Mineralogy and Petrology

, Volume 112, Supplement 1, pp 133–147 | Cite as

Resolution and uncertainty in lithospheric 3-D geological models

  • David B. SnyderEmail author
  • Ernst Schetselaar
  • Mark Pilkington
  • Andrew J. Schaeffer
Original Paper


As three-dimensional (3-D) modelling of the subcontinental mantle lithosphere is increasingly performed with ever more data and better methods, the robustness of such models is increasingly questioned. Resolution thresholds and uncertainty within deep multidisciplinary 3-D models based on geophysical observations exist at a minimum of three levels. Seismic waves and potential field measurements have inherent limitations in resolution related to their dominant wavelengths. Formal uncertainties can be assigned to grid-search type forward or inverse models of observable parameter sets. Both of these uncertainties are typically minor when compared to resolution limitations related to the density and shape of a specific observation array used in seismological or potential field surveys. Seismic wave source distribution additionally applies in seismology. A fourth, more complex level of uncertainty relates to joint inversions of multiple data sets. Using independent seismic wave phases or combining diverse methods provides another measure of uncertainty of particular physical properties. Extremely sparse xenolith suites provide the only direct correlation of rock type with observed or modelled physical properties at depths greater than a few kilometers. Here we present one case study of the Canadian Mohorovičić (Moho) discontinuity using only two data sets. Refracted and converted seismic waves form the primary determinations of the Moho depth, gravity field modeling provide a secondary constraint on lateral variations, the slope of the Moho, between the sparse seismic estimates. Although statistically marginal, the resulting co-kriged Moho surface correlates better with surface geology and is thus deemed superior.


Mantle lithosphere Uncertainty Resolution 3-D models Geophysical methods 



Early versions of this manuscript were improved by comments from Guillaume Caumon, Michael Hillier, Jonathan Perry-Houts, Gene Humphreys, Alan G. Jones, Gautier Laurent, Mark Lindsay and anonymous reviewers. This represents contribution 20150488 to the Open Geoscience Program of Natural Resources Canada.


