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Full waveform inversion (FWI) updates the subsurface model from an initial model by comparing observed and synthetic seismograms. Due to high nonlinearity, FWI is easy to be trapped into local minima. Extended domain FWI, including wavefield reconstruction inversion (WRI) and extended source waveform inversion (ESI) are attractive options to mitigate this issue. This paper makes an in-depth analysis for FWI in the extended domain, identifying key challenges and searching for potential remedies towards practical applications. WRI and ESI are formulated within the same mathematical framework using Lagrangian-based adjoint-state method with a special focus on time-domain formulation using extended sources, while putting connections between classical FWI, WRI and ESI: both WRI and ESI can be viewed as weighted versions of classic FWI. Due to symmetric positive definite Hessian, the conjugate gradient is explored to efficiently solve the normal equation in a matrix free manner, while both time and frequency domain wave equation solvers are feasible. This study finds that the most significant challenge comes from the huge storage demand to store time-domain wavefields through iterations. To resolve this challenge, two possible workaround strategies can be considered, i.e., by extracting sparse frequencial wavefields or by considering time-domain data instead of wavefields for reducing such challenge. We suggest that these options should be explored more intensively for tractable workflows. [ABSTRACT FROM AUTHOR]

Abstract: Interpolating the missing traces of regularly or irregularly sampled seismic record is an exceedingly important issue in the geophysical community. Many modern acquisition and reconstruction methods are designed to exploit the transform domain sparsity of the few randomly recorded but informative seismic data using thresholding techniques. In this paper, to regularize randomly sampled seismic data, we introduce two accelerated, analysis-based two-step interpolation algorithms, the analysis-based FISTA (fast iterative shrinkage-thresholding algorithm) and the FPOCS (fast projection onto convex sets) algorithm from the IST (iterative shrinkage-thresholding) algorithm and the POCS (projection onto convex sets) algorithm. A MATLAB package is developed for the implementation of these thresholding-related interpolation methods. Based on this package, we compare the reconstruction performance of these algorithms, using synthetic and real seismic data. Combined with several thresholding strategies, the accelerated convergence of the proposed methods is also highlighted. [Copyright &y& Elsevier]

Abstract: An exceedingly important inverse problem in the geophysical community is the interpolation of the seismic data, which are usually nonuniformly recorded from the wave field by the receivers. Researchers have proposed many useful methods to regularize the seismic data. Recently, sparseness-constrained seismic data interpolation has attracted much interest of geophysicists due to the surprisingly convincing results obtained. In this article, a new derivation of the projection onto convex sets (POCS) interpolation algorithm is presented from the well known iterative shrinkage–thresholding (IST) algorithm, following the line of sparsity. The curvelet transform is introduced into the POCS method to characterize the local features of seismic data. In contrast to soft thresholding in IST, hard thresholding is advocated in this curvelet-based POCS interpolation to enhance the sparse representation of seismic data. The effectiveness and the validity of our method are demonstrated by the example studies on the synthetic and real marine seismic data. [Copyright &y& Elsevier]