{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T02:44:18Z","timestamp":1771555458261,"version":"3.50.1"},"reference-count":98,"publisher":"American Geophysical Union (AGU)","issue":"B2","license":[{"start":{"date-parts":[[2012,2,3]],"date-time":"2012-02-03T00:00:00Z","timestamp":1328227200000},"content-version":"vor","delay-in-days":2,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Geophys. Res."],"published-print":{"date-parts":[[2012,2]]},"abstract":"<jats:p>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\u2010offs). 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\u2010East Australia) are jointly inverted to provide a probabilistic 1D model of shear\u2010wave velocity beneath a given station.<\/jats:p>","DOI":"10.1029\/2011jb008560","type":"journal-article","created":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T09:12:12Z","timestamp":1322903532000},"source":"Crossref","is-referenced-by-count":333,"title":["Transdimensional inversion of receiver functions and surface wave dispersion"],"prefix":"10.1029","volume":"117","author":[{"given":"T.","family":"Bodin","sequence":"first","affiliation":[]},{"given":"M.","family":"Sambridge","sequence":"additional","affiliation":[]},{"given":"K.","family":"Gallagher","sequence":"additional","affiliation":[]},{"given":"N.","family":"Rawlinson","sequence":"additional","affiliation":[]}],"member":"13","published-online":{"date-parts":[[2012,2,3]]},"reference":[{"key":"e_1_2_11_2_1","unstructured":"Ammon C.(1992) A comparison of deconvolution techniques Rep. UCID\u2010ID\u2010111667 Lawrence Livermore Natl. Lab. Livermore Calif."},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1029\/JB095iB10p15303"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1029\/2009GL041974"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2003.02094.x"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstl.1763.0053"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2009.04226.x"},{"key":"e_1_2_11_8_1","volume-title":"Bayesian Inference in Statistical Inference","author":"Box G.","year":"1973"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1190\/1.2356112"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1071\/EG08110"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1078551"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120030110"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2117.2008.00369.x"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2117.2008.00370.x"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1029\/2009JB006386"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1976.tb01267.x"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2007.03606.x"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1029\/1999JB900317"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(01)00073-1"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.2736514"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.2832619"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.3147489"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.3500674"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1998.tb07128.x"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246x.1999.00945.x"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2478.1988.tb02198.x"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2478.1988.tb02199.x"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246X.2003.02043.x"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.marpetgeo.2009.01.003"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsl.2011.09.015"},{"key":"e_1_2_11_31_1","volume-title":"Bayesian Data Analysis","author":"Gelman A.","year":"2004"},{"issue":"4","key":"e_1_2_11_32_1","first-page":"359","article-title":"Simulation procedures and likelihood inference for spatial point processes","volume":"21","author":"Geyer C.","year":"1994","journal-title":"Scand. J. Stat."},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.1029\/97JB02933"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246X.2002.01598.x"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/82.4.711"},{"key":"e_1_2_11_36_1","first-page":"179","article-title":"Trans\u2010dimensional Markov chain Monte Carlo","volume":"27","author":"Green P.","year":"2003","journal-title":"Highly Struct. Stochastic Syst."},{"key":"e_1_2_11_37_1","doi-asserted-by":"publisher","DOI":"10.1785\/BSSA0430010017"},{"key":"e_1_2_11_38_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/57.1.97"},{"key":"e_1_2_11_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10950-007-9060-4"},{"key":"e_1_2_11_40_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2007.03596.x"},{"key":"e_1_2_11_41_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2009.04192.x"},{"key":"e_1_2_11_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11004-005-9019-3"},{"key":"e_1_2_11_43_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246x.2000.00217.x"},{"key":"e_1_2_11_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0040-1951(03)00196-3"},{"key":"e_1_2_11_45_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1995.tb03520.x"},{"key":"e_1_2_11_46_1","doi-asserted-by":"publisher","DOI":"10.1029\/92JB02651"},{"key":"e_1_2_11_47_1","doi-asserted-by":"publisher","DOI":"10.1029\/JB084iB09p04749"},{"key":"e_1_2_11_48_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120030172"},{"key":"e_1_2_11_49_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1997.tb01220.x"},{"key":"e_1_2_11_50_1","doi-asserted-by":"publisher","DOI":"10.1785\/BSSA0890051395"},{"key":"e_1_2_11_51_1","unstructured":"Lombardi D.(2007) Alpine crustal and upper\u2010mantle structure from receiver functions A PhD thesis ETH Zurich Zurich Switzerland."