Inverse scattering series and seismic exploration

This paper presents an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series. There are both significant symmetries and critical subtle differences between the forward scattering series construction and the inverse scattering series processing of seismic events. These similarities and differences help explain the efficiency and effectiveness of different inversion objectives. The inverse series performs all of the tasks associated with inversion using the entire wavefield recorded on the measurement surface as input. However, certain terms in the series act as though only one specific task, and no other task, existed. When isolated, these terms constitute a task-specific subseries. We present both the rationale for seeking and methods of identifying uncoupled task-specific subseries that accomplish: (1) free-surface multiple removal; (2) internal multiple attenuation; (3) imaging primaries at depth; and (4) inverting for earth material properties. A combination of forward series analogues and physical intuition is employed to locate those subseries. We show that the sum of the four task-specific subseries does not correspond to the original inverse series since terms with coupled tasks are never considered or computed. Isolated tasks are accomplished sequentially and, after each is achieved, the problem is restarted as though that isolated task had never existed. This strategy avoids choosing portions of the series, at any stage, that correspond to a combination of tasks, i.e., no terms corresponding to coupled tasks are ever computed. This inversion in stages provides a tremendous practical advantage. The achievement of a task is a form of useful information exploited in the redefined and restarted problem; and the latter represents a critically important step in the logic and overall strategy. The individual subseries are analysed and their strengths, limitations and prerequisites exemplified with analytic, numerical and field data examples.

[1]  Prediction of the Wavefield Anywhere Above an Ordinary Towed Streamer: Application to Source Waveform Estimation, Demultiple, Deghosting, Data Reconstruction And Imaging , 2000 .

[2]  Are Osen,et al.  Wavelet estimation from marine pressure measurements , 1998 .

[3]  Devaney.  Structure determination from intensity measurements in scattering experiments. , 1989, Physical review letters.

[4]  Arthur B. Weglein,et al.  Forward Scattering Series and Seismic Events: Far Field Approximations, Critical and Postcritical Events , 2004, SIAM J. Appl. Math..

[5]  P. M. van den Berg,et al.  Seismic applications of acoustic reciprocity , 1993 .

[6]  Roger G. Newton,et al.  Inversion of reflection data for layered media: a review of exact methods , 1981 .

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

[8]  Lonnie Hamm,et al.  GLOBAL OPTIMIZATION METHODS , 2002 .

[9]  A. Weglein,et al.  Generalized linear inversion and the first Born theory for acoustic media , 1983 .

[10]  A. Weglein,et al.  A comparison of three multiple-attenuation methods applied to a hard water-bottom data set , 1999 .

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

[12]  W. E. Boyse.  Wave propagation and inversion in slightly inhomogeneous media , 1986 .

[13]  Mrinal K. Sen,et al.  Global Optimization Methods in Geophysical Inversion , 1995 .

[14]  Jack K. Cohen,et al.  An Inverse Method for Determining Small Variations in Propagation Speed , 1977 .

[15]  A. Devaney,et al.  Inverse scattering using the Heitler equation , 1989 .

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

[17]  Arthur B. Weglein,et al.  Examples of a Nonlinear Inversion Method Based On the T Matrix of Scattering Theory: Application to Multiple Suppression , 1991 .

[18]  Arthur B. Weglein,et al.  Nonlinear Inverse Scattering For Multiple Suppression: Application to Real Data. Part I , 1992 .

[19]  Internal multiple attenuation , 1994 .

[20]  R. Newton.  Scattering theory of waves and particles , 1966 .

[21]  Roel Snieder,et al.  The role of the Born approximation in nonlinear inversion , 1990 .

[22]  H. Moses,et al.  Calculation of the Scattering Potential from Reflection Coefficients , 1956 .

[23]  M. Razavy,et al.  Determination of the wave velocity in an inhomogeneous medium from the reflection coefficient , 1975 .

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

[25]  Lasse Amundsen.  Elimination of free-surface related multiples without need of the source wavelet , 2001 .

[26]  Arthur B. Weglein,et al.  Internal multiple attenuation using inverse scattering: Results from prestack 1 & 2D acoustic and elastic synthetics , 1996 .

[27]  Arthur B. Weglein,et al.  Inverse scattering internal multiple attenuation: an analytic example and subevent interpretation , 1998, Optics & Photonics.

[28]  A. J. Berkhout,et al.  Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation , 1980 .

[29]  Jerry A. Ware,et al.  Continuous and Discrete Inverse‐Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence , 1969 .

[30]  E. Wolf.  Three-dimensional structure determination of semi-transparent objects from holographic data , 1969 .

[31]  Robert W. Clayton,et al.  A Born-WKBJ inversion method for acoustic reflection data , 1981 .

[32]  Obtaining three-dimensional velocity information directly from reflection seismic data: An inverse scattering formalism , 1981 .

[33]  Jon F. Claerbout,et al.  Predictive deconvolution in shot-receiver space , 1983 .

[34]  Brian Kennett,et al.  THE SUPPRESSION OF SURFACE MULTIPLES ON SEISMIC RECORDS , 1979 .

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

[36]  Jon F. Claerbout,et al.  2-D multiple reflections , 1976 .

[37]  Reese T. Prosser,et al.  Formal solutions of inverse scattering problems. III. , 1969 .

[38]  Arthur B. Weglein,et al.  Source signature estimation based on the removal of first-order multiples , 1997 .

[39]  Roel Snieder.  An extension of Backus-Gilbert theory to nonlinear inverse problems , 1991 .

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

[41]  Reese T. Prosser,et al.  Formal solutions of inverse scattering problems. IV. Error estimates , 1982 .

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

[43]  Arthur B. Weglein,et al.  Migration-inversion revisited (1999) , 1999 .

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

[45]  Arthur B. Weglein,et al.  Multiple attenuation; an overview of recent advances and the road ahead (1999) , 1999 .

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