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International audience; The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), a constrained nonlinear optimization problem whereby we seek model parameters and wavefields that minimize the data residuals and satisfy the wave-equation constraint. The AL-based wavefield reconstruction inversion, also known as iteratively refined wavefield reconstruction inversion, extends the search space of FWI in the source dimension and decreases the sensitivity of the inversion to the initial model accuracy. Furthermore, it benefits from the advantages of the alternating direction method of multipliers, such as generality and decomposability for dealing with nondifferentiable regularizers, e.g., total variation regularization, and large-scale problems, respectively. In practice, any extension of the method aiming at improving its convergence and decreasing the number of wave-equation solves would have great importance. To achieve this goal, we recast the method as a general fixed-point iteration problem, which enables us to apply sophisticated acceleration strategies such as Anderson acceleration. The accelerated algorithm stores a predefined number of previous iterates and uses their linear combination together with the current iteration to predict the next iteration. We investigate the performance of our accelerated algorithm on a simple checkerboard model and the benchmark Marmousi II and 2004 BP salt models through numerical examples. These numerical results confirm the effectiveness of our algorithm in terms of convergence rate and the quality of the final estimated model.

Seismic attribute analysis has been a useful tool for interpretation objectives; therefore, high-resolution images of them are of particular concern. The calculation of these attributes by conventional methods is susceptible to noise, and the conventional filtering supposed to lessen the noise causes the loss of the spectral bandwidth. The challenge of having a high-resolution and robust signal processing tool motivated us to propose a sparse time–frequency decomposition which is stabilised for random noise. The procedure initiates by using sparsity-based, adaptive S-transform to regularise abrupt variations in the frequency content of the non-stationary signals. An adaptive filter is then applied to the previously sparsified time–frequency spectrum. The proposed zero adaptive filter enhances the high-amplitude frequency components while suppressing the lower ones. The performance of the proposed method is compared to the sparse S-transform and the robust window Hilbert transform in the estimation of instantaneous attributes through studying synthetic and real data sets. Seismic attributes estimated by the proposed method are superior to the conventional ones, in terms of robustness and high-resolution imaging. The proposed approach has a detailed application in the interpretation and classification of geological structures.

International audience; Partial differential equation (PDE) constrained optimization problems such as seismic full waveform inversion (FWI) frequently arise in the geoscience and related fields. For such problems, many observations are usually gathered by multiple sources, which form the right-hand-sides of the PDE constraint. Solving the inverse problem with such massive data sets is computationally demanding, in particular when dealing with large number of model parameters.This paper proposes a novel randomized source sketching method for the efficient resolution of multisource PDE constrained optimization problems.We first formulate the different source-encoding strategies used in seismic imaging into a unified framework based on a randomized sketching. To this end, the source dimension of the problem is projected in a smaller domain by a suitably defined projection matrix that gathers the physical sources in super-sources through a weighted summation. This reduction in the number of physical sources decreases significantly the number of PDE solves while suitable sparsity-promoting regularization can efficiently mitigate the footprint of the cross-talk noise to maintain the convergence speed of the algorithm. We implement the randomized sketching method in an extended search-space formulation of frequency-domain FWI, which relies on the alternating-direction method of multipliers (ADMM). Numerical examples carried out with a series of well-documented 2D benchmarks demonstrate that the randomized sketching algorithm reduces the cost of large-scale problems by at least one order of magnitude compared to the original deterministic algorithm.

Summary We present a new finite difference scheme for the frequency-domain quasi-acoustic wave equations for vertical transversely isotropic (VTI) media. Compared to the optimized scheme, the proposed one enhances the overall performance and accuracy of the frequency domain solution as it significantly reduces the numerical dispersion error without any amount of extra cost. It improves upon the discretization rule of 4 grid points per minimum wavelength and reduces it to 2.5. The numerical examples of wave propagation in homogeneous and highly heterogenous models prove the validity and precision of the proposed scheme.

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.