A Pre-Stack Seismic Inversion with L1 Constraints and Uncertainty Estimation Using the Expectation Maximization Algorithm

We present an algorithm that provides improved Earth model reconstruction over Gaussian, or Tikhonov, regulated inversions. By utilizing a dynamic noise estimation, linear error propagation theory and a Bayesian construction this algorithm can: objectively indicate the amount of recoverable independent information, provide a framework on how to weight prior information, and to communicate the uncertainty of the estimates.

[1]  H. L. Taylor,et al.  Deconvolution with the l 1 norm , 1979 .

[2]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[3]  I. Barrodale,et al.  An Improved Algorithm for Discrete $l_1 $ Linear Approximation , 1973 .

[4]  Rui Zhang,et al.  Seismic sparse-layer reflectivity inversion using basis pursuit decomposition , 2011 .

[5]  C. Dossal.  SPARSE SPIKE DECONVOLUTION WITH MINIMUM SCALE , .

[6]  Scott L. Painter,et al.  On the distribution of seismic reflection coefficients and seismic amplitudes , 1995 .

[7]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

[8]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[9]  Danilo R. Velis,et al.  Estimating the distribution of primary reflection coefficients , 2003 .

[10]  P. Riel,et al.  Lp-NORM DECONVOLUTION1 , 1990 .

[11]  Mauricio D. Sacchi,et al.  High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy , 2013 .

[12]  James Gunning,et al.  Wavelet extractor: A Bayesian well-tie and wavelet extraction program , 2006, Comput. Geosci..

[13]  Mauricio D. Sacchi,et al.  Reweighting strategies in seismic deconvolution , 1997 .

[14]  G. Casella,et al.  The Bayesian Lasso , 2008 .

[15]  M. R. Osborne,et al.  On the LASSO and its Dual , 2000 .

[16]  Michael E. Glinsky,et al.  Noise-thresholding sparse-spike inversion with global convergence: calibration and applications , 2013 .

[17]  A. T. Walden,et al.  The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution , 1986 .