1887
Volume 37 Number 1
  • E-ISSN: 1365-2478

Abstract

A

For the correct interpretation of data gathered in the seismic prospecting of complex heterogeneous structures, elastic effects must often be taken into consideration. The use of the elastic wave equations to model the seismic response of an hypothesized geological structure is a valuable tool for relating observed seismic data to the earth's inhomogeneities and verify an interpretation.

Several methods may be used to integrate numerically the partial differential equations describing elastic wave propagation. Pseudospectral (Fourier) methods represent the leading numerical integration technique. Their main advantage is high accuracy and suitability to vector and parallel computer architectures, while their main drawback is high computational cost. However, for a given accuracy, the required grid size with pseudospectral methods is smaller than that required by finite‐difference schemes, thus balancing the computational cost. We describe a two‐dimensional pseudospectral elastic model implemented on the vector multiprocessor IBM 3090 VF. The algorithm has been suitably adapted to fully exploit the computer architecture and thereby maximize the performance.

The elastic model has been validated in a variety of problems in geophysics and, in particular, in the amplitude‐versus‐offset analysis which has proved to be an effective technique to extract additional information from the recorded (prestack) data. With proper conditioning and processing of seismic data, and separating amplitude variations due to changes in reflectivity from variations due to other effects, the resulting offset signatures have been successfully used, for instance, to distinguish true bright spots due to gas‐bearing sands, from false ones associated with lithological changes. To interpret the observed amplitude‐versus‐offset signatures, it is necessary to know the reflection coefficients as a function of angle and frequency for planar interfaces, as well as for other structures of geological interest.

The modelling is first validated by computing the reflection coefficients for planar interfaces, and then used to analyse the reflection signatures of thin beds, corrugated interfaces and multilayers. Their implications, as well as impact on amplitude‐versus‐offset analysis, are discussed. We conclude that elastic modelling is an effective and valuable tool to further our understanding of the amplitude anomalies observed in field data.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1989.tb01819.x
2006-04-27
2020-03-31
Loading full text...

Full text loading...

