Clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data

Linearinversionisdefinedasthelinearapproximationofa direct-inverse solution. This definition leads to data requirements and specific direct-inverse algorithms, which differ with all current linear and nonlinear approaches, and is immediately relevant for target identification and inversion in an elastic earth. Common practice typically starts with a directforwardormodelingexpressionandseekstosolveaforward equation in an inverse sense. Attempting to solve a direct forward problem in an inverse sense is not the same as solvinganinverseproblemdirectly.Distinctionsincludedifferences in algorithms, in the need for a priori information, and in data requirements. The simplest and most accessible examples are the direct-inversion tasks, derived from the inverse scattering series ISS, for the removal of free-surface and internal multiples.The ISS multiple-removal algorithms require no subsurface information, and they are independent ofearthmodeltype.Adirectforwardmethodsolvedinaninverse sense, for modeling and subtracting multiples, would require accurate knowledge of every detail of the subsurface the multiple has experienced. In addition, it requires a different modeling and subtraction algorithm for each different earth-model type. The ISS methods for direct removal of multiples are not a forward problem solved in an inverse sense. Similarly, the direct elastic inversion provided by the ISSisnotamodelingformulaforPPdatasolvedinaninverse sense. Direct elastic inversion calls for PP, PS, SS, … data, for direct linear and nonlinear estimates of changes in mechanical properties. In practice, a judicious combination of directandindirectmethodsarecalleduponforeffectivefield dataapplication.

[1]  A. Weglein,et al.  Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series , 2009 .

[2]  Kristopher A. Innanen,et al.  Adaptive separation of free-surface multiples through independent component analysis , 2008 .

[3]  Paulo M. Carvalho,et al.  Wavelet estimation for surface multiple attenuation using a simulated annealing algorithm , 1994 .

[4]  A. Tarantola Inversion of seismic reflection data in the acoustic approximation , 1984 .

[5]  D. J. Verschuur,et al.  Estimation of multiple scattering by iterative inversion, Part I: Theoretical considerations , 1997 .

[6]  Arthur B. Weglein,et al.  Inverse scattering series and seismic exploration , 2003 .

[7]  K. Aki,et al.  Quantitative Seismology, 2nd Ed. , 2002 .

[8]  Haiyan Zhang Direct non-linear acoustic and elastic inversion: Towards fundamentally new comprehensive and realistic target identification , 2006 .

[9]  Sergey Fomel,et al.  Path‐integral seismic imaging , 2006 .

[10]  Arthur B. Weglein A New, Clear And Meaningful Definition of Linear Inversion: Implications For Seismic Inversion of Primaries And Removing Multiples , 2009 .

[11]  Arthur B. Weglein,et al.  Direct nonlinear inversion of 1D acoustic media using inverse scattering subseries , 2009 .

[12]  Joseph B. Keller,et al.  Inverse elastic scattering in three dimensions , 1986 .

[13]  Ken H. Matson An overview of wavelet estimation using free-surface multiple removal , 2000 .

[14]  Mrinal K. Sen,et al.  Nonlinear multiparameter optimization using genetic algorithms; inversion of plane-wave seismograms , 1991 .

[15]  Arthur B. Weglein,et al.  An inverse-scattering series method for attenuating multiples in seismic reflection data , 1997 .

[16]  R. Pratt Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[17]  R. G. Keys Polarity reversals in reflections from layered media , 1989 .

[18]  Denes Vigh,et al.  3D prestack plane-wave, full-waveform inversion , 2008 .

[19]  Guy Chavent,et al.  Inverse Problems in Wave Propagation , 1997 .

[20]  R. Gerhard Pratt,et al.  Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies , 2004 .

[21]  Ray Abma,et al.  Comparisons of adaptive subtraction methods for multiple attenuation , 2005 .

[22]  D. Schmitt,et al.  Detecting Subsurface Hydrocarbons with Elastic Wavefields , 1997 .

[23]  Arthur B. Weglein,et al.  Migration and inversion of seismic data , 1985 .

[24]  D. J. Verschuur,et al.  Adaptive surface-related multiple elimination , 1992 .