GNGTS 2019 - Atti del 38° Convegno Nazionale

564 GNGTS 2019 S essione 3.1 Synthetic examples. Trough a synthetic example we were able to systematically test the interpolation/denoising CNN by designing several different experiments, with different noise and missing traces statistics. To this end we leveraged 1348 shot gathers extracted from the well-known BP-2004 benchmark. The central frequency is 27Hz, sampling is 6ms with a group spacing of 12.5m. We split data using 250 shot gathers for training and validation and the remaining for evaluation. After setup experiments we end up with batches of 135 non overlapping patches of 128×128 samples. The process involves more than 25000 training patches, more than 8500 validation patches, and more than 145000 testing patches for each experiment. Through this dataset we performed the following experiments. • Interpolation of uniformly distributed missing traces. We build 3 different datasets from the reference one, deleting (with uniform distribution) 10%, 30% and 50% of the traces, respectively, for each shot gather. In this case we are able to achieve S/N of 32.8dB , 24.2dB and 18.8dB respectively for increasing percentage of missing traces. • Interpolation of bursts of missing traces. We exploited a more sophisticated corruption model based on the consideration that missing traces are likely to appear in groups. We propose a burstymissing traces model inspired by packet loss models of telecommunication networks. The term burst refers to groups of consecutive events (i.e. consecutive missing traces). The more bursty a distribution of missing traces is, the more the missing traces are likely to cluster. The model is a two states Markov model with two parameters, α and β: α is the probability of a missing trace, β is the average number of adjacent missing traces. We select various percentage of missing traces α (10%, 30%, 50%) and average burst lengths β (1, 2, 3). Larger average gaps increase gap size dispersion also. Indeed β=1 leads to isolated missing traces only; on the contrary β=3 provides a maximum gap up to 30 traces (375m). Table 1 displays the achieved results: the larger the burst length, the lower the resulting S/N. This enlightens the need of further investigations. Nonetheless, even in the worst case, i.e., (α, β) = (50, 3), the U-net achieves acceptable S/N. Table 1 - Results of interpolation for bursty model of random missing traces. β =1 β =2 β =3 α =10 38.4 dB 25.3 dB 21.9 dB α =30 32.8 dB 21.7 dB 18.1 dB α =50 29.9 dB 18.7 dB 15.7 dB • Interpolation of regularly missing traces. This is a challenging interpolation problem, especially when dips are aliased: methods based on transforms and low-rank constraints have limited application because of the strong spatial aliased energies. We test the conjecture that network training extracts high-level features of data which are robust to alias, therefore implicitly including an anti-aliasing strategy. The achieved S/N is 30 dB and results achieved over a shot gather region characterized by steep dips are shown in Fig. 1. As a reference, a recent industrial software based on f-x deconvolution achieves S/N = 22.7 dB on the same data. Fig. 1 includes the absolute value of the Fourier spectrum of the original shot gather, the corrupted one, and the recovered one, showing that the alias introduced in the corrupted shot gather is recovered. • AWGN noise model . We add white gaussian noise in order to obtain three datasets with S/N equal to −3 dB , 0 dB and 3 dB , respectively. In this case the average results obtained on shot gathers belonging to the evaluation set are 12.8 dB , 14.4 dB and 16.3 dB . These results can be considered an upper bound for the achievable performances since they are obtained assuming to have clean data available for the training phase, which is never the case for field data.