Exploration Geophysics Exploration Geophysics Society
Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Trans-dimensional Bayesian inversion of airborne electromagnetic data for 2D conductivity profiles

Rhys Hawkins 1 3 Ross C. Brodie 2 Malcolm Sambridge 1
+ Author Affiliations
- Author Affiliations

1 Research School of Earth Sciences, Australian National University, Canberra, ACT 2601, Australia.

2 Geoscience Australia, Canberra, ACT 2609, Australia.

3 Corresponding author. Email: rhys.hawkins@anu.edu.au

Exploration Geophysics - https://doi.org/10.1071/EG16139
Submitted: 11 November 2016  Accepted: 30 January 2017   Published online: 24 February 2017

Abstract

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.

Key words: airborne electromagnetic inversion, Bayesian, non-uniqueness, trans-dimensional, uncertainty.


References

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
An introduction to the use of airborne technologies for watershed characterization in mined areas:CrossRef |

Akaike, H., 1974, A new look at the statistical model identification: IEEE Transactions on Automatic Control, 19, 716–723
A new look at the statistical model identification:CrossRef |

Ando, T., 2007, Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models: Biometrika, 94, 443–458
Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models:CrossRef |

Ando, T., 2010, Bayesian model selection and statistical modelling: CRC Press.

Backus, G., and Gilbert, F., 1968, The resolving power of gross earth data: Geophysical Journal of the Royal Astronomical Society, 16, 169–205
The resolving power of gross earth data:CrossRef |

Bayes, T., 1763, An essay towards solving a problem in the doctrine of chances: Philosophical Transactions of the Royal Society, 53, 370–418
An essay towards solving a problem in the doctrine of chances:CrossRef |

Bodin, T., and Sambridge, M., 2009, Seismic tomography with the reversible jump algorithm: Geophysical Journal International, 178, 1411–1436
Seismic tomography with the reversible jump algorithm:CrossRef |

Bodin, T., Sambridge, M., Tkalčić, H., Arroucau, P., Gallagher, L., and Rawlinson, N., 2012a, Trans-dimensional inversion of receiver functions and surface wave dispersion: Journal of Geophysical Research, 117, B02301
Trans-dimensional inversion of receiver functions and surface wave dispersion:CrossRef |

Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P., 2012b, Transdimensional tomography with unknown data noise: Geophysical Journal International, 189, 1536–1556
Transdimensional tomography with unknown data noise:CrossRef |

Brodie, R. C., 2010, Holistic inversion of airborne electromagnetic data: Ph.D. thesis, Australian National University.

Brodie, R. C., 2016, Geoscience Australia AEM source code repository. Available at: https://github.com/GeoscienceAustralia/ga-aem (accessed 20 September 2016).

Brodie, R., and Sambridge, M., 2006, A holistic approach to inversion of frequency domain airborne EM data: Geophysics, 71, G301–G312
A holistic approach to inversion of frequency domain airborne EM data:CrossRef |

Brodie, R., and Sambridge, M., 2012, Transdimensional Monte Carlo inversion of AEM data: 22nd ASEG International Geophysical Conference and Exhibition, 1–4.

Brooks, S., Gelman, A., Jones, G. L., and Meng, X., eds., 2011, Handbook of Markov chain Monte Carlo: Chapman and Hall/CRC.

Cohen, A., Daubechies, I., and Feauveau, J. C., 1992, Biorthogonal bases of compactly supported wavelets: Communications on Pure and Applied Mathematics, 45, 485–560
Biorthogonal bases of compactly supported wavelets:CrossRef |

Constable, S. C., Parker, R. L., and Constable, C. G., 1987, Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data: Geophysics, 52, 289–300
Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data:CrossRef |

Dettmer, J., Molnar, S., Steininger, G., Dosso, S. E., and Cassidy, J. F., 2012, Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models: Geophysical Journal International, 188, 719–734
Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models:CrossRef |

Dettmer, J., Hawkins, R., Cummins, P. R., Hossen, J., Sambridge, M., Hino, R., and Inazu, D., 2016, Tsunami source uncertainty estimation: the 2011 Japan tsunami: Journal of Geophysical Research: Solid Earth, 121, 4483–4505
Tsunami source uncertainty estimation: the 2011 Japan tsunami:CrossRef |

Dosso, S. E., Holland, C. W., and Sambridge, M., 2012, Parallel tempering in strongly nonlinear geoacoustic inversion: The Journal of the Acoustical Society of America, 132, 3030–3040
Parallel tempering in strongly nonlinear geoacoustic inversion:CrossRef |

Earl, D. J., and Deem, M. W., 2005, Parallel tempering: theory, applications, and new perspectives: Physical Chemistry Chemical Physics, 7, 3910–3916
Parallel tempering: theory, applications, and new perspectives:CrossRef | 1:CAS:528:DC%2BD28XhsFWnsb0%3D&md5=cb6dfe4207320d7e97addc2c14a8de47CAS |

