GNGTS 2014 - Atti del 33° Convegno Nazionale

66 GNGTS 2014 S essione 3.1 We also specify that both our implementations of MP and CGP make use of three different stopping criteria: the maximum number of iterations, and a tolerance both on the norm of the residual and on the norm of the coefficient contribution. The tolerances on the two norms have fixed value which are the same for both algorithms. Instead, as already observed, the maximum number of iteration is a parameter of the algorithm, which, together with the number of components selected at each iteration, is to be tuned depending on the input sampling irregularity. Numerical examples. We compare MP and CGP interpolation results on a marine seismic data set. The 3D data set is sorted by Common Shot Gather and indexed by the two-dimensional offset vector. Time sampling rate is 2 ms. Nominal spatial sampling is 12.5 m along inline direction and 100 m along crossline direction. As the time sampling is regular, the interpolation schemes is applied in the space-frequency domain in frequency slices on both spatial directions simultaneously. Once the Fourier coefficients are obtained, the spectrum is back-transformed to the below specified grids. Results of reconstruction on three different grids are reported. In all those processing examples an NMO correction is previously applied to input data and afterward removed. Moreover, the interpolation method is applied by overlapping windows. The three processing settings are described by the top two graphics of Fig.1 to Fig.3. In first example (see Fig. 1) the input grid shows only minor irregularities, which are intrinsically due to the marine acquisition. In this first case a double upsampling along both inline and crossline direction is performed. The second example aims to underline the robustness of the Fig. 1 – Soft upsampling example: a) geometry description: sampling before (left) and after (right) processing; b) results of the interpolation, inline visualization, from top to bottom: MP result, input data, CGP result. Fig. 2 – Soft upsampling and missing traces infilling example: a) geometry description: sampling before (left) and after (right) processing; b) results of the interpolation, inline visualization, from top to bottom: MP result, input data, CGP result.