Relating source-receiver interferometry to an inverse-scattering series to derive a new method to estimate internal multiples

We have evaluated an explicit relationship between the representations of internal multiples by source-receiver interferometry and an inverse-scattering series. This provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect. A downside of the existing representations is that their computational cost is extremely high, which can be a precluding factor especially in 3D applications. Using our insight from source-receiver interferometry, we have developed an alternative, computationally more efficient way to predict internal multiples. The new formula is based on crosscorrelation and convolution: two operations that are computationally cheap and routinely used in interferometric methods. We have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set.

[1]  A. Curtis,et al.  Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions , 2013 .

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

[3]  K. Wapenaar.  Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation. , 2004, Physical review letters.

[4]  Arthur B. Weglein,et al.  Inverse Scattering Series For Multiple Attenuation: An Example With Surface And Internal Multiples , 1994 .

[5]  Johan O. A. Robertsson,et al.  Interferometric modeling of wave propagation in inhomogeneous elastic media using time reversal and reciprocity , 2006 .

[6]  Jyoti Behura,et al.  A practical approach to prediction of internal multiples and ghosts , 2012 .

[7]  William Menke,et al.  Tomographic investigation of the wear along the San Jacinto fault, southern California , 2006 .

[8]  Max Born,et al.  Principles of optics - electromagnetic theory of propagation, interference and diffraction of light (7. ed.) , 1999 .

[9]  A. Curtis,et al.  Automatic identification of multiply diffracted waves and their ordered scattering paths. , 2015, The Journal of the Acoustical Society of America.

[10]  A. Curtis,et al.  Diffracted and pseudo-physical waves from spatially limited arrays using source–receiver interferometry (SRI) , 2014 .

[11]  A. Curtis,et al.  Fingerprinting ordered diffractions in multiply diffracted waves , 2014 .

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

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

[14]  Bjørn Ursin,et al.  Seismic Imaging and Illumination with Internal Multiples , 2009 .

[15]  David Halliday,et al.  Source-receiver wave field interferometry. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Matteo Ravasi,et al.  Internal multiple prediction and removal using marchenko autofocusing and seismic interferometry , 2015 .

[17]  A. Curtis,et al.  Nonlinear Scattering-based Imaging in Elastic Media , 2013 .

[18]  A. Curtis,et al.  Beyond conventional migration: non-linear elastic subsalt imaging with transmissions and two-sided illumination , 2014 .

[19]  Helmut Jakubowicz,et al.  Wave Equation Prediction And Removal of Interbed Multiples , 1998 .

[20]  Source-Receiver Wavefield Interferometry , 2010 .

[21]  Helmut Jakubowicz.  Wave Equation Prediction And Removal of Interbed Multiples , 1998 .

[22]  A. Curtis,et al.  An interferometric theory of source-receiver scattering and imaging , 2010 .

[23]  Eric Verschuur.  Ebook: Seismic Multiple Removal Techniques: Past, present and future. Revised Edition , 2013 .

[24]  Clement Fleury,et al.  Increasing illumination and sensitivity of reverse‐time migration with internal multiples , 2013 .

[25]  Roel Snieder,et al.  Interferometry by deconvolution. Part 1 -Theory for acoustic waves and numerical examples , 2008 .

[26]  H. Calandra,et al.  Identification of image artifacts from internal multiples , 2007 .

[27]  The benefit of hindsight in observational science: Retrospective seismological observations , 2012 .

[28]  R. Snieder,et al.  Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  K. Wapenaar,et al.  Green's function representations for seismic interferometry , 2006 .

[30]  I. Vasconcelos,et al.  Imaging condition for nonlinear scattering-based imaging: Estimate of power loss in scattering , 2012 .

[31]  Andrew Curtis,et al.  Modeling of wave propagation in inhomogeneous media. , 2005, Physical review letters.

[32]  A. Malcolm,et al.  A method for inverse scattering based on the generalized Bremmer coupling series , 2005 .

[33]  R. Snieder.  Extracting the Green's function from the correlation of coda waves: a derivation based on stationary phase. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Source-receiver interferometry for seismic wavefield construction and ground-roll removal , 2011 .

[35]  Andrew Curtis,et al.  Suppressing nonphysical reflections in Green's function estimates using source-receiver interferometry , 2012 .

[36]  David Halliday,et al.  Virtual seismometers in the subsurface of the Earth from seismic interferometry , 2009 .

[37]  Barry Hung,et al.  Internal demultiple methodology without identifying the multiple generators , 2012 .

[38]  Fons ten Kroode,et al.  Prediction of internal multiples , 2002 .

[39]  P. Sava,et al.  Nonlinear extended images via image-domain interferometry , 2010 .

[40]  O. Poliannikov.  Retrieving reflections by source-receiver wavefield interferometry , 2011 .

[41]  A. Curtis,et al.  Physical and non-physical energy in scattered wave source-receiver interferometry. , 2013, The Journal of the Acoustical Society of America.

[42]  Gerard T. Schuster,et al.  Migration methods for imaging different‐order multiples , 2007 .

[43]  A. Curtis,et al.  Constructing new seismograms from old earthquakes: Retrospective seismology at multiple length scales , 2015 .

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

[45]  Dan Hampson,et al.  Inverse Velocity Stacking For Multiple Elimination , 1986 .

[46]  J. Schwinger,et al.  Variational Principles for Scattering Processes. I , 1950 .