98 A new concept of karst development based on hydrogeology and geophysics 5.3 Full waveform acoustic logging Processing based on Singular Value Decomposition (Mari & Porel, 2018) was conducted independently on the two offset sections (3 m and 3.25 m) recorded with the acoustic tool. The processing is done to extract the wavelets associated with the different waves (refracted P-wave, converted refracted S-wave, and Stoneley wave) on the two sections. For a wave type (for example, the refracted P-wave), the correlation of the two wavelets observed at offsets 3 m and 3.25 m enables the simultaneous computation of the formation velocity V, the correlation coefficient between the wavelets, and the amplitude of each wavelet. The amplitude measurements can be used to compute amplitude ratio and attenuation logs, which can be expressed in dB and dB/m. Figure 9 shows the velocity, correlation, and attenuation logs computed from acoustic sections (Fig. 2c) recorded in borehole C1. In the 50–53 m depth interval, which corresponds to a karstic level, we notice a significant decrease in velocity, a very low correlation coefficient, and strong attenuation. The same observations can be made in the 85–90 m depth interval on the correlation and attenuation logs. SVD processing leads to the calculation of a specific attribute used to detect karstic levels. The attribute, called Karstic Index, is the product of three normalized terms: • a velocity term: CV = 1 – (V/Vmax). The lower the velocity, the higher the velocity term. In karstic zones, a high CV coefficient is observed; • an amplitude ratio term: CAR = 1 – (AR/ARmax), where AR is amplitude ratio. In karstic zones, a high CAR coefficient is observed; (a) (b) Figure 9 FWAL at well C1: Refracted P-waves. (a) Velocity log and its associated correlation coefficient log. (b) Attenuation log. Modified after Delay et al., 2022.
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