  1. Abbott DH, Mooney WD, VanTongeren JA (2013) The character of the Moho and lower crust within Archean cratons and the tectonic implications. Tectonophysics 609:690–705CrossRefGoogle Scholar
  2. Abt DL, Fischer KM, French SW, Ford HA, Yuan H, Romanowicz, B (2010) North American lithospheric discontinuity structure imaged by Ps and Sp receiver functions. J Geophys Res-Sol Ea 115:B09301Google Scholar
  3. Afonso JC, Fullea J, Griffin WL, Yang JAG, Connolly JAD, O'Reilly SY (2013a) 3-D multi-observable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. I: A priori petrological information and geophysical observables. J Geophys Res-Sol Ea 118:2586–2617CrossRefGoogle Scholar
  4. Afonso JC, Fullea J, Yang Y, Connolly JAD, Jones AG (2013b) 3-D multi-observable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. II: general methodology and resolution analysis. J Geophys Res-Sol Ea 118:1650–1676CrossRefGoogle Scholar
  5. Bedle H, van der Lee S (2009) S-velocity variations beneath North America. J Geophys Res-Sol Ea 114. B07308Google Scholar
  6. Benson GD, Ritzwoller MH, Barmin MP, Levshin AL, Lin F, Moschetti MP, Shapiro NM, Yang Y (2007) Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements. Geophys J Int 169:1239–1260CrossRefGoogle Scholar
  7. Bevington, PR, Robinson DK (2002) Data reduction and error analysis for the physical sciences (3rd ed.). McGraw-Hill, ISBN 0-07-119926-8Google Scholar
  8. Bodin T, Sambridge M (2009) Seismic tomography with the reversible jump algorithm. Geophys J Int 178:1411–1436CrossRefGoogle Scholar
  9. Bodin T, Sambridge M, Rawlinson N, Arroucau P (2012) Transdimensional tomography with unknown data noise. Geophys J Int 189:1536–1556CrossRefGoogle Scholar
  10. Bodin T, Yuan H, Romanowicz B (2013) Inversion of receiver functions without deconvolution—application to the Indian craton. Geophys J Int 196:1025–1033CrossRefGoogle Scholar
  11. Bostock MG (1998) Seismic stratigraphy and evolution of the Slave province. J Geophys Res-Sol Ea 103:21183–21200CrossRefGoogle Scholar
  12. Brenders AJ, Pratt RG (2007) Full waveform tomography for lithospheric imaging: results from a blind test in a realistic crustal model. Geophys J Inter 168:133–151Google Scholar
  13. Brittan J, Warner M (1996) Seismic velocity, heterogeneity, and the composition of the lower crust. Tectonophysics 264:249–259CrossRefGoogle Scholar
  14. Brown L, Barazangi M, Kaufman S, Oliver J (1986) The first decade of COCORP: 1974–1984. Geodynamics 13:107–120CrossRefGoogle Scholar
  15. Burdick S, de Hoop MVS, Wang S, van der Hilst RD (2014) Reverse-time migration-based reflection tomography using teleseismic free surface multiples. Geophys J Int 196:996–1017CrossRefGoogle Scholar
  16. Chen M, Tromp J (2007) Theoretical and numerical investigations of global and regional seismic wave propagation in weakly anisotropic earth models. Geophys J Int 168:1130–1152CrossRefGoogle Scholar
  17. Chiles JP, Delfiner P (1999) Geostatistics: Modelling spatial uncertainty. Wiley, New YorkCrossRefGoogle Scholar
  18. Christensen NI (1996) Poisson's ratio and crustal seismology. J Geophys Res 101(B2):3139–3156CrossRefGoogle Scholar
  19. Cook FA (2002) Fine structure of the continental reflection Moho. Geol Soc Am Bull 114:64–79CrossRefGoogle Scholar
  20. Cook FA, Albaugh DS, Brown LD, Kaufman S, Oliver JE, Hatcher RD Jr (1979) Thin-skinned tectonics in the crystalline southern Appalachians; COCORP seismic-reflection profiling of the Blue Ridge and Piedmont. Geology 7:563–567CrossRefGoogle Scholar
  21. Cook FA, White DJ, Jones AG, Eaton DW, Hall J, Clowes RM (2010) How the crust meets the mantle: Lithoprobe perspectives on the Mohorovičić discontinuity and crust–mantle transition. Can J Earth Sci 47:315–351CrossRefGoogle Scholar
  22. Eaton DW, Darbyshire F, Evans RL, Grutter H, Jones AG, Yuan X (2009) The elusive lithosphere-asthenosphere boundary (LAB) beneath cratons. Lithos 109:1–22CrossRefGoogle Scholar
  23. Fernández Viejo G, Clowes RM (2003) Lithospheric structure beneath the Archaean Slave Province and Proterozoic Wopmay orogen, northwestern Canada, from a Lithoprobe refraction/wide-angle reflection survey. Geophys J Int 153:1–19CrossRefGoogle Scholar
  24. Fichtner A, Kennett BLN, Igel H, Bunge H-P (2009) Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophys J Int 179:1703–1725CrossRefGoogle Scholar
  25. Fichtner A, Saygin E, Taymaz T, Cupillard P, Capdeville Y, Trampert J (2013) The deep structure of the North Anatolian fault zone. Earth Planet Sc Lett 373:109–117CrossRefGoogle Scholar
  26. Godfrey NJ, Christensen NI, Okaya DA (2000) Anisotropy of schists: contribution of crustal anisotropy to active source seismic experiments and shear wave splitting observations. J Geophys Res 105(B12):27–991CrossRefGoogle Scholar
  27. Goovaerts P (2000) Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. J Hydrol 228:113–129CrossRefGoogle Scholar
  28. Hillier MJ, Schetselaar EM, de Kemp EA, Perron G (2014) Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions. Math Geosci 46:931–953CrossRefGoogle Scholar
  29. Holden DH, Archibald NJ, Boschetti F, Jessell MW (2000) Inferring geological structures using wavelet-based multi-scale edge analysis and forward models. Explor Geophys 31:617–621CrossRefGoogle Scholar
  30. IRIS DMC (2010) Data services products: EARS EarthScope Automated Receiver Survey, CrossRefGoogle Scholar
  31. Jones AG, Ledo J, Ferguson IJ, Craven JA, Unsworth MJ, Chouteau M, Spratt JE (2014) The electrical resistivity of Canada’s lithosphere and correlation with other parameters: contributions from Lithoprobe and other programmes. Can J Earth Sci 51:573–617CrossRefGoogle Scholar
  32. Kaban MK, Tesauro M, Mooney WD, Cloetingh SA (2014) Density, temperature, and composition of the North American lithosphere—new insights from a joint analysis of seismic, gravity, and mineral physics data: 1. Density structure of the crust and upper mantle. Geochem Geophys Geosyst 15:4781–4807CrossRefGoogle Scholar
  33. Kamei R, Miyoshi T, Pratt RG, Takanashi M, Masaya S (2015) Application of waveform tomography to a crooked-line 2D land seismic data set. Geophysics 80(5):B115–B129CrossRefGoogle Scholar
  34. Kustowski B, Ekstrom G, Dziewonski A (2008) Anisotropic shear-wave velocity of the Earth’s mantle: a global model. J Geophys Res-Sol Ea 113:1–23CrossRefGoogle Scholar
  35. Lebedev S, van der Hilst R (2008) Global upper mantle tomography with the automatic multimode inversion of surface and S-wave forms. Geophys J Int 173:505–518CrossRefGoogle Scholar
  36. Lebedev S, Adam JM-C, Meier T (2013) Mapