1887
Volume 50, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Various aspects of structural inversion are considered. The aim of the inversion is limited to finding the shape of an isolated 2D homogeneous body, although the technique may be generalized to the case of interfaces with steep fragments, faults or overhangs. The unknown parameters are shifts of border points. The shift directions can be normal to the initial heterogeneity configuration or to another contour. Medium properties (seismic velocities, densities, etc.) within the heterogeneity are assumed to be known. The optimal shape is determined iteratively, a quadratic objective function being minimized at each iteration with the conjugate‐gradient method. Special attention is paid to preventing self‐intersections, for which purpose each unknown parameter is forced to lie within a certain predetermined interval. In order to achieve this, the classical conjugate‐gradient method has been modified accordingly. Three numerical examples are considered. These illustrate how the developed technique can be applied to different practical problems. The first example is devoted to monitoring an oil/steam interface by gravity gradiometry measurements. In the second example, a cross‐hole seismic experiment is simulated. It is shown that a structural inversion can restore the configuration of a local body much more accurately than traditional seismic tomography. In the third example, the shape of a salt dome is reconstructed by joint inversion of refracted traveltimes and gravity measurements. This example demonstrates how different kinds of data, used simultaneously in a structural inversion, can complement each other.

Loading

Article metrics loading...

/content/journals/10.1046/j.1365-2478.2002.00308.x
2002-11-23
2024-03-28
Loading full text...

Full text loading...

