A comparison of methods to estimate seismic phase delays: numerical examples for coda wave interferometry

Abstract

S U M M A R YTime-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross-correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here we implement Dynamic Time Warping (DTW) to estimate the warping function -a vector of local time shifts that globally minimizes the misfit between two seismic traces. We compare all three methods using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross-correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has good time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements.

Improved moving window cross‐spectral analysis for resolving large temporal seismic velocity changes in permafrost

“…If the SNR is too low, the MWCS approach is less accurate [Hadziioannou et al, 2009;Mikesell et al, 2015]. The expected seasonal trend was not evident.…”

“…The expected seasonal trend was not evident. Second, cycle-skipping appears when the delay time is larger than the dominant period of the correlations [Mikesell et al, 2015]. Cycle-skipping can occur for three reasons.…”

“…Many instantaneous jumps in δt values were visible in δt/t plots, indicating that cycle-skipping occurred between the daily cross correlations and the reference. Lastly, cycle-skipping might occur if changes in scattering and interference have altered the waveforms so much that persistent scattered arrivals disappear and the waveforms are too dissimilar to be compared [Mikesell et al, 2015]. If the SNR is too low, the MWCS approach is less accurate [Hadziioannou et al, 2009;Mikesell et al, 2015].…”

“…Previous CWI studies have measured small perturbations in seismic velocity (typically less than 5%) in volcanic edifices [Sens-Schönfelder and Wegler, 2006;Brenguier et al, 2008a;Duputel et al, 2009;Mordret et al, 2010;Brenguier et al, 2011], along a landslide slip interface [Mainsant et al, 2012], within fault zones [Wegler and Sens-Schönfelder, 2007;Brenguier et al, 2008b], and hydrocarbon or CO 2 reservoirs [Verdon et al, 2010, Draganov et al, 2013Gassenmeier et al, 2015]. There are three main approaches for measuring the delay times (δt) between two seismic traces: stretching [Sens-Schönfelder and Wegler, 2006;Mainsant et al, 2012], dynamic-time warping [Mikesell et al, 2015], and moving window cross-spectral analysis (MWCS) . There are three main approaches for measuring the delay times (δt) between two seismic traces: stretching [Sens-Schönfelder and Wegler, 2006;Mainsant et al, 2012], dynamic-time warping [Mikesell et al, 2015], and moving window cross-spectral analysis (MWCS) .…”

“…Larger velocity changes, like those expected in permafrost regions, have not been monitored with this method. Cycle-skipping, in which the incorrect phases are matched between the current and reference trace, is a common drawback of MWCS [Mikesell et al, 2015]. These methods assume that the EGFs remain stable through time except for small perturbations in phase times.…”