192 Geophysics in Geothermal Exploration on observation purpose and on the characteristics of the noise distribution. If the seismic noise sources are globally stable in both time and space, it is possible to extract the waveform evolution over time and perform a velocity variation analysis. Several strategies can be considered, such as studying velocity variation measured on the ballistic part of the wavefield, often corresponding to surface waves, or on the so-called coda waves, which correspond to late arrival time and represents the multiple contribution of highly diffracted waves within the medium. The choice between the two strategies can depend on the noise stability characteristics, the coda waves often being favored in case of unstable ballistic wave reconstruction. Various methods exist for extracting velocity variations (for a review, see Yuan et al., 2021). The doublet method (Poupinet et al., 1984) is preferred for working with the coda, as it is more effective in cases of strong decoherence across seismic signals and small velocity variations (~10–1%) (Olivier et al., 2017). Windowed crosscorrelation (Snieder, 2006) and stretching methods (Sens-Schönfelder and Wegler, 2006), on the other hand, can be more easily applied to ballistic waves, as they tend to have a high signal-to-noise ratio and show strong velocity variations (Voisin et al., 2016). An illustration of the stretching method is shown in Figure 6.4. The correlogram is a collection of EGFs reconstructed at different times. A reference waveform is selected or computed (e.g. average waveform) which is then stretched and compressed applying multiple coefficients. A semblance analysis is then performed with each waveform of the correlogram. The stretching coefficient that shows the highest semblance with a given waveform yields the corresponding velocity variation, also often referred to as the dv/v value. Figure 6.4 Illustration of the stretching process. (i) Raw correlogram, (ii) chosen stack and time windows to perform the stretching process (red waveform), (iii) sketch of the application of the stretching/compression on a waveform by an epsilon factor (shift to red, compression, shift to blue, stretch), (iv) coherency matrix of the resulting stretching process, where the yellow show the best correlation coefficient between each stretched/compressed seismic trace and each line of the correlogram. The dv/v value is extracted from this matrix. The velocity of seismic waves can vary depending on several physical parameters and hence provide capacity for monitoring different phenomenon within the subsurface. As a non-exhaustive summary, Wada et al. (2017) demonstrate that variations in
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