Seismic wave field restoration using spare representations and quantitative analysis

Abstract : This thesis deals with two different problems within the framework of convex and non convex optimization. The first one is an application to multiple removal in seismic data with adaptive filters and the second one is an application to blind deconvolution problem that produces characteristics closest to the Earth layers. More precisely : unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, datas parsity and slow filter variation in parsimony-promoting wavelet transforms. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyper parameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulatedand real field seismic data. In seismic exploration, a seismic signal (e.g. primary signal) is often represented as the results of a convolution between the “seismic wavelet” and the reflectivity series. The second goal of this thesis is to deconvolve them from the seismic signal which is presented in Chapter 6. The main idea of this work is to use an additional premise that the reflections occur as sparsely restricted, for which a study on the “sparsity measure”is considered. Some well known methods that fall in this category are proposed such as[Sacchi et al., 1994; Sacchi, 1997]. We propose a new penalty based on a smooth approximation of the l1/l2 function that makes a difficult non convex minimization problem. We develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term
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Mai-Quyen Pham. Seismic wave field restoration using spare representations and quantitative analysis. Signal and Image Processing. Université Paris-Est, 2015. English. ⟨NNT : 2015PESC1028⟩. ⟨tel-01355498⟩

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