Review of Ray Theory Applications in Modelling and Imaging of Seismic Data

Throughout the last twenty years, 3D seismic ray modelling has developed from a research tool to a more operational tool that has gained growing interest in the petroleum industry. Various areas of application have been established and new ones are under development. Many of these applications require a modelling system with flexible, robust and efficient modelling algorithms in the core. The present paper reviews the basic elements of such a system, based on the ‘open model’ concept and the ‘wavefront construction’ technique. In the latter, Červený's dynamic ray tracing is an intrinsic part. The modelling system can be used for generating ray attributes and synthetic seismograms for realistic 3D surveys with tens of thousands of shots and receivers. Moreover, some other types of application areas are illustrated: Production of Green's functions for prestack depth migration and hybrid modelling (combined ray and finite-difference modelling), attribute mapping and illumination analysis, both for survey planning and interpretation. Finally, the concepts of ‘isochron rays’ and ‘velocity rays’ related to seismic isochrons have been introduced recently, with very interesting future applications.

[1]  Vlastislav Červený,et al.  Ray method in seismology , 1977 .

[2]  Shunhua Cao,et al.  Calculation of the seismic first-break time field and its ray path distribution using a minimum traveltime tree algorithm , 1993 .

[3]  Victor Pereyra,et al.  TWO‐POINT RAY TRACING IN GENERAL 3D MEDIA1 , 1992 .

[4]  P. Thore,et al.  Fresnel zone effect on seismic velocity resolution , 1999 .

[5]  P. Podvin,et al.  Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools , 1991 .

[6]  Isabelle Lecomte.  Hybrid Modeling With Ray Tracing And Finite Difference. , 1996 .

[7]  Raul Madariaga,et al.  Seismic waveform modeling in heterogeneous media by ray perturbation theory , 1987 .

[8]  Leiv-J. Gelius,et al.  Have a look at the resolution of prestack depth migration for any model, survey and wavefields. , 1998 .

[9]  Håvar Gjøystdal,et al.  Inversion of reflection times in three dimensions , 1981 .

[10]  Jean Brac,et al.  Can we image complex structures with first‐arrival traveltime? , 1993 .

[11]  J. Mispel,et al.  3D Wavefront Construction for P and SV Waves in Transversely Isotropic Media , 2001 .

[12]  J. Virieux,et al.  Iterative asymptotic inversion in the acoustic approximation , 1992 .

[13]  Yu Zhang,et al.  Exact And Approximate Weights For Kirchhoff Migration , 2000 .

[14]  Isabelle Lecomte,et al.  Local and controlled prestack depth migration in complex areas , 1999 .

[15]  C. Sassolas,et al.  The benefits of 3D ray tracing in acquisition feasibility , 1999 .

[16]  Leiv-J. Gelius,et al.  New insights in migration through analogies between Generalized Diffraction Tomography and Syn- thetic Aperture Radar. , 2001 .

[17]  Albert C. Reynolds,et al.  Boundary conditions for the numerical solution of wave propagation problems , 1978 .

[18]  Håvar Gjøystdal,et al.  Estimation of multivalued arrivals in 3D models using wavefront construction , 1993 .

[19]  J. Vidale.  Finite-difference calculation of travel times , 1988 .

[20]  B. Kennett,et al.  Lg-wave propagation in heterogeneous media , 1989 .

[21]  Anthony J. Devaney,et al.  Geophysical diffraction tomography in a layered background , 1991 .

[22]  Olav Holberg,et al.  Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena , 1985 .

[23]  Alfredo Muñoz,et al.  Model based simulation for survey planning and optimization , 1999 .

[24]  E. Iversen,et al.  Event-oriented velocity estimation based on pre-stack data in time or depth domain , 1994 .

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

[26]  Tor Arne Johansen,et al.  Fast repeated seismic modelling of local complex targets. , 1998 .

[27]  Moshe Reshef,et al.  Migration of common‐shot gathers , 1986 .

[28]  William W. Symes,et al.  Upwind finite-difference calculation of traveltimes , 1991 .

[29]  J. O. Hansen,et al.  Prestack map migration as an engine for parameter estimation in TI media , 2000 .

[30]  Håvar Gjøystdal,et al.  Traveltime and amplitude estimation using wavefront construction , 1993 .

[31]  Jon F. Claerbout,et al.  Imaging the Earth's Interior , 1985 .

