Oriented extrapolation of common‐midpoint gathers in the absence of near‐offset data using predictive painting

Abstract

Seismic reconstruction of missing traces is an extremely important subject in seismic data processing. It includes both interpolation and extrapolation of sparsely recorded data. Extrapolation is often performed in the absence of near-offset seismic data recorded through marine acquisition. Several reconstruction methods have been designed to circumvent this sparsity in time-offset, frequency-offset and timefrequency domains. In this research, I propose an oriented extrapolation workflow to reconstruct near-offset missing traces. The term oriented or velocity-independent refers to those techniques that are based on the use of local slopes. In the proposed workflow, I use an oriented time-warping algorithm called predictive painting. This algorithm is suitable to predict two-way traveltimes between two distinctive points of an event. Seismic events recorded by an off-end array very rarely contain dips of both signs with respect to their zero-offset location in common-midpoint domain. This makes the domain an ideal choice to run the algorithm. The proposed algorithm is demonstrated on synthetic and field data examples. I decimate near-offset seismic traces and reconstruct them through the algorithm. The reconstruction results are compared with the original data before decimation. Furthermore, insensitivity of the proposed workflow to the presence of class II amplitude-versus-offset anomalies is demonstrated on a synthetic example. I also perform a velocity-dependent (a normalmoveout-based) technique on the field data and compare the corresponding outcomes with the results achieved by the application of the proposed velocity-independent approach. All the results suggest that the proposed technique has the potential to be used in the exploration industry.

Near offset reconstruction for marine seismic data using a convolutional neural network

“…The simplest method is to copy a normal moveout (NMO)‐corrected trace from the nearest available offset and use it to replace all the missing traces. More sophisticated interpolation techniques include wave‐equation trace interpolation (Ronen, 1987), trend‐spline interpolation (Vershuur, 1991), the parabolic Radon transform (Nurul Kabir & Verschuur, 1995), frequency–space ($$f$$–$$x$$) domain gap‐filling algorithms (Sacchi & Ulrych, 1997), differential offset and shot continuation (Fomel, 2003), inverse shot record dip moveout (Baumstein, 2004), and predictive painting (Khoshnavaz, 2022). Additionally, there is a significant amount of work on interferometric interpolation methods using pseudoprimaries (cross‐correlations of multiples with primary reflections) together with prediction‐error or least‐squares matching filters to perform near offset reconstruction (Curry & Shan, 2010; Guo et al., 2011; Wang et al., 2009; Xu et al., 2018).…”

“…This is because trends in transformed domains are often easier to follow than the hyperbolic moveouts of seismic reflections, because there can be more heterogeneities in shot gathers compared to common midpoint (CMP) or common offset gathers, and because the near offset gap can consist of fewer traces to interpolate (for instance in CMP gathers vs. shots). Thus, many studies on seismic interpolation utilize transformations of the data, for example into the wavelet domain (Greiner et al., 2020), the CMP domain (Khoshnavas, 2022; Nurul Kabir & Verschuur, 1995), the Radon domain (Nurul Kabir & Verschuur, 1995; Xu et al., 2018), the common offset domain (Baumstein, 2004), Fourier domains such as $$f$$–$$x$$ and $$f$$–$$k$$ (Naghizadeh & Innanen, 2011; Schonewille et al., 2013; Spitz, 1991; Xu et al., 2005), or transformation through de‐migration into regularized source–receiver configurations (Hlebnikov et al., 2022).…”