Coherent noise attenuation using Inverse Problems and Prediction Error Filters

Two iterative methods that handle coherent noise effects during the inversion of 2-D prestack data are tested. One method approximates the inverse covariance matrices with PEFs, and the other introduces a coherent noise modeling operator in the objective function. This noise modeling operator is a PEF that has to be estimated before the inversion from a noise model or directly from the data. These two methods lead to Independent, Identically Distributed (IID) residual variables, thus guaranteeing a stable convergence of the inversion schemes and permitting coherent noise filtering/separation.

[1]  Antoine Guitton,et al.  Robust and stable velocity analysis using the Huber function , 1999 .

[2]  Dave Nichols,et al.  Velocity-stack inversion using Lp norms , 2001 .

[3]  Robert G. Clapp,et al.  (t,x) domain, pattern‐based ground roll removal , 2000 .

[4]  operatorGuy Chavent,et al.  An optimal true amplitude least squares prestack depthmigration , 1998 .

[5]  R. Gerhard Pratt,et al.  Sensitivities of seismic traveltimes and amplitudes in reflection tomography , 1997 .

[6]  Jon F. Claerbout,et al.  Multidimensional recursive filters via a helix , 1998 .

[7]  Robert Soubaras.  Signal-preserving Random Noise Attenuation By the F-x Projection , 1994 .

[8]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[9]  J. Claerbout,et al.  Robust Modeling With Erratic Data , 1973 .

[10]  G. Chavent,et al.  An optimal true-amplitude least-squares prestack depth-migration operator , 1999 .

[11]  K. Bube,et al.  Hybrid l 1 /l 2 minimization with applications to tomography , 1997 .

[12]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[13]  Robert G. Clapp,et al.  (t x) domain, pattern-based multiple separation , 2000 .

[14]  J. R. Thorson.  Velocity stack and slant stack inversion methods , 1984 .

[15]  Simon Spitz,et al.  Pattern recognition, spatial predictability, and subtraction of multiple events , 1999 .

[16]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[17]  Gerard T. Schuster,et al.  Separation of signal and coherent noise by migration filtering , 2000 .

[18]  J. Claerbout,et al.  Lateral prediction for noise attenuation by t-x and f-x techniques , 1995 .

[19]  J. Claerbout.  Earth Soundings Analysis: Processing Versus Inversion , 1992 .

[20]  Prestack multiple attenuation using the hyperbolic Radon transform A comparison of inversion schemes , 2000 .

[21]  Jon F. Claerbout,et al.  Interpolation with smoothly nonstationary prediction-error filters , 1999 .

[22]  R. White,et al.  Seismic amplitude inversion for interface geometry: practical approach for application , 2000 .

[23]  Mauricio D. Sacchi,et al.  High‐resolution velocity gathers and offset space reconstruction , 1995 .