Research note: deblended‐data reconstruction using generalized blending and deblending models

Abstract

We introduce a concept of generalized blending and deblending, develop its models and accordingly establish a method of deblended‐data reconstruction using these models. The generalized models can handle real situations by including random encoding into the generalized operators both in the space and time domain, and both at the source and receiver side. We consider an iterative optimization scheme using a closed‐loop approach with the generalized blending and deblending models, in which the former works for the forward modelling and the latter for the inverse modelling in the closed loop. We applied our method to existing real data acquired in Abu Dhabi. The results show that our method succeeded to fully reconstruct deblended data even from the fully generalized, thus quite complicated blended data. We discuss the complexity of blending properties on the deblending performance. In addition, we discuss the applicability to time‐lapse seismic monitoring as it ensures high repeatability of the surveys. Conclusively, we should acquire blended data and reconstruct deblended data without serious problems but with the benefit of blended acquisition.

Blended acquisition with temporally signatured/modulated and spatially dispersed source array: Concept and method

“…The blended data, P″, were numerically synthesized with blending concepts introduced in the above section, which are represented by the blending operators for each case. Using the generalized blending model (Berkhout, 2008;Berkhout et al, 2009;Ishiyama et al, 2019), a forward model is described as…”

“…The blended data, P ″, were numerically synthesized with blending concepts introduced in the above section, which are represented by the blending operators for each case. Using the generalized blending model (Berkhout, 2008; Berkhout et al., 2009; Ishiyama et al., 2019), a forward model is described as $$$$\begin{equation} {\mathbf{P}}^{\prime\prime}={\bm{\Gamma}}_{\mathrm{D}}\mathbf{P}{\bm{\Gamma}}_{\mathrm{S}}, \end{equation}$$$$where P ″ is the blended data; P is the unblended data. Γ S and Γ D are the generalized blending operators (i.e.…”

“…In the examples in this paper, this was implemented by deblended‐data reconstruction of Ishiyama et al. (2019) using an iterative optimization scheme of sparse inversion, outputting the deblended data, 〈 P 〉. Then, P and 〈 P 〉 were compared, and the S/N was computed as $$$$\begin{equation} {\rm S/N}=10\,{\mathrm{\log}}_{10}\left({\left\|\mathbf{P}\right\|}_{2}^{2}/{\left\|\mathbf{P}-\left\langle {{\bf P}} \right\rangle \right\|}_{2}^{2}\right).$$…”

“…A sparse representation of the metrics, thus the model parameters in a transform domain is required for robust parameter estimation and selection, where the blending signal is sparsely compressed, whereas the blending noise is randomly scattered. See, for example, iterative optimization schemes of sparse inversion in the Fourier domain (Mahdad et al., 2011; Ishiyama et al., 2019), in the Radon domain (Ibrahim & Sacchi, 2014), in the curvelet domain (Lin & Herrman, 2009) and in the focal domain (Kontakis & Verschuur, 2014).…”

“…Recently, Ishiyama et al. (2019) established a generalized blending model, which can explain any blended‐acquisition method by including the encoding into the generalized operators. In this paper, using this highly flexible and tolerant model, we introduce a blended‐acquisition method: a temporally signatured and/or modulated and spatially dispersed source array.…”