References

  1. Achenbach, J.D.1975. Wave Propagation in Elastic Solids. North Holland .
    [Google Scholar]
  2. Agarwal, R.C. and Cooley, J.W.1986. Fourier transform and convolution subroutines for the IBM 3090 Vector Facility. IBM Journal of Research and Development30, (2), 145–162.
    [Google Scholar]
  3. Backus, M.M.1983. The reflection seismogram in a layered earth. Bulletin of the American Association of Petroleum Geologists67, 416–417.
    [Google Scholar]
  4. Cerjan, G, Kosloff, D., Kosloff, R. and Reshef, M.1985. A non reflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics50, 705–708.
    [Google Scholar]
  5. Cooley, J.W. and Tukey, J.W.1965. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation19, 297.
    [Google Scholar]
  6. de Voogd, N. and den Rooijen, H.1983. Thin layer response and spectral bandwidth. Geophysics48, 12–18.
    [Google Scholar]
  7. Eisner, E., Chen, K.H. and Gangi, A.1986. Computer technology and seismic modeling. 56th SEG meeting, Houston , Expanded Abstracts, 669.
    [Google Scholar]
  8. Flynn, M.1972. Some computer organizations and their effectiveness. IEEE Transactions in ComputersC‐21, 948–960.
    [Google Scholar]
  9. Fokkema, J.T.1980. Reflection and transmission of elastic waves by the spatially periodic interface between two solids (theory of the integral‐equation method). Wave Motion2, 375–393.
    [Google Scholar]
  10. Fokkema, J.T.1981a. Reflection and transmission of elastic waves by the spatially periodic interface between two solids (numerical results for the sinusoidal interface). Wave Motion3, 33–48.
    [Google Scholar]
  11. Fokkema, J.T.1981b. Reflection and transmission of acoustic waves by the periodic interface between a solid and a fluid. Wave Motion3, 145–157.
    [Google Scholar]
  12. Fornberg, B.1987. The pseudospectral method: comparisons with finite differences for the elastic wave equation. Geophysics52, 483–501.
    [Google Scholar]
  13. Gassaway, G.S. and Richgels, H.J.1983. Sample, seismic amplitude measurement for primary lithology estimation. 53th SEG meeting, Las Vegas , Exanded Abstracts, 610–613.
    [Google Scholar]
  14. Gazdag, J.1981. Modeling of the acoustic wave equation with transform methods. Geophysics46, 854–859.
    [Google Scholar]
  15. Gelfand, V., Ng, P., Nguyen, H. and Larner, K.1986. Seismic lithologic modeling of amplitude‐versus‐offset data. 56th SEG meeting, Houston , Expanded Abstracts, 332–334.
    [Google Scholar]
  16. Hindlet, F.1986. Thin layer analysis using offset/amplitude data. 56th SEG meeting, Houston , Expanded Abstracts, 346–349.
    [Google Scholar]
  17. Hill, N.R. and Lerche, I.1986. Acoustic reflections from undulating surfaces. Geophysics51, 2160–2161.
    [Google Scholar]
  18. Hockney, R.W. and Jesshope, C.R.1981. Parallel Computers. Adam Hilger Ltd, Bristol .
    [Google Scholar]
  19. Hwang, K.1984. Supercomputers: Design and Applications. IEEE Computer Society Press.
    [Google Scholar]
  20. Kindelan, M., Sguazzero, P. and Kamel, A.1987. Elastic modeling with Fourier methods on the IBM 3090 vector multiprocessor. Scientific computing on IBM vector multiprocessors, R.Benzi and P.Sguazzero (eds), IBM European Centre for Scientific and Engineering Computing, Rome , 635–674.
    [Google Scholar]
  21. Knott, C.G.1899. Reflection and refraction of elastic waves, with seismological applications. Philosophical Magazine 5th ser., 48, 64–97.
    [Google Scholar]
  22. Koefoed, O. and de Voogd, N.1980. The linear properties of thin layers, with an application to synthetic seismograms over coal seams. Geophyics45, 1254–1268.
    [Google Scholar]
  23. Kosloff, D. and Baysal, E.1982. Forward modeling by a Fourier method. Geophysics47, 1402–1412.
    [Google Scholar]
  24. Kosloff, D., Reshef, M. and Lowenthal, D.1984. Elastic wave calculations by the Fourier method. Bulletin of the Seismological Society of America74, 875–899.
    [Google Scholar]
  25. Meissner, R. and Hegazy, M.A.1981. The ratio of the PP‐ to SS‐reflection coefficient as a possible future method to estimate oil and gas reservoirs. Geophysical Prospecting29, 533–540.
    [Google Scholar]
  26. Ostrander, W.J.1984. Plane wave reflection coefficients for gas sands at nonnormal angles of incidence. Geophysics49, 1637–1648.
    [Google Scholar]
  27. Schmidt, N. and Johnson, O.1984. A vector elastic model for the CYBER 205. Research Computation Laboratory, University of Houston.
    [Google Scholar]
  28. Schoenberger, M. and Levin, F.K.1976. Reflected and transmitted filter functions for simple subsurface geometries. Geophysics41, 1305–1317.
    [Google Scholar]
  29. Shuey, R.T.1985. A simplification of Zoeppritz equations. Geophysics50, 609–614.
    [Google Scholar]
  30. Stephens, R.B. and Sheng, P.1985. Acoustic reflections from complex strata. Geophysics50, 1100–1107.
    [Google Scholar]
  31. Tarantola, A.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1256.
    [Google Scholar]
  32. Tolstoy, I.1973. Wave Propagation. McGraw‐Hill Book Co.
    [Google Scholar]
  33. White, B., Nair, B. and Bayliss, A.1986. Seismic amplitude anomalies. 56th SEG meeting, Houston , Expanded Abstracts, 624–626.
    [Google Scholar]
  34. Widess, M.B.1973. How thin is a thin bed. Geophysics38, 1176–1180.
    [Google Scholar]
  35. Wright, J.1986. Reflection coefficients at pore‐fluid contacts as a function of offset. Geophysics51, 1858–1860.
    [Google Scholar]
  36. Young, G.B. and Braile, L.W.1976. A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations. Bulletin of the Seismological Society of America66, (6), 1881–1885.
    [Google Scholar]
  37. Yu, G.1985. Offset‐amplitude variation and controlled‐amplitude processing. Geophysics50, 2697–2708.
    [Google Scholar]
  38. Zoeppritz, K.1919. Über Reflexion und Durchgang seismischer Wellen durch Unstetigkeitsflächen. Über Erdbebenwellen VII B. Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math‐Phys. K57–84.
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1989.tb01819.x
Loading
  • Article Type: Research Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error