CoChat
Sign Up
Cited by 462Seismic Waves and AnalysisSeismic Imaging and Inversion TechniquesMarkov Chains and Monte Carlo Methods

Transdimensional inversion of receiver functions and surface wave dispersion

Open access
Bodin, T., Sambridge, M., Gallagher, K., Rawlinson, N.·2012·Journal of Geophysical Research: Solid Earth
DOI 10.1029/2011jb008560
Open this paper in CoChat — free accountOpen PDF

Abstract

We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1029/2011jb008560

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 73

  1. Arroucau, P., N. Rawlinson, and M. Sambridge (2010), New insight into Cainozoic sedimentary basins and Palaeozoic suture zones in southeast Australia from ambient noise surface wave tomography, Geophys. Res. Lett., 37, L07303, doi:10.1029/2009GL041974. · DOI
  2. Bannister, S., J. Yu, B. Leitner, and B. L. N. Kennett (2003), Variations in crustal structure across the transition from West to East Antarctica, South- ern Victoria Land, Geophys. J. Int., 155(3), 870-880.
  3. Bayes, T. (1763), An essay towards solving a problem in the doctrine of chances, Philos. Trans. R. Soc. London, 53, 370-418. [Reprinted in Biometrika, 45, 295-315, 1958.
  4. Bodin, T., and M. Sambridge (2009), Seismic tomography with the revers- ible jump algorithm, Geophys. J. Int., 178(3), 1411-1436.
  5. Box, G., and G. Tiao (1973), Bayesian Inference in Statistical Inference, Wiley-Intersci., Hoboken, N. J.
  6. Brodie, R., and M. Sambridge (2009), Holistic inversion of frequency- domain airborne electromagnetic data with minimal prior information, Explor. Geophys., 40(1), 8-16.
  7. Campillo, M., and A. Paul (2003), Long-range correlations in the diffuse seismic coda, Science, 299(5606), 547-549.
  8. Chang, S., C. Baag, and C. Langston (2004), Joint analysis of teleseismic receiver functions and surface wave dispersion using the genetic algorithm, Bull. Seismol. Soc. Am., 94(2), 691-704.
  9. Charvin, K., K. Gallagher, G. Hampson, and R. Labourdette (2009a), A Bayesian approach to inverse modelling of stratigraphy, part 1: Method, Basin Res., 21(1), 5-25.
  10. Charvin, K., G. Hampson, K. Gallagher, and R. Labourdette (2009b), A Bayesian approach to inverse modelling of stratigraphy, part 2: Valida- tion tests, Basin Res., 21(1), 27-45.
  11. Chen, Y., F. Niu, R. Liu, Z. Huang, H. Tkalčić, L. Sun, and W. Chan (2010), Crustal structure beneath China from receiver function analysis, J. Geophys. Res., 115, B03307, doi:10.1029/2009JB006386. · DOI
  12. Clayton, R., and R. Wiggins (1976), Source shape estimation and deconvo- lution of teleseismic bodywaves, Geophys. J. R. Astron. Soc., 47(1), 151-177.
  13. Clifford, P., S. Greenhalgh, G. Houseman, and F. Graeber (2007), 3-D seismic tomography of the Adelaide fold belt, Geophys. J. Int., 172(1), 167-186.
  14. Denison, D., N. Adams, C. Holmes, and D. Hand (2002), Bayesian partition modelling, Comput. Stat. Data Anal., 38(4), 475-485.
  15. Di Bona, M., et al. (1998), Variance estimate in frequency-domain decon- volution for teleseismic receiver function computation, Geophys. J. Int., 134(2), 634-646.
  16. Du, Z., and G. Foulger (1999), The crustal structure beneath the northwest fjords, Iceland, from receiver functions and surface waves, Geophys. J. Int., 139(2), 419-432.
  17. Duijndam, A. (1988a), Bayesian estimation in seismic inversion. Part I: Principles, Geophys. Prospect., 36(8), 878-898.
  18. Frederiksen, A., H. Folsom, and G. Zandt (2003), Neighbourhood inversion of teleseismic Ps conversions for anisotropy and layer dip, Geophys. J. Int., 155(1), 200-212.
  19. Gallagher, K., K. Charvin, S. Nielsen, M. Sambridge, and J. Stephenson (2009), Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems, Mar. Pet. Geol., 26(4), 525-535.
  20. Geyer, C., and J. Møller (1994), Simulation procedures and likelihood inference for spatial point processes, Scand. J. Stat., 21(4), 359-373.
  21. Graeber, F., G. Houseman, and S. Greenhalgh (2002), Regional teleseismic tomography of the western Lachlan Orogen and the Newer Volcanic Province, southeast Australia, Geophys. J. Int., 149(2), 249-266.
  22. Haskell, N. (1953), The dispersion of surface waves on multilayered media, Bull. Seismol. Soc. Am., 43(1), 17-34.
  23. Hetényi, G., and Z. Bus (2007), Shear wave velocity and crustal thickness in the Pannonian Basin from receiver function inversions at four perma- nent stations in Hungary, J. Seismol., 11(4), 405-414.
  24. Hopcroft, P., K. Gallagher, and C. Pain (2007), Inference of past climate from borehole temperature data using Bayesian Reversible Jump Markov chain Monte Carlo, Geophys. J. Int., 171(3), 1430-1439.
  25. Hopcroft, P., K. Gallagher, and C. Pain (2009), A Bayesian partition mod- elling approach to resolve spatial variability in climate records from bore- hole temperature inversion, Geophys. J. Int., 178(2), 651-666.
  26. Jasra, A., D. Stephens, K. Gallagher, and C. Holmes (2006), Bayesian mix- ture modelling in geochronology via Markov chain Monte Carlo, Math. Geol., 38(3), 269-300.
  27. Juliá, J., C. Ammon, R. Herrmann, and A. Correig (2000), Joint inversion of receiver function and surface wave dispersion observations, Geophys. J. Int., 143(1), 99-112.
  28. Juliá, J., C. Ammon, and R. Herrmann (2003), Lithospheric structure of the Arabian Shield from the joint inversion of receiver functions and surface- wave group velocities, Tectonophysics, 371(1-4), 1-21.
  29. Kind, R., G. Kosarev, and N. Petersen (1995), Receiver functions at the sta- tions of the German Regional Seismic Network (GRSN), Geophys. J. Int., 121(1), 191-202.
  30. Lawrence, J., and D. Wiens (2004), Combined receiver-function and sur- face wave phase-velocity inversion using a niching genetic algorithm: Application to Patagonia, Bull. Seismol. Soc. Am., 94(3), 977-987.
  31. Levin, V., and J. Park (1997), P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation, Geophys. J. Int., 131(2), 253-266.
  32. Ligorria, J., and C. Ammon (1999), Iterative deconvolution and receiver- function estimation, Bull. Seismol. Soc. Am., 89(5), 1395-1400.
  33. Lombardi, D. (2007), Alpine crustal and upper-mantle structure from receiver functions, A PhD thesis, ETH Zurich, Zurich, Switzerland.
  34. Lowrie, W. (1997), Fundamentals of Geophysics, Cambridge Univ. Press, New York.
  35. Lucente, F., N. Piana Agostinetti, M. Moro, G. Selvaggi, and M. Di Bona (2005), Possible fault plane in a seismic gap area of the southern Apennines (Italy) revealed by receiver function analysis, J. Geophys. Res., 110, B04307, doi:10.1029/2004JB003187. · DOI
  36. Luo, X. (2010), Constraining the shape of a gravity anomalous body using reversible jump Markov chain Monte Carlo, Geophys. J. Int., 180(3), 1067-1079.
  37. MacKay, D. (2003), Information Theory, Inference, and Learning Algorithms, Cambridge Univ. Press, New York.
  38. Mahalanobis, P. (1936), On the generalised distance in statistics, Proc. Natl. Acad. Sci. India, 12, 49-55.
  39. Malinverno, A. (2002), Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem, Geophys. J. Int., 151(3), 675-688.
  40. Malinverno, A., and V. Briggs (2004), Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes, Geophysics, 69, 1005, doi:10.1190/1.1778243. · DOI
  41. Malinverno, A., and R. Parker (2006), Two ways to quantify uncertainty in geophysical inverse problems, Geophysics, 71, W15, doi:10.1190/ 1.2194516. · DOI
  42. Metropolis, N., et al. (1953), Equations of state calculations by fast compu- tational machine, J. Chem. Phys., 21(6), 1087-1091.
  43. Moorkamp, M., A. Jones, and S. Fishwick (2010), Joint inversion of receiver functions, surface wave dispersion, and magnetotelluric data, J. Geophys. Res., 115, B04318, doi:10.1029/2009JB006369. · DOI
  44. Nicholson, T., M. Bostock, and J. Cassidy (2005), New constraints on sub- duction zone structure in northern Cascadia, Geophys. J. Int., 161(3), 849-859.
  45. Nicollin, F., D. Gibert, P. Bossart, C. Nussbaum, and C. Guervilly (2008), Seismic tomography of the excavation damaged zone of the Gallery 04 in the Mont Terri Rock Laboratory, Geophys. J. Int., 172(1), 226-239.
  46. Özalaybey, S., M. Savage, A. Sheehan, J. Louie, and J. Brune (1997), Shear-wave velocity structure in the northern Basin and Range province from the combined analysis of receiver functions and surface waves, Bull. Seismol. Soc. Am., 87(1), 183-199.
  47. Piana Agostinetti, N., and C. Chiarabba (2008), Seismic structure beneath Mt Vesuvius from receiver function analysis and local earthquakes tomography: evidences for location and geometry of the magma chamber, Geophys. J. Int., 175(3), 1298-1308.
  48. Piana Agostinetti, N., and A. Malinverno (2010), Receiver function inversion by trans-dimensional Monte Carlo sampling, Geophys. J. Int., 181(2), 858-872.
  49. Piana Agostinetti, N., F. Lucente, G. Selvaggi, and M. Di Bona (2002), Crustal structure and Moho geometry beneath the Northern Apennines (Italy), Geophys. Res. Lett., 29(20), 1999, doi:10.1029/2002GL015109. · DOI
