This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 1 Interpolating Seismic Data With Conditional Generative Adversarial Networks Dario A. B. Oliveira , Rodrigo S. Ferreira , Reinaldo Silva, and Emilio Vital Brazil Abstract— Having dense and regularly sampled data is becom- ing increasingly important in seismic processing. However, due to physical or financial constraints, seismic data sets can be often undersampled. Occasionally, these data sets may also present bad or dead traces the geoscientist must deal with. Many works have tackled this problem using prestack data and can be classified in three main categories: wave-equation, domain transform, and prediction-error-filter methods. In this letter, we assess the performance of a conditional generative adversarial network for the interpolation problem in poststack seismic data sets. To the best of our knowledge, this is the first work to evaluate a deep learning approach in this context. Quantitative and qualitative evaluations of our experiments indicate that deep networks may present an interesting alternative to classical methods. Index Terms— Geoscience, geophysical image processing, mul- tilayer neural network. I. I NTRODUCTION S EISMIC surveys are usually undersampled, either due to physical limitations during the acquisition or financial constraints. Besides, the resulting seismic data sets may also present bad or dead traces. The high number of available data interpolation/extrapolation methods confirms the relevance of the issue for the oil and gas industry. The most important methods may be divided in three main categories: wave- equation, domain transform, and prediction-error-filter meth- ods [1]. Typically, they are based on prestack data and aim to improve the quality of gathers for subsequent processing or to reduce the near-offset data problem. An important drawback of wave-equation based methods— such as differential offset continuation [2], data mapping and reconstruction [3], SPDR2 [4], EPSI [5], and CRS [6]—is their need for a velocity model. They use the physics of wave propagation to reconstruct seismic data. Essentially, they are regression approaches based on wave equation principles. Domain transform methods are data-driven and do not require any information about the subsurface. Examples of this category are Pyramid [7], Curvelet [8] and Focal trans- forms [9], unaliased F-K interpolation [10], generalized F-K interpolation [11], projection onto convex sets [12], Interferometric interpolation [13], matching pursuit [14], and minimum weight norm interpolation [15]. These methods Manuscript received June 1, 2018; revised July 17, 2018; accepted August 14, 2018. (Corresponding author: Dario A. B. Oliveira.) The authors are with IBM Research, Rio de Janeiro 22290-240, Brazil (e-mail: dariobo@br.ibm.com; rosife@br.ibm.com; rmozart@br.ibm.com; evital@br.ibm.com). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2018.2866199 involve data transformations between different domains, e.g., time, frequency, pyramid, curvelet, focal, and wavenumber domains. Lastly, the prediction-error filters learn a filter from the known data and construct missing data by minimizing the convolution of the learned filter with the unknown model. The most important methods in this category are Spitz’s [16], Gulu- nay’s, and Claerbout’s, although the last two are modifications of Spizt’s method, one of the most well-known interpolation methods, which is based on a Fourier transform of the input traces. In this letter, we evaluate a different aspect of the missing data problem in seismic surveys, focusing on data interpo- lation in poststack seismic images, which may be caused by problems in data acquisition or processing issues. We leverage the power and flexibility of conditional generative adversarial networks (cGANs) to provide the interpreter with the most complete data set possible for his work. In a broad sense, convolutional neural networks (CNNs) can be seen as a combination of domain transforms and prediction- error-filter methods. They present the data-driven characteristic of the former with the convolutional filter learning of the latter, but without any assumptions or time/frequency transforms. The data transforms and filters are learned by the network during training. This letter is organized as follows. Section II presents the main concepts of seismic data acquisition and processing. Section III introduces cGANs and the topology of the CNN used in this letter. In Section IV, we discuss the experiments that were performed and the results obtained, and finally, in Section V, we conclude this letter and point out future research directions. II. SEISMIC DATA Seismic surveys are a powerful tool to obtain information about the subsurface. In a seismic survey, waves are generated and sent into the earth. Some of these waves are reflected and return to the surface where they are recorded by geophones (in land surveys) or hydrophones (in marine surveys). In a 2-D acquisition, geophones are laid down along a single line on the ground yielding a set of seismic traces, which represent the intensity of the vibrations captured by each geophone. In a 3-D survey, source and receiver points are distributed over the area of interest in parallel lines so that source lines are usually perpendicular to receiver lines. In marine surveys (2-D or 3-D), sound waves are created by an air gun that is fired between the seismic vessel and the 1545-598X © 2018 IEEE. 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