Nonlinear regularization techniques for seismic tomography

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Loris, I.¹  Douma, H.²  Nolet, G.³  Daubechies, I.⁴  Regone, C.⁵ 

[1] Vrije Univ Brussel, Dept Math, B-1090 Brussels, Belgium

[2] Princeton Univ, Dept Geosci, Princeton, NJ 08544 USA

[3] Univ Nice Sophia Antipolis, CNRS, IRD, F-06560 Sophia Antipolis, France

[4] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[5] BP Amer Inc, Houston, TX 77079 USA

关键词: Inverse problem;    One-norm;    Sparsity;    Tomography;    Wavelets;    Regularization;   

DOI  :  10.1016/j.jcp.2009.10.020

来源: Elsevier

【 摘 要 】

The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, l(2) penalties are compared to so-called sparsity promoting l(1), and l(0) penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an l(2) norm works almost as well as minimizing the total variation but is much more efficient. If gradients (edges of anomalies) should be resolved with a minimum of distortion, we prefer l(1) damping of Daubechies-4 wavelet coefficients. It has the additional advantage of yielding a noiseless reconstruction, contrary to simple l(2) minimization ('Tikhonov regularization') which should be avoided. In some of our examples, the to method produced notable artifacts. In addition we show how nonlinear l(1) methods for finding sparse models can be competitive in speed with the widely used l(2) methods, certainly under noisy conditions, so that there is no need to shun l(1) penalizations. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free