  50. Rawlinson, N., and B. Kennett (2008), Teleseismic tomography of the upper mantle beneath the southern Lachlan Orogen, Australia, Phys. Earth Planet. Inter., 167(1-2), 84-97.
  51. Rawlinson, N., and M. Urvoy (2006), Simultaneous inversion of active and passive source data sets for 3-D seismic structure with application to Tasmania, Geophys. Res. Lett., 33, L24313, doi:10.1029/2006GL028105. · DOI
  52. Rawlinson, N., A. Reading, and B. Kennett (2006), Lithospheric structure of Tasmania from a novel form of teleseismic tomography, J. Geophys. Res., 111, B02301, doi:10.1029/2005JB003803. · DOI
  53. Reading, A., B. Kennett, and M. Dentith (2003), Seismic structure of the Yilgarn Craton, Western Australia, Aust. J. Earth Sci., 50(3), 427-438.
  54. Reading, A., T. Bodin, M. Sambridge, S. Howe, and M. Roach (2010), Down the borehole but outside the box: Innovative approaches to wireline log data interpretation, paper presented at 21st International Geophysics Conference and Exhibition, Aust. Soc. of Explor. Geophys., Sydney, Australia.
  55. Rosenthal, J. (2000), Parallel computing and Monte Carlo algorithms, Far East J. Theor. Stat., 4(2), 207-236.
  56. Saito, M. (1988), DISPER80: A subroutine package for the calculation of seis- mic normal-mode solutions, in Seismological Algorithms: Computational Methods and Computer Programs, pp. 293-319, Academic, London.
  57. Sambridge, M. (1999a), Geophysical inversion with a neighbourhood algo- rithm I. Searching a parameter space, Geophys. J. Int., 138(2), 479-494.
  58. Sambridge, M. (1999b), Geophysical inversion with a neighbourhood algo- rithm II. Appraising the ensemble, Geophys. J. Int., 138(3), 727-746.
  59. Scales, J., and R. Snieder (1997), To Bayes or not to Bayes, Geophysics, 62(4), 1045-1046.
  60. Scales, J., and R. Snieder (1998), What is noise, Geophysics, 63(4), 1122-1124.
  61. Shapiro, N., and M. Campillo (2004), Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise, Geophys. Res. Lett., 31, L07614, doi:10.1029/2004GL019491. · DOI
  62. Sisson, S. (2005), Transdimensional Markov chains: A decade of progress and future perspectives, J. Am. Stat. Assoc., 100(471), 1077-1090.
  63. Smith, A. (1991), Bayesian computational methods, Philos. Trans. R. Soc. A, 337(1647), 369-386.
  64. Stehly, L., B. Fry, M. Campillo, N. Shapiro, J. Guilbert, L. Boschi, and D. Giardini (2009), Tomography of the Alpine region from observations of seismic ambient noise, Geophys. J. Int., 178(1), 338-350.
  65. Stephenson, J., K. Gallagher, and C. Holmes (2004), Beyond kriging: Dealing with discontinuous spatial data fields using adaptive prior information and Bayesian partition modelling, Geol. Soc. Spec. Publ., 239(1), 195-209.
  66. Stephenson, J., K. Gallagher, and C. Holmes (2006), Low temperature thermochronology and strategies for multiple samples 2: Partition mod- elling for 2D/3D distributions with discontinuities, Earth Planet. Sci. Lett., 241(3-4), 557-570.
  67. Tarantola, A., and B. Valette (1982), Inverse problems = quest for information, J. Geophys., 50(3), 150-170.
  68. Tkalčić, H., M. Pasyanos, A. Rodgers, R. Gok, W. Walter, and A. Al-Amri (2006), A multistep approach for joint modeling of surface wave disper- sion and teleseismic receiver functions: Implications for lithospheric structure of the Arabian Peninsula, J. Geophys. Res., 111, B11311, doi:10.1029/2005JB004130. · DOI
  69. Tokam, A., C. Tabod, A. Nyblade, J. Julià, D. Wiens, and M. Pasyanos (2010), Structure of the crust beneath Cameroon, West Africa, from the joint inversion of Rayleigh wave group velocities and receiver functions, Geophys. J. Int., 183(2), 1061-1076.
  70. Vinnik, L., C. Reigber, I. Aleshin, G. Kosarev, M. Kaban, S. Oreshin, and S. Roecker (2004), Receiver function tomography of the central Tien Shan, Earth Planet. Sci. Lett., 225(1-2), 131-146.
  71. Vinnik, L., I. Aleshin, M. Kaban, S. Kiselev, G. Kosarev, S. Oreshin, and C. Reigber (2006), Crust and mantle of the Tien Shan from data of the receiver function tomography, Izv. Phys. Solid Earth, 42(8), 639-651.
  72. Yoo, H., R. Herrmann, K. Cho, and K. Lee (2007), Imaging the three- dimensional crust of the Korean Peninsula by joint inversion of surface- wave dispersion and teleseismic receiver functions, Bull. Seismol. Soc. Am., 97(3), 1002-1011.
  73. Zhao, L., M. Sen, P. Stoffa, and C. Frohlich (1996), Application of very fast simulated annealing to the determination of the crustal structure beneath Tibet, Geophys. J. Int., 125(2), 355-370.

Cited by

Sorted by citations

Authors
Bodin, T., Sambridge, M., Gallagher, K., & Rawlinson, N.
Affiliations
Australian National University (AU)
ORCID
Venue
Journal of Geophysical Research: Solid Earth
Publisher
American Geophysical Union (AGU)
Published
2012-02
Volume
117
Issue
B2
Pages
B02301
ISSN
0148-0227 (ISSN-L)
DOI
10.1029/2011jb008560
OpenAlex
W2113559499
Cited by
462
References
1
Citations by year
2026: 27 · 2025: 30 · 2024: 41 · 2023: 43 · 2022: 36 · 2021: 43 · 2020: 45 · 2019: 40 · 2018: 36 · 2017: 31 · 2016: 24 · 2015: 20 · 2014: 16 · 2013: 22 · 2012: 8
FWCI
13.14
Type
journal article
Language
en
Open access
Licence
onlinelibrary.wiley.com/termsAndConditions#vor (vor, 2 d)
Locations
  • Journal of Geophysical Research Atmospheres (publishedVersion)
  • HAL (submittedVersion, other-oa)
  • ANU Open Research (Australian National University) (submittedVersion)
Topics
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › Seismic Waves and Analysis
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › Seismic Imaging and Inversion Techniques
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Keywords
transdimensional inversion, receiver functions, surface wave dispersion, joint inversion, hierarchical Bayesian inference, Markov chain Monte Carlo, uncertainty quantification, seismic velocity structure, shear wave velocity, teleseismic receiver functions, background noise

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review