GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 Figure 2: Equivariant imaging training strategy for seismic data interpolation. Finally, the equivariant learning strategy enforces both the measurement consistency in Equation 4 and the equivariance condition in Equation 5. The forward pass of the training is illustrated in Figure 2: we first compute as an estimation of the actual model. According to the equivariance property, we subsequently randomly shift the estimation and obtain . Finally, we feed the undersampled shifted data to the CNN and obtain . The training is performed by minimizing the following loss function: (6) For other training details, in the following data examples, the used network architecture is U-Net (Chen et al, 2021), the optimizer is Adam method. And we run 500 epochs with a fixed learning rate as 5e-4. NUMERICAL EXAMPLES In this section, we use one field data to estimate our method. In which, we erased one trace per two traces regularly, which means that there are 50% missing traces. In order to assess the interpolation performance quantitatively, we use the signal-to-noise ratio (SNR) (7)