Farquharson, C. G., and Oldenburg, D. W., 1993, Inversion of time-domain electromagnetic data for a horizontally layered Earth: Geophysical Journal International, 114, 433–442
Inversion of time-domain electromagnetic data for a horizontally layered Earth:CrossRef |

Farquharson, C. G., and 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
A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems:CrossRef |

Fitterman, D. V., and Deszcz-Pan, M., 1998, Helicopter EM mapping of saltwater intrusion in Everglades National Park, Florida: Exploration Geophysics, 29, 240–243
Helicopter EM mapping of saltwater intrusion in Everglades National Park, Florida:CrossRef |

Gelman, A., and Rubin, D. B., 1992, Inference from iterative simulation using multiple sequences: Statistical Science, 7, 457–472
Inference from iterative simulation using multiple sequences:CrossRef |

Gelman, A., Carlin, J. B., Hal, S., and Rubin, D. B., 2004, Bayesian data analysis (2nd edition): CRC Press.

Geyer, C. J., and Møller, J, 1994, Simulation procedures and likelihood inference for spatial point processes: Scandinavian Journal of Statistics, 21, 359–373

Green, P. J., 1995, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination: Biometrika, 82, 711–732
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination:CrossRef |

Green, A., and Lane, R., 2003, Estimating noise levels in AEM data: 16th ASEG Geophysical Conference and Exhibition, Extended Abstracts, 1–5.

Hanke, M., 1996, Limitations of the L-curve method in ill-posed problems: BIT Numerical Mathematics, 36, 287–301
Limitations of the L-curve method in ill-posed problems:CrossRef |

Hansen, P. C., 1992, Analysis of discrete ill-posed problems by means of the L-curve: SIAM Review, 34, 561–580
Analysis of discrete ill-posed problems by means of the L-curve:CrossRef |

Hastings, W. K., 1970, Monte Carlo sampling methods using Markov chains and their applications: Biometrika, 57, 97–109
Monte Carlo sampling methods using Markov chains and their applications:CrossRef |

Hauser, J., Gunning, J., and Annetts, D., 2015, Probabilistic inversion of airborne electromagnetic data under spatial constraints: Geophysics, 80, E135–E146
Probabilistic inversion of airborne electromagnetic data under spatial constraints:CrossRef |

Hawkins, R., and Sambridge, M., 2015, Geophysical imaging using trans-dimensional trees: Geophysical Journal International, 203, 972–1000
Geophysical imaging using trans-dimensional trees:CrossRef |

Hopcroft, P. O., Gallagher, K., and 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
Inference of past climate from borehole temperature data using Bayesian reversible jump Markov chain Monte Carlo:CrossRef |

Hyndman, R. J., 1996, Computing and graphing highest density regions: The American Statistician, 50, 120–126

Iaffaldano, G., Hawkins, R., and 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
Bayesian noise-reduction in Arabia/Somalia and Nubia/Arabia finite rotations since ~20 Ma: implications for Nubia/Somalia relative motion:CrossRef |

Jaynes, E. T., 2003, Probability theory: the logic of science: Cambridge University Press.

Jeffreys, H., 1939, Theory of probability (3rd edition): Clarendon Press.

Kass, R. E., and Raftery, A. E., 1995, Bayes factors: Journal of the American Statistical Association, 90, 773–795
Bayes factors:CrossRef |

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).

Lawrie, K. C., Munday, T. J., Dent, D. L., Gibson, D. L., Brodie, R. C., Wilford, J., Reilly, N. S., Chan, R. N., and 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

Lochbühler, T., Vrugt, J. A., Sadegh, M., and Linde, N., 2015, Summary statistics from training images as prior information in probabilistic inversion: Geophysical Journal International, 201, 157–171
Summary statistics from training images as prior information in probabilistic inversion:CrossRef |

Malinverno, A., 2002, Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem: Geophysical Journal International, 151, 675–688
Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem:CrossRef |

Malinverno, A., and Briggs, V. A., 2004, Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes: Geophysics, 69, 1005–1016
Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes:CrossRef |

Maxwell, J. C., 1881, A treatise on electricity and magnetism, vol. 1: Clarendon Press.

