Bayesian Inversion of Gravity and Resistivity Data: Detection of Lava Tunnel

  • Published : 2002.01.31

Abstract

Bayesian inversion for gravity and resistivity data was performed to investigate the cavity structure appearing as a lava tunnel in Cheju Island, Korea. Dipole-dipole DC resistivity data were proposed for a prior information of gravity data and we applied the geostatistical techniques such as kriging and simulation algorithms to provide a prior model information and covariance matrix in data domain. The inverted resistivity section gave the indicator variogram modeling for each threshold and it provided spatial uncertainty to give a prior PDF by sequential indicator simulations. We also presented a more objective way to make data covariance matrix that reflects the state of the achieved field data by geostatistical technique, cross-validation. Then Gaussian approximation was adopted for the inference of characteristics of the marginal distributions of model parameters and Broyden update for simple calculation of sensitivity matrix and SVD was applied. Generally cavity investigation by geophysical exploration is difficult and success is hard to be achieved. However, this exotic multiple interpretations showed remarkable improvement and stability for interpretation when compared to data-fit alone results, and suggested the possibility of diverse application for Bayesian inversion in geophysical inverse problem.

Keywords

References

  1. Mathematical Geology v.19 The practice of fast conditional simulations through the LU decomposition of the covariance matrix Alabert, F. https://doi.org/10.1007/BF00897191
  2. reprinted in Biometrika v.45 An essay towards solving a problem in the doctrine of chances Bayes, T.
  3. Mathematical Computation v.19 A class of method for solving nonlinear simultaneous equations Broyden, C.G. https://doi.org/10.2307/2003941
  4. Geophysics v.52 Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data Constable, S.C.;Parker, R.L. https://doi.org/10.1190/1.1442303
  5. Geophysics v.61 resistivity inversion using spline parameterization and simulated annealing Chynduru, R.K.;Sen, M.K.;Stoffa, P.L. https://doi.org/10.1190/1.1443935
  6. Methematical Geology v.19 Production of conditional simulations via the LU triangluar decomposition of the covariance matrx Davis, M.W.
  7. GSLIB: Geostatistical software library and user's guide Deutsch, C.V.;Journel, A.G.
  8. Geophysical Prospecting v.27 Resistivity modelling for arbitary shaped two-dimensional resistivity structure Dey, A.;Morrison, H.F. https://doi.org/10.1111/j.1365-2478.1979.tb00961.x
  9. Geophysical Prospecting v.36 Bayesian estimation in seismic inversion;Principles Duijndam, A.J.W. https://doi.org/10.1111/j.1365-2478.1988.tb02198.x
  10. Geophysical Prospecting v.36 Bayesian estimation in seismic inversion;Uncertainty analysis Duijndam, A.J.W. https://doi.org/10.1111/j.1365-2478.1988.tb02199.x
  11. Change of Support by direct conditional block simulation Glacken, I.
  12. A stochastic approach to the simulation of block conductivity fields conditional upon data measured at a smaller scale Gomez-Hemandez, J.
  13. Geostatistics for Natural Resources Evaluation Goovaerts, P.
  14. Bayesian seismic waveform data invesion: Prarameter estimation and uncertainty analysis Gouveia, W.P.
  15. An Introduction to Applied Geostatistics Isaaks E.H.;Srivastava, R.M.
  16. The application of Monte Carlo Methods to the Analysis of Spatially Correlated Data Isaaks, E.H.
  17. Probability theory: the logic of science Jaynes, E.T.
  18. Mining Geostatistics Journel A.,G.;Huijbregts, C.J.
  19. Fast two-dimensional magnetotelluric incersion using approximate update of sensitivity in wavelet domain Jung, H.J.
  20. Economic and Environmental Geology v.31 Application of multiple geophysical methods in investigating the lava tunnel of Manjanggul in Cheju island Kwon, B.D.;Lee, S.J.;Oh, S.H.;Lee, C.K.
  21. Linear differential operator Lanczos, C.
  22. Geophysical Prospecting v.32 Tutorial: A Review of Least-Squares Inversion and Its Application to Geophysical Problems Lines, L.R.;Treital, S. https://doi.org/10.1111/j.1365-2478.1984.tb00726.x
  23. Maximum Entropy an Bayesian Methods From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics Loredo, T.J.;P.F.(ed.)
  24. The application of marginalization and local distributions to multidimensional Bayesian inverse problems Moraes, F.S.
  25. Journal of Geophysical Research v.100 Monte Carlo sampling of solutions to inverse problem Mosegaard, K.;Tarantola, A. https://doi.org/10.1029/94JB03097
  26. Geophysical invesion with a neighbourhood algorithm Ⅱ;Appraising the ensemble Sambridge, M.
  27. An example of geologic prior information in a Bayesian seismic inverse calculation Scales, J.A.;Tarantola, A.
  28. Inverse problem theory: Methods for data fitting and model parameter estimation Tarantola, A.