References

  1. BakushinskiyA.B., GoncharskyA.V. and StepanovaL.D.1986. The use of iterative regularization algorithms for the solution of inverse gravimetric problems.Izvestiya, Physics of the Solid Earth22, 812–817.
    [Google Scholar]
  2. BarbosaV.C.F., SilvaJ.B.C. and MedeirosW.E.1997. Gravity inversion of basement relief using approximate equality constraints on depths.Geophysics62, 1745–1757.
    [Google Scholar]
  3. BarbosaV.C.F., SilvaJ.B.C. and MedeirosW.E.1999. Stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations.Geophysics64, 754–764.
    [Google Scholar]
  4. BertsekasD.P.1982. Constrained Optimization and Lagrange Multiplier Methods. Academic Press, Inc.
  5. BishopT.N., BubeK.P., CutlerR.T., LanganR.T., LoveP.L., ResnickR.T., SpindlerD.A. and WyldH.W.1985. Tomographic determination of velocity and depth in laterally varying media.Geophysics50, 903–923.
    [Google Scholar]
  6. BoschM.1999. Lithologic tomography: from plural geophysical data to lithology estimation.Journal of Geophysical Research104(B1), 749–766.
    [Google Scholar]
  7. CamachoA.G., MontesinosF.G. and VieiraR.2000. Gravity inversion by means of growing bodies.Geophysics65, 95–101.
    [Google Scholar]
  8. ChiuS.K.L., KanasewichE.R. and PhadkeS.1986. Three‐ dimensional determination of structure and velocity by seismic tomography.Geophysics51, 1559–1571.
    [Google Scholar]
  9. ConstableS., ParkerR. and ConstableC.1987. Occam's inversion: a practical algorithm for smooth models from electromagnetic sounding data.Geophysics52, 289–300.
    [Google Scholar]
  10. DitmarP.G.1993. Algorithm for tomographic processing of seismic data assuming smoothness of sought‐for function.Izvestiya, Physics of the Solid Earth29, 5–11.
    [Google Scholar]
  11. DitmarP.G. and MakrisJ.1996. Tomographic inversion of 2D WARP data based on Tikhonov regularization. 66th SEG meeting, Denver, USA, Expanded Abstracts,2015–2018.
  12. ForteA.M., WoodwardR.L. and DziewonskiA.M.1994. Joint inversions of seismic and geodynamic data for models of three‐dimensional mantle heterogeneity.Journal of Geophysical Research99(B11), 21857–21887.
    [Google Scholar]
  13. GoudswaardJ.C.M., TenKroode, F.P.E.,Snieder, R.K. and VerdelA.R.1998. Detection of lateral velocity contrasts by crosswell traveltime tomography.Geophysics63, 523–533.
    [Google Scholar]
  14. GuiziouJ.L., MalletJ.L. and MadariagaR.1996. 3D reflection tomography on top of the GOCAD depth modeler.Geophysics61, 1499–1510.
    [Google Scholar]
  15. HaberE. and OldenburgD.1997. Joint inversion: a structural approach.Inverse Problems13, 63–77.DOI: 10.1088/0266-5611/13/1/006
    [Google Scholar]
  16. HestenesM.R. and StiefelE.1952. Methods of conjugate gradients for solving linear systems.Journal of Research of the National Bureau of Standards49, 409–436.
    [Google Scholar]
  17. HuangH., SpencerC. and GreenA.1986. A method for the inversion of refraction and reflection travel times for laterally varying velocity structures.Bulletin of the Seismological Society of America76, 837–846.
    [Google Scholar]
  18. LeesJ.M. and VanDecarJ.C.1991. Seismic tomography constrained by Bouguer anomalies: application in Western Washington.Pure and Applied Geophysics135, 31–52.
    [Google Scholar]
  19. MurthyI.V.R. and RaoR.1993. Inversion of gravity and magnetic anomalies of two‐dimensional polygonal cross‐sections.Computers and Geosciences19, 1213–1228.
    [Google Scholar]
  20. PedersenL.B.1977. Interpretation of potential field data – a generalized inverse approach.Geophysical Prospecting25, 199–230.
    [Google Scholar]
  21. PedersenL.B.1979. Constrained inversion of potential field data.Geophysical Prospecting27, 726–748.
    [Google Scholar]
  22. PereyraV.1996. Modeling, ray tracing, and block nonlinear travel‐time inversion in 3D.Pure and Applied Geophysics148, 345–386.
    [Google Scholar]
  23. PhillipsW.S. and FehlerM.S.1991. Traveltime tomography: a comparison of popular methods.Geophysics56, 1639–1649.
    [Google Scholar]
  24. PortniaguineO. and ZhdanovM.S.1999. Focusing geophysical inversion images.Geophysics64, 874–887.
    [Google Scholar]
  25. RenéR.M.1986. Gravity inversion using open, reject, and `shape‐of‐anomaly' fill criteria.Geophysics51, 988–994.
    [Google Scholar]
  26. RenéR.M.1999. Three‐dimensional `shape‐of‐anomaly' inversion of gravity and magnetic fields. 69th SEG meeting, Houston, USA, Expanded Abstracts,417–420.
  27. StorkC. and ClaytonW.1991. Linear aspects of tomographic velocity analysis.Geophysics56, 483–495.
    [Google Scholar]
  28. TalwaniM., SchweitzerM., FeldmanW., DiFrancescoD. and KonigW.1999. Time lapse gravity gradiometry. 69th SEG meeting, Houston, USA, Expanded Abstracts, 397.
  29. TikhonovA.N. and ArseninV.Y.1977. Solutions of Ill‐Posed Problems.V.H. Winston and Sons, Washington, DC.
    [Google Scholar]
  30. WangB. and BraileL.W.1995. Effective approaches to handling non‐uniform data coverage problem for wide‐aperture refraction/reflection profiling. 65th SEG meeting, Houston, USA, Expanded Abstracts,659–662.
  31. WangB. and BraileL.W.1996. Simultaneous inversion of reflection and refraction seismic data and application to field data from the northern Rio Grande rift.Geophysical Journal International125, 443–458.
    [Google Scholar]
  32. WangY.1999. Simultaneous inversion for model geometry and elastic parameters.Geophysics131, 618–642.
    [Google Scholar]
  33. WangY. and HousemanG.A.1994. Inversion of reflection seismic amplitude data for interface geometry.Geophysical Journal International117, 92–110.
    [Google Scholar]
  34. ZeltC.A. and SmithR.B.1992. Seismic traveltime inversion for 2D crustal velocity structure.Geophysical Journal International108, 16–34.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1046/j.1365-2478.2002.00308.x
Loading
/content/journals/10.1046/j.1365-2478.2002.00308.x
Loading

Data & Media loading...

  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

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