[32]  J. E. Reinhardsen,et al.  COMPUTER REPRESENTATION OF COMPLEX 3‐D GEOLOGICAL STRUCTURES USING A NEW “SOLID MODELING” TECHNIQUE* , 1985 .

[33]  Vlastislav Cerveny,et al.  Fresnel volume ray tracing , 1992 .

[34]  Martin Tygel,et al.  Three-dimensional true-amplitude zero-offset migration , 1991 .

[35]  Jean-Laurent Mallet,et al.  GOCAD project: Geometric modeling of complex geological surfaces , 1989 .

[36]  Leiv-J. Gelius,et al.  The resolution function in linearized born and Kirchhoff inversion , 2000 .

[37]  Martin Tygel,et al.  3-D true‐amplitude finite‐offset migration , 1993 .

[38]  Einar Iversen,et al.  Macro-model Construction By Integration of Local Prestack Depth Imaging, Event Interpretation, And Nonzero Offset Ray-theoretical Depth Conversion , 1994 .

[39]  P. Hubral,et al.  True amplitude migration of 2D synthetic data , 1992 .

[40]  S. L. Bégat,et al.  Sensitivity of qP-wave traveltimes and polarization vectors to heterogeneity, anisotropy and interfaces , 1995 .

[41]  Larry Lines,et al.  Theory of seismic diffractions , 1994 .

[42]  V. Červený,et al.  Seismic Ray Theory , 2001, Encyclopedia of Solid Earth Geophysics.

[43]  Martin Tygel,et al.  Seismic Image Waves , 1996 .

[44]  J. Sochacki.  Absorbing boundary conditions for the elastic wave equations , 1988 .

[45]  Jean Virieux,et al.  SH-wave propagation in heterogeneous media; velocity-stress finite-difference method , 1984 .

[46]  A. Devaney.  A filtered backpropagation algorithm for diffraction tomography. , 1982, Ultrasonic imaging.

[47]  Ian A. Watson,et al.  The construction of subsurface illumination and amplitude maps via ray tracing , 2000 .

[48]  First-Order Perturbation Theory for Seismic Isochrons , 2001 .

[49]  M. Kvasnička,et al.  3-D network ray tracing , 1994 .

[50]  Hideki Sailo,et al.  Traveltimes And Raypaths of First Arrival Seismic Waves: Computation Method Based On Huygens’ Principle , 1989 .

[51]  Håvar Gjøystdal,et al.  Estimation of multivalued arrivals in 3D models using wavefront construction—Part I , 1996 .

[52]  Håvar Gjøystdal,et al.  Part II: Tracing and interpolation1 , 1996 .

[53]  V. Vinje,et al.  3-D ray modeling by wavefront construction in open models , 1999 .

[54]  M. Toksöz,et al.  Diffraction tomography and multisource holography applied to seismic imaging , 1987 .

[55]  F. Hron,et al.  The ray series method and dynamic ray tracing system for three-dimensional inhomogeneous media , 1980 .

[56]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

[57]  William A. Schneider,et al.  INTEGRAL FORMULATION FOR MIGRATION IN TWO AND THREE DIMENSIONS , 1978 .

[59]  E. Iversen.  Derivatives of reflection point coordinates with respect to model parameters , 1996 .

[60]  J. Virieux.  P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

[61]  M. Nafi Toksöz,et al.  Ultrasonic laboratory tests of geophysical tomographic reconstruction , 1988 .

[62]  Migrating around in circles ‐ Part III , 1997 .

[63]  F. Adler.  Kirchhoff image propagation , 2000 .

[64]  Gregory Beylkin,et al.  A new slant on seismic imaging: Migration and integral geometry , 1987 .

[65]  V. Vinje,et al.  PreStack Depth Migration and illumination maps , 2001 .

[66]  Gregory Beylkin,et al.  Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform , 1985 .

[67]  N. Bleistein.  On the imaging of reflectors in the earth , 1987 .

[68]  Håvar Gjøystdal,et al.  Event-oriented velocity estimation based on prestack data in time or depth domain1 , 1996 .

[69]  Jean-Pierre Faye,et al.  Prestack Migration Velocities From Focusing Depth Analysis , 1986 .

[70]  Leiv-J. Gelius,et al.  A generalized diffraction tomography algorithm , 1991 .