},{"key":"e_1_2_11_52_1","volume-title":"Fundamentals of Geophysics","author":"Lowrie W.","year":"1997"},{"key":"e_1_2_11_53_1","doi-asserted-by":"publisher","DOI":"10.1029\/2004JB003187"},{"key":"e_1_2_11_54_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2009.04479.x"},{"key":"e_1_2_11_55_1","volume-title":"Information Theory, Inference, and Learning Algorithms","author":"MacKay D.","year":"2003"},{"key":"e_1_2_11_56_1","first-page":"49","article-title":"On the generalised distance in statistics","volume":"12","author":"Mahalanobis P.","year":"1936","journal-title":"Proc. Natl. Acad. Sci. India"},{"key":"e_1_2_11_57_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246X.2002.01847.x"},{"key":"e_1_2_11_58_1","doi-asserted-by":"publisher","DOI":"10.1190\/1.1778243"},{"key":"e_1_2_11_59_1","doi-asserted-by":"publisher","DOI":"10.1190\/1.2194516"},{"key":"e_1_2_11_60_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699114"},{"key":"e_1_2_11_61_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2011.05165.x"},{"key":"e_1_2_11_62_1","doi-asserted-by":"publisher","DOI":"10.1029\/2009JB006369"},{"key":"e_1_2_11_63_1","doi-asserted-by":"publisher","DOI":"10.1029\/94JB03097"},{"key":"e_1_2_11_64_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2005.02605.x"},{"key":"e_1_2_11_65_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2007.03615.x"},{"key":"e_1_2_11_66_1","doi-asserted-by":"publisher","DOI":"10.1029\/JB089iB09p07783"},{"issue":"1","key":"e_1_2_11_67_1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1785\/BSSA0870010183","article-title":"Shear\u2010wave velocity structure in the northern Basin and Range province from the combined analysis of receiver functions and surface waves","volume":"87","author":"\u00d6zalaybey S.","year":"1997","journal-title":"Bull. Seismol. Soc. Am."},{"key":"e_1_2_11_68_1","doi-asserted-by":"publisher","DOI":"10.1029\/JZ069i014p02997"},{"key":"e_1_2_11_69_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2008.03868.x"},{"issue":"2","key":"e_1_2_11_70_1","first-page":"858","article-title":"Receiver function inversion by trans\u2010dimensional Monte Carlo sampling","volume":"181","author":"Piana Agostinetti N.","year":"2010","journal-title":"Geophys. J. Int."},{"key":"e_1_2_11_71_1","doi-asserted-by":"publisher","DOI":"10.1029\/2002GL015109"},{"key":"e_1_2_11_72_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pepi.2008.02.007"},{"key":"e_1_2_11_73_1","doi-asserted-by":"publisher","DOI":"10.1029\/2006GL028105"},{"key":"e_1_2_11_74_1","doi-asserted-by":"publisher","DOI":"10.1029\/2005JB003803"},{"key":"e_1_2_11_75_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1440-0952.2003.01000.x"},{"key":"e_1_2_11_76_1","doi-asserted-by":"crossref","unstructured":"Reading A. T.Bodin M.Sambridge S.Howe andM.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.","DOI":"10.1081\/22020586.2010.12041870"},{"issue":"2","key":"e_1_2_11_77_1","first-page":"207","article-title":"Parallel computing and Monte Carlo algorithms","volume":"4","author":"Rosenthal J.","year":"2000","journal-title":"Far East J. Theor. Stat."},{"key":"e_1_2_11_78_1","first-page":"293","volume-title":"Seismological Algorithms: Computational Methods and Computer Programs","author":"Saito M.","year":"1988"},{"key":"e_1_2_11_79_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2010.04891.x"},{"key":"e_1_2_11_80_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246X.1999.00876.x"},{"key":"e_1_2_11_81_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-246x.1999.00900.x"},{"key":"e_1_2_11_82_1","doi-asserted-by":"publisher","DOI":"10.1190\/1.6241045.1"},{"key":"e_1_2_11_83_1","doi-asserted-by":"publisher","DOI":"10.1190\/1.1444411"},{"key":"e_1_2_11_84_1","doi-asserted-by":"publisher","DOI":"10.1029\/2004GL019491"},{"key":"e_1_2_11_85_1","doi-asserted-by":"publisher","DOI":"10.1029\/96GL01671"},{"key":"e_1_2_11_86_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000664"},{"key":"e_1_2_11_87_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1991.0130"},{"key":"e_1_2_11_88_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2009.04132.x"},{"key":"e_1_2_11_89_1","doi-asserted-by":"publisher","DOI":"10.1144\/GSL.SP.2004.239.01.13"},{"key":"e_1_2_11_90_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsl.2005.11.027"},{"issue":"3","key":"e_1_2_11_91_1","first-page":"150","article-title":"Inverse problems = quest for information","volume":"50","author":"Tarantola A.","year":"1982","journal-title":"J. Geophys."},{"key":"e_1_2_11_92_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699629"},{"key":"e_1_2_11_93_1","doi-asserted-by":"publisher","DOI":"10.1029\/2005JB004130"},{"key":"e_1_2_11_94_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2011.05132.x"},{"key":"e_1_2_11_95_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2010.04776.x"},{"key":"e_1_2_11_96_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsl.2004.05.039"},{"key":"e_1_2_11_97_1","doi-asserted-by":"publisher","DOI":"10.1134\/S1069351306080027"},{"key":"e_1_2_11_98_1","doi-asserted-by":"publisher","DOI":"10.1785\/0120060134"},{"key":"e_1_2_11_99_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1996.tb00004.x"}],"container-title":["Journal of Geophysical Research: Solid Earth"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1029%2F2011JB008560","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/agupubs.onlinelibrary.wiley.com\/doi\/pdf\/10.1029\/2011JB008560","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T04:47:22Z","timestamp":1698641242000},"score":1,"resource":{"primary":{"URL":"https:\/\/agupubs.onlinelibrary.wiley.com\/doi\/10.1029\/2011JB008560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2]]},"references-count":98,"journal-issue":{"issue":"B2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["10.1029\/2011JB008560"],"URL":"https:\/\/doi.org\/10.1029\/2011jb008560","archive":["Portico"],"relation":{},"ISSN":["0148-0227"],"issn-type":[{"value":"0148-0227","type":"print"}],"subject":[],"published":{"date-parts":[[2012,2]]},"article-number":"2011JB008560"}}