Menke, W., 1989, Geophysical data analysis: discrete inverse theory: Academic Press.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E., 1953, Equation of state calculations by fast computing machines: The Journal of Chemical Physics, 21, 1087–1092
Equation of state calculations by fast computing machines:CrossRef | 1:CAS:528:DyaG3sXltlKhsw%3D%3D&md5=df73e3fe91cd9561c21affbbeeac0744CAS |

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
A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data:CrossRef |

Palacky, G. J., 1993, Use of airborne electromagnetic methods for resource mapping: Advances in Space Research, 13, 5–14
Use of airborne electromagnetic methods for resource mapping:CrossRef |

Piana Agostinetti, N., and Malinverno, A., 2010, Receiver function inversion by transdimensional Monte Carlo sampling: Geophysical Journal International, 181, 858–872

Piana Agostinetti, N., Giacomuzzi, G., and Malinverno, A., 2015, Local 3D earthquake tomography by trans-dimensional Monte Carlo sampling: Geophysical Journal International, 201, 1598–1617
Local 3D earthquake tomography by trans-dimensional Monte Carlo sampling:CrossRef |

Ray, A., and Key, K., 2012, Bayesian inversion of marine CSEM data with a trans-dimensional self-parametrizing algorithm: Geophysical Journal International, 191, 1135–1151

Ray, A., Alumbaugh, D. L., Hoversten, G. M., and Key, K., 2013, Robust and accelerated Bayesian inversion of marine controlled-source electromagnetic data using parallel tempering: Geophysics, 78, E271–E280
Robust and accelerated Bayesian inversion of marine controlled-source electromagnetic data using parallel tempering:CrossRef |

Ray, A., Key, K., Bodin, T., Meyer, D., and 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
Bayesian inversion of marine CSEM data from the Scarborough gas field using transdimensional 2-D parameterization:CrossRef |

Rosas-Carbajal, M., Linde, N., Kalscheuer, T, and 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
Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data:CrossRef |

Rudolph, M. L., Lekic, V., and Lithgow-Bertelloni, C., 2015, Viscosity jump in Earth’s mid mantle: Science, 350, 1349–1352
Viscosity jump in Earth’s mid mantle:CrossRef | 1:CAS:528:DC%2BC2MXhvFKru77N&md5=82aed8752a571e16be4d602509f2abe3CAS |

Sambridge, M., 2014, A parallel tempering algorithm for probabilistic sampling and multimodal optimization: Geophysical Journal International, 196, 357–374
A parallel tempering algorithm for probabilistic sampling and multimodal optimization:CrossRef |

Sambridge, M., and Mosegaard, K., 2002, Monte Carlo methods in geophysical inverse problems: Reviews of Geophysics, 40, 1–29
Monte Carlo methods in geophysical inverse problems:CrossRef |

Sambridge, M., Gallagher, K., Jackson, A., and Rickwood, P., 2006, Trans-dimensional inverse problems, model comparison and the evidence: Geophysical Journal International, 167, 528–542
Trans-dimensional inverse problems, model comparison and the evidence:CrossRef |

Sattel, D., and Kgotlhang, L., 2004, Groundwater exploration with AEM in the Boteti area, Botswana: Exploration Geophysics, 35, 147–156
Groundwater exploration with AEM in the Boteti area, Botswana:CrossRef |

Skilling, J., 2006, Nested sampling for general Bayesian computation: Bayesian Analysis, 1, 833–859
Nested sampling for general Bayesian computation:CrossRef |

Sorensen, K. I., and Auken, E., 2004, SkyTEM – a new high-resolution helicopter transient electromagnetic system: Exploration Geophysics, 35, 191–199

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A., 2002, Bayesian measures of model complexity and fit: Journal of the Royal Statistical Society, Series B: Methodological, 64, 583–639
Bayesian measures of model complexity and fit:CrossRef |

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.

Tarantola, A., 2005, Inverse problem theory and methods for model parameter estimation: Society for Industrial Mathematics.

Tikhonov, A. N., 1943, On the stability of inverse problems: Doklady Akademii Nauk SSSR, 39, 195–198

Tkalčić, H., Young, M., Bodin, T., Ngo, S., and Sambridge, M., 2013, The shuffling rotation of the Earth’s inner core revealed by earthquake doublets: Nature Geoscience, 6, 497–502
The shuffling rotation of the Earth’s inner core revealed by earthquake doublets:CrossRef |

Unser, M., and Blu, T., 2003, Mathematical properties of the JPEG2000 wavelet filters: IEEE Transactions on Image Processing, 12, 1080–1090
Mathematical properties of the JPEG2000 wavelet filters:CrossRef |

Vogel, C. R., 1996, Non-convergence of the L-curve regularization parameter selection method: Inverse Problems, 12, 535–547
Non-convergence of the L-curve regularization parameter selection method:CrossRef |

Yang, D., and Oldenburg, D. W., 2012, Three-dimensional inversion of airborne time domain electromagnetic data with applications to a porphyry deposit: Geophysics, 77, B23–B34
Three-dimensional inversion of airborne time domain electromagnetic data with applications to a porphyry deposit:CrossRef |

Young, M. K., Tkalčić, H., Bodin, T., and Sambridge, M., 2013, Global P wave tomography of Earth’s lowermost mantle from partition modeling: Journal of Geophysical Research. Solid Earth, 118, 5467–5486
Global P wave tomography of Earth’s lowermost mantle from partition modeling:CrossRef |



Export Citation

View Altmetrics