GNGTS 2018 - 37° Convegno Nazionale

754 GNGTS 2018 S essione 3.3 constraints and elimination of badly acquired traces cause irregular spatial sampling in almost all seismic acquisitions. Unfortunately, most state-of-the-art seismic processing algorithms require high quality and regularly sampled data. Consequently, a vast majority of seismic processing pipelines needs data pre-processing steps, including effective trace interpolation algorithms. Moreover, due to the increasing size of the acquisitions, a key factor of these procedures for industrial application is their computational burden, in term of both memory requirements and computational time. For this reason, manifold interpolation algorithms to densely reconstruct coarse data have been proposed so far, based on different strategies. For instance, some approaches rely on prediction filters (Spitz, 1991), which assume seismic data to be a local superposition of plane waves, but also Fourier reconstruction methods (Duijndam, 1999) are another way for handling the problem. Nevertheless, these algorithms are effective only for regularly sampled data, which is a heavy limitation. More recently, compressive sensing strategies exploits data sparsity in the frequency-wavenumber domain (Xu, 2005) and in Seislet and Dreamlet domains (Gan, 2015; Wang, 2014). Similarly, recent strategies propose to recast interpolation as a low rank matrix completion problem (Oropeza, 2011). In the latest years, the outstanding advancements brought by Deep Learning and Convolutional Neural Networks (CNNs) have greatly impacted the signal processing world. In particular, innovative strategies for data interpolation have been proposed so far in various image processing tasks, often exceeding the state-of-the-art. However, these methods have barely started to be explored by the geophysical community for the interpolation problem. In example, first promising results have been reported through Residual Neural Networks (Jin, 2018) and Generative Adversarial Networks (Siahkoohi, 2018). The goal of this paper is interpolating irregular pre-stack seismic data, investigating them in the shot-gather domain. Inspired by the important contributions achieved in image processing problems, we propose to exploit a particular kind of CNN denoted as ConvolutionalAutoencoder (CA), as a novel and strongly competitive strategy for reconstruction of missing traces in pre- stack seismic images. Results show promising performances of our method compared to state- of-the-art techniques. Convolutional Autoencoders for Data Interpolation. AConvolutional Autoencoder (CA) is a specific kind of CNN whose architecture can be logically split in two separate components. To be precise, let us refer to Fig. 1 for analyzing the structure: (i) the encoder, represented by the operator E (·), maps the input x into the hidden representation h = E ( x ); (ii) the decoder, represented by the operator D (·), transforms the hidden representation into an estimate of the input xˆ = D ( h ). As in standard CNNs, both the encoder and decoder are composed by series of convolutions, optionally followed by non linear functions (e.g., sigmoid, hyperbolic tangent, etc.). Regarding image processing problems, CA proved to be a very powerful instrument for inpainting tasks (Pathak, 2016). The rationale behind the use of CA for inpainting shares some common concepts with the transform-based and dictionary learning techniques. Indeed, CA is trained so that h results in a compact representation of the clean data, where the interference due to missing samples is not mapped in. Therefore, if the compact representation is correctly built, the result of the decoder is a dense image without missing samples. Consequently, it is possible to recover densely sampled gathers from the corrupted ones. Fig. 1 - Scheme of an autoencoder architecture.