key Words
subsurface monitoring, coda-wave interferometry, numerical full wavefield simulations, ambient noise monitoring

Yuan, C., Byran, J., & Denolle, M. A. (2020). Comparing approaches to measuring seismic phase variations in the time, frequency, and wavelet domains. Geophysical Journal International, (submitted).