Trans-dimensional Bayesian inversion of airborne electromagnetic data for 2D conductivity profiles
Rhys Hawkins 1 3 Ross C. Brodie 2 Malcolm Sambridge 11 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 49(2) 134-147 https://doi.org/10.1071/EG16139
Submitted: 11 November 2016 Accepted: 30 January 2017 Published: 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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar | 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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar | 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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar | 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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
Skilling, J., 2006, Nested sampling for general Bayesian computation: Bayesian Analysis, 1, 833–859
| Nested sampling for general Bayesian computation:Crossref | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |
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 | GoogleScholarGoogle Scholar |