GNGTS 2019 - Atti del 38° Convegno Nazionale

762 GNGTS 2019 S essione 3.3 taking advantage of the multi-resolution approach of CWT, the presented functional can perform robust coherency measures against the noise and velocity spectra with high-resolution in time, velocity and scale (or frequency). In addition, the availability of 3D spectra is particularly useful for the analysis of data-sets characterized by the occurrence of non-stationary signals. The first part of this work describes the coherency functional; the second part shows an application to a synthetic case and to a field data-set characterized by very low signal-to-noise ratio, strong multiple contamination and weak sub-basalt primary reflections. In both cases, the results are compared with those carried out by traditional Semblance and by the unconventional Complex-Matched Semblance high-resolution functional. Method In the 2D form, i.e. considering a fixed scale, the wavelet-based coherency functional can be defined as: (1) where W is the common scale (or common frequency) section computed by the Continuous Wavelet Transfo a common midpoint gather (CMP). Index i refers to the M traces and T is the width of the timewindow. The coherencymeasure C W is then repeated for all the scales considered giving a 3D space defined by: time, velocity and scale (frequency). Equation 1 is similar to the semblance coefficient formula. Here, the energy evaluated along the trial hyperbolic trajectory normalized to the total energy estimated along the same trajectory is computed in the time-scale domain. In the next section the spectra computed by the new wavelet-based functional will be compared with those performed by the standard Semblance and by the unconventional Complex Matched Semblance (Tognarelli et al. , 2013, 2016), which uses an estimated or known analytic wavelet to filter the data before computing the coherency measure. Results. The first example refers to synthetic data. Fig. 1 shows the depth model used to generate the simulated CMP by means of the reflectivity method. The model consists of six Fig. 1 - Depth model (from Tognarelli et al. , 2013) used to compute the synthetic CMP gather.