Dual‐sensor wavefield separation in a compressed domain using parabolic dictionary learning

Abstract

In the marine seismic industry, the size of the recorded and processed seismic data is continuously increasing and tends to become very large. Hence, applying compression algorithms specifically designed for seismic data at an early stage of the seismic processing sequence helps to save cost on storage and data transfer. Dictionary learning methods have been shown to provide state‐of‐the‐art results for seismic data compression. These methods capture similar events from the seismic data and store them in a dictionary of atoms that can be used to represent the data in a sparse manner. However, as with conventional compression algorithms, these methods still require the data to be decompressed before a processing or imaging step is carried out. Parabolic dictionary learning is a dictionary learning method where the learned atoms follow a parabolic travel time move out and are characterized by kinematic parameters such as the slope and the curvature. In this paper, we present a novel method where such kinematic parameters are used to allow the dual‐sensor (or two‐components) wavefield separation processing step directly in the dictionary learning compressed domain for 2D seismic data. Based on a synthetic seismic data set, we demonstrate that our method achieves similar results as an industry‐standard FK‐based method for wavefield separation, with the advantage of being robust to spatial aliasing without the need for data preconditioning such as interpolation and reaching a compression rate around 13. Using a field data set of marine seismic acquisition, we observe insignificant differences on a 2D stacked seismic section between the two methods, whereas reaching a compression ratio higher than 15 when our method is used. Such a method could allow full bandwidth data transfer from vessels to onshore processing centres, where the compressed data could be used to reconstruct not only the recorded data sets, but also the up‐ and down‐going parts of the wavefield.

Low‐frequency seismic deghosting in a compressed domain using parabolic dictionary learning

“…The parameters 𝑠 𝑘 , 𝑐 𝑘 and 𝑜 ref 𝑘 are referred to as the kinematic parameters. Further details on PDL are available in Turquais et al (2018) andFaouzi Zizi et al (2023).…”

“…The idea behind applying the deghosting operator in the compressed domain is to use these kinematic parameters to apply the deghosting operator in the frequency-space domain without the need for wave-plane decomposition. Indeed, we know that in the PDL domain, each atom 𝐝 𝑘 contains several traces, and that the slope 𝑠 𝑖 𝑘 of each trace 𝑖 related to a receiver position 𝑜 𝑖 𝑘 can be written as (Faouzi Zizi et al, 2023)…”

“…However, in the case of our PDL approach, the 3D case might become computationally very expensive. Suggestions were already made by Faouzi Zizi et al (2023) to achieve such generalization in the case of dual-sensor wavefield separation. Indeed, applying the 3D deghosting operator involves learning 3D atoms with five kinematic parameters (two slopes, two curvatures and one parameter correlating both directions) instead of only two in the 2D case.…”

“…Recently, Faouzi Zizi et al. (2023) developed a parabolic dictionary learning method for wavefield separation (WSPDL) that directly decomposes the wavefield recorded by a dual‐sensor streamer into its up‐ and down‐going parts in a compressed domain without the need for plane‐wave decomposition. This method uses parabolic dictionary learning (PDL) to extract local kinematic parameters, such as slope and curvature, to derive local incidence angles for each trace.…”

“…) and FaouziZizi et al (2023). Hence, after applying PDL, quantization and coding, we obtain the compressed format of our data, where the compression ratio (CR) is calculated as follows:…”