1887
Volume 49, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

We apply a novel trans-dimensional Bayesian approach using a wavelet parameterisation to airborne electromagnetic (AEM) inversions using data from the Broken Hill region. This approach allows exploration of a range of plausible subsurface conductivity models and provides more robust uncertainty estimates while accounting for potential non-uniqueness.

,

This paper presents the application of a novel trans-dimensional sampling approach to a time domain airborne electromagnetic (AEM) inverse problem to solve for plausible conductivities of the subsurface. Geophysical inverse field problems, such as time domain AEM, are well known to have a large degree of non-uniqueness. Common least-squares optimisation approaches fail to take this into account and provide a single solution with linearised estimates of uncertainty that can result in overly optimistic appraisal of the conductivity of the subsurface. In this new non-linear approach, the spatial complexity of a 2D profile is controlled directly by the data. By examining an ensemble of proposed conductivity profiles it accommodates non-uniqueness and provides more robust estimates of uncertainties.

]
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2018-04-01
2026-01-13

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References

  1. Ackman T. E. 2003 An introduction to the use of airborne technologies for watershed characterization in mined areas: Mine Water and the Environment 22 62 68 10.1007/s10230‑003‑0002‑2
    https://doi.org/10.1007/s10230-003-0002-2 [Google Scholar]
  2. Akaike H. 1974 A new look at the statistical model identification: IEEE Transactions on Automatic Control 19 716 723 10.1109/TAC.1974.1100705
    https://doi.org/10.1109/TAC.1974.1100705 [Google Scholar]
  3. Ando T. 2007 Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models: Biometrika 94 443 458 10.1093/biomet/asm017
    https://doi.org/10.1093/biomet/asm017 [Google Scholar]
  4. Ando, T., 2010, Bayesian model selection and statistical modelling: CRC Press.
  5. Backus G. Gilbert F. 1968 The resolving power of gross earth data: Geophysical Journal of the Royal Astronomical Society 16 169 205 10.1111/j.1365‑246X.1968.tb00216.x
    https://doi.org/10.1111/j.1365-246X.1968.tb00216.x [Google Scholar]
  6. Bayes T. 1763 An essay towards solving a problem in the doctrine of chances: Philosophical Transactions of the Royal Society 53 370 418 10.1098/rstl.1763.0053
    https://doi.org/10.1098/rstl.1763.0053 [Google Scholar]
  7. Bodin T. Sambridge M. 2009 Seismic tomography with the reversible jump algorithm: Geophysical Journal International 178 1411 1436 10.1111/j.1365‑246X.2009.04226.x
    https://doi.org/10.1111/j.1365-246X.2009.04226.x [Google Scholar]
  8. Bodin T. Sambridge M. Tkalčić H. Arroucau P. Gallagher L. Rawlinson N. 2012 a Trans-dimensional inversion of receiver functions and surface wave dispersion: Journal of Geophysical Research 117 B02301 10.1029/2011JB008560
    https://doi.org/10.1029/2011JB008560 [Google Scholar]
  9. Bodin T. Sambridge M. Rawlinson N. Arroucau P. 2012 b Transdimensional tomography with unknown data noise: Geophysical Journal International 189 1536 1556 10.1111/j.1365‑246X.2012.05414.x
    https://doi.org/10.1111/j.1365-246X.2012.05414.x [Google Scholar]
  10. Brodie, R. C., 2010, Holistic inversion of airborne electromagnetic data: Ph.D. thesis, Australian National University.
  11. Brodie, R. C., 2016, Geoscience Australia AEM source code repository. Available at: https://github.com/GeoscienceAustralia/ga-aem (accessed 20 September 2016).
  12. Brodie R. Sambridge M. 2006 A holistic approach to inversion of frequency domain airborne EM data: Geophysics 71 G301 G312 10.1190/1.2356112
    https://doi.org/10.1190/1.2356112 [Google Scholar]
  13. Brodie, R., and Sambridge, M., 2012, Transdimensional Monte Carlo inversion of AEM data: 22nd ASEG International Geophysical Conference and Exhibition, 1–4.
  14. Brooks, S., Gelman, A., Jones, G. L., and Meng, X., eds., 2011, Handbook of Markov chain Monte Carlo: Chapman and Hall/CRC.
  15. Cohen A. Daubechies I. Feauveau J. C. 1992 Biorthogonal bases of compactly supported wavelets: Communications on Pure and Applied Mathematics 45 485 560 10.1002/cpa.3160450502
    https://doi.org/10.1002/cpa.3160450502 [Google Scholar]
  16. Constable S. C. Parker R. L. Constable C. G. 1987 Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data: Geophysics 52 289 300 10.1190/1.1442303
    https://doi.org/10.1190/1.1442303 [Google Scholar]
  17. Dettmer J. Molnar S. Steininger G. Dosso S. E. Cassidy J. F. 2012 Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models: Geophysical Journal International 188 719 734 10.1111/j.1365‑246X.2011.05302.x
    https://doi.org/10.1111/j.1365-246X.2011.05302.x [Google Scholar]
  18. Dettmer J. Hawkins R. Cummins P. R. Hossen J. Sambridge M. Hino R. Inazu D. 2016 Tsunami source uncertainty estimation: the 2011 Japan tsunami: Journal of Geophysical Research: Solid Earth 121 4483 4505 10.1002/2015JB012764
    https://doi.org/10.1002/2015JB012764 [Google Scholar]
  19. Dosso S. E. Holland C. W. Sambridge M. 2012 Parallel tempering in strongly nonlinear geoacoustic inversion: The Journal of the Acoustical Society of America 132 3030 3040 10.1121/1.4757639
    https://doi.org/10.1121/1.4757639 [Google Scholar]
  20. Earl D. J. Deem M. W. 2005 Parallel tempering: theory, applications, and new perspectives: Physical Chemistry Chemical Physics 7 3910 3916 10.1039/b509983h
    https://doi.org/10.1039/b509983h [Google Scholar]
  21. Farquharson C. G. Oldenburg D. W. 1993 Inversion of time-domain electromagnetic data for a horizontally layered Earth: Geophysical Journal International 114 433 442 10.1111/j.1365‑246X.1993.tb06977.x
    https://doi.org/10.1111/j.1365-246X.1993.tb06977.x [Google Scholar]
  22. Farquharson C. G. Oldenburg D. W. 2004 A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems: Geophysical Journal International 156 411 425 10.1111/j.1365‑246X.2004.02190.x
    https://doi.org/10.1111/j.1365-246X.2004.02190.x [Google Scholar]
  23. Fitterman D. V. Deszcz-Pan M. 1998 Helicopter EM mapping of saltwater intrusion in Everglades National Park, Florida: Exploration Geophysics 29 240 243 10.1071/EG998240
    https://doi.org/10.1071/EG998240 [Google Scholar]
  24. Gelman A. Rubin D. B. 1992 Inference from iterative simulation using multiple sequences: Statistical Science 7 457 472 10.1214/ss/1177011136
    https://doi.org/10.1214/ss/1177011136 [Google Scholar]
  25. Gelman, A., Carlin, J. B., Hal, S., and Rubin, D. B., 2004, Bayesian data analysis (2nd edition): CRC Press.
  26. Geyer C. J. Møller J 1994 Simulation procedures and likelihood inference for spatial point processes: Scandinavian Journal of Statistics 21 359 373
    [Google Scholar]
  27. Green P. J. 1995 Reversible jump Markov chain Monte Carlo computation and Bayesian model determination: Biometrika 82 711 732 10.1093/biomet/82.4.711
    https://doi.org/10.1093/biomet/82.4.711 [Google Scholar]
  28. Green, A., and Lane, R., 2003, Estimating noise levels in AEM data: 16th ASEG Geophysical Conference and Exhibition, Extended Abstracts, 1–5.
  29. Hanke M. 1996 Limitations of the L-curve method in ill-posed problems: BIT Numerical Mathematics 36 287 301 10.1007/BF01731984
    https://doi.org/10.1007/BF01731984 [Google Scholar]
  30. Hansen P. C. 1992 Analysis of discrete ill-posed problems by means of the L-curve: SIAM Review 34 561 580 10.1137/1034115
    https://doi.org/10.1137/1034115 [Google Scholar]
  31. Hastings W. K. 1970 Monte Carlo sampling methods using Markov chains and their applications: Biometrika 57 97 109 10.1093/biomet/57.1.97
    https://doi.org/10.1093/biomet/57.1.97 [Google Scholar]
  32. Hauser J. Gunning J. Annetts D. 2015 Probabilistic inversion of airborne electromagnetic data under spatial constraints: Geophysics 80 E135 E146 10.1190/geo2014‑0389.1
    https://doi.org/10.1190/geo2014-0389.1 [Google Scholar]
  33. Hawkins R. Sambridge M. 2015 Geophysical imaging using trans-dimensional trees: Geophysical Journal International 203 972 1000 10.1093/gji/ggv326
    https://doi.org/10.1093/gji/ggv326 [Google Scholar]
  34. Hopcroft P. O. Gallagher K. Pain C. C. 2007 Inference of past climate from borehole temperature data using Bayesian reversible jump Markov chain Monte Carlo: Geophysical Journal International 171 1430 1439 10.1111/j.1365‑246X.2007.03596.x
    https://doi.org/10.1111/j.1365-246X.2007.03596.x [Google Scholar]
  35. Hyndman R. J. 1996 Computing and graphing highest density regions: The American Statistician 50 120 126
    [Google Scholar]
  36. Iaffaldano G. Hawkins R. Sambridge M. 2014 Bayesian noise-reduction in Arabia/Somalia and Nubia/Arabia finite rotations since ~20 Ma: implications for Nubia/Somalia relative motion: Geochemistry Geophysics Geosystems 15 845 854 10.1002/2013GC005089
    https://doi.org/10.1002/2013GC005089 [Google Scholar]
  37. Jaynes, E. T., 2003, Probability theory: the logic of science: Cambridge University Press.
  38. Jeffreys, H., 1939, Theory of probability (3rd edition): Clarendon Press.
  39. Kass R. E. Raftery A. E. 1995 Bayes factors: Journal of the American Statistical Association 90 773 795 10.1080/01621459.1995.10476572
    https://doi.org/10.1080/01621459.1995.10476572 [Google Scholar]
  40. Lawrie, K., 2016, Broken Hill managed aquifer recharge. Available at: http://www.ga.gov.au/about/projects/water/broken-hill-managed-aquifer-recharge (accessed 20 September 2016).
  41. Lawrie K. C. Munday T. J. Dent D. L. Gibson D. L. Brodie R. C. Wilford J. Reilly N. S. Chan R. N. Baker P. 2000 A geological systems approach to understanding the processes involved in land and water salinisation; the Gilmore project area, central west New South Wales: AGSO Research Newsletter 32 13 15
    [Google Scholar]
  42. Lochbühler T. Vrugt J. A. Sadegh M. Linde N. 2015 Summary statistics from training images as prior information in probabilistic inversion: Geophysical Journal International 201 157 171 10.1093/gji/ggv008
    https://doi.org/10.1093/gji/ggv008 [Google Scholar]
  43. Malinverno A. 2002 Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem: Geophysical Journal International 151 675 688 10.1046/j.1365‑246X.2002.01847.x
    https://doi.org/10.1046/j.1365-246X.2002.01847.x [Google Scholar]
  44. Malinverno A. Briggs V. A. 2004 Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes: Geophysics 69 1005 1016 10.1190/1.1778243
    https://doi.org/10.1190/1.1778243 [Google Scholar]
  45. Maxwell, J. C., 1881, A treatise on electricity and magnetism, vol. 1: Clarendon Press.
  46. Menke, W., 1989, Geophysical data analysis: discrete inverse theory: Academic Press.
  47. Metropolis N. Rosenbluth A. W. Rosenbluth M. N. Teller A. H. Teller E. 1953 Equation of state calculations by fast computing machines: The Journal of Chemical Physics 21 1087 1092 10.1063/1.1699114
    https://doi.org/10.1063/1.1699114 [Google Scholar]
  48. Minsley B. J. 2011 A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data: Geophysical Journal International 187 252 272 10.1111/j.1365‑246X.2011.05165.x
    https://doi.org/10.1111/j.1365-246X.2011.05165.x [Google Scholar]
  49. Palacky G. J. 1993 Use of airborne electromagnetic methods for resource mapping: Advances in Space Research 13 5 14 10.1016/0273‑1177(93)90196‑I
    https://doi.org/10.1016/0273-1177(93)90196-I [Google Scholar]
  50. Piana Agostinetti N. Malinverno A. 2010 Receiver function inversion by transdimensional Monte Carlo sampling: Geophysical Journal International 181 858 872
    [Google Scholar]
  51. Piana Agostinetti N. Giacomuzzi G. Malinverno A. 2015 Local 3D earthquake tomography by trans-dimensional Monte Carlo sampling: Geophysical Journal International 201 1598 1617 10.1093/gji/ggv084
    https://doi.org/10.1093/gji/ggv084 [Google Scholar]
  52. Ray A. Key K. 2012 Bayesian inversion of marine CSEM data with a trans-dimensional self-parametrizing algorithm: Geophysical Journal International 191 1135 1151
    [Google Scholar]
  53. Ray A. Alumbaugh D. L. Hoversten G. M. Key K. 2013 Robust and accelerated Bayesian inversion of marine controlled-source electromagnetic data using parallel tempering: Geophysics 78 E271 E280 10.1190/geo2013‑0128.1
    https://doi.org/10.1190/geo2013-0128.1 [Google Scholar]
  54. Ray A. Key K. Bodin T. Meyer D. Constable S. 2014 Bayesian inversion of marine CSEM data from the Scarborough gas field using transdimensional 2-D parameterization: Geophysical Journal International 199 1847 1860 10.1093/gji/ggu370
    https://doi.org/10.1093/gji/ggu370 [Google Scholar]
  55. Rosas-Carbajal M. Linde N. Kalscheuer T Vrugt J 2014 Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data: Geophysical Journal International 196 1508 1524 10.1093/gji/ggt482
    https://doi.org/10.1093/gji/ggt482 [Google Scholar]
  56. Rudolph M. L. Lekic V. Lithgow-Bertelloni C. 2015 Viscosity jump in Earth’s mid mantle: Science 350 1349 1352 10.1126/science.aad1929
    https://doi.org/10.1126/science.aad1929 [Google Scholar]
  57. Sambridge M. 2014 A parallel tempering algorithm for probabilistic sampling and multimodal optimization: Geophysical Journal International 196 357 374 10.1093/gji/ggt342
    https://doi.org/10.1093/gji/ggt342 [Google Scholar]
  58. Sambridge M. Mosegaard K. 2002 Monte Carlo methods in geophysical inverse problems: Reviews of Geophysics 40 1 29 10.1029/2000RG000089
    https://doi.org/10.1029/2000RG000089 [Google Scholar]
  59. Sambridge M. Gallagher K. Jackson A. Rickwood P. 2006 Trans-dimensional inverse problems, model comparison and the evidence: Geophysical Journal International 167 528 542 10.1111/j.1365‑246X.2006.03155.x
    https://doi.org/10.1111/j.1365-246X.2006.03155.x [Google Scholar]
  60. Sattel D. Kgotlhang L. 2004 Groundwater exploration with AEM in the Boteti area, Botswana: Exploration Geophysics 35 147 156 10.1071/EG04147
    https://doi.org/10.1071/EG04147 [Google Scholar]
  61. Skilling J. 2006 Nested sampling for general Bayesian computation: Bayesian Analysis 1 833 859 10.1214/06‑BA127
    https://doi.org/10.1214/06-BA127 [Google Scholar]
  62. Sorensen K. I. Auken E. 2004 SkyTEM – a new high-resolution helicopter transient electromagnetic system: Exploration Geophysics 35 191 199
    [Google Scholar]
  63. Spiegelhalter D. J. Best N. G. Carlin B. P. van der Linde A. 2002 Bayesian measures of model complexity and fit: Journal of the Royal Statistical Society, Series B: Methodological 64 583 639 10.1111/1467‑9868.00353
    https://doi.org/10.1111/1467-9868.00353 [Google Scholar]
  64. Street, G. J., Pracilio, G., Nallan-Chakravartula, P., Nash, C., Sattel, D., Owers, M., Triggs, D., and Lane, R., 1998, National dryland salinity program airborne geophysical surveys to assist planning for salinity control; 1. Willaura SALTMAP survey interpretation report, National Airbourne Geophysics Project, World Geoscience Corporation.
  65. Tarantola, A., 2005, Inverse problem theory and methods for model parameter estimation: Society for Industrial Mathematics.
  66. Tikhonov A. N. 1943 On the stability of inverse problems: Doklady Akademii Nauk SSSR 39 195 198
    [Google Scholar]
  67. Tkalčić H. Young M. Bodin T. Ngo S. Sambridge M. 2013 The shuffling rotation of the Earth’s inner core revealed by earthquake doublets: Nature Geoscience 6 497 502 10.1038/ngeo1813
    https://doi.org/10.1038/ngeo1813 [Google Scholar]
  68. Unser M. Blu T. 2003 Mathematical properties of the JPEG2000 wavelet filters: IEEE Transactions on Image Processing 12 1080 1090 10.1109/TIP.2003.812329
    https://doi.org/10.1109/TIP.2003.812329 [Google Scholar]
  69. Vogel C. R. 1996 Non-convergence of the L-curve regularization parameter selection method: Inverse Problems 12 535 547 10.1088/0266‑5611/12/4/013
    https://doi.org/10.1088/0266-5611/12/4/013 [Google Scholar]
  70. Yang D. Oldenburg D. W. 2012 Three-dimensional inversion of airborne time domain electromagnetic data with applications to a porphyry deposit: Geophysics 77 B23 B34 10.1190/geo2011‑0194.1
    https://doi.org/10.1190/geo2011-0194.1 [Google Scholar]
  71. Young M. K. Tkalčić H. Bodin T. Sambridge M. 2013 Global P wave tomography of Earth’s lowermost mantle from partition modeling: Journal of Geophysical Research. Solid Earth 118 5467 5486 10.1002/jgrb.50391
    https://doi.org/10.1002/jgrb.50391 [Google Scholar]
/content/journals/10.1071/EG16139
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Trans-dimensional Bayesian inversion of airborne electromagnetic data for 2D conductivity profiles
Exploration Geophysics 49, 134 (2018); https://doi.org/10.1071/EG16139
/content/journals/10.1071/EG16139
/content/journals/10.1071/EG16139
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  • Article Type: Research Article
Keyword(s): airborne electromagnetic inversion; Bayesian; non-uniqueness; trans-dimensional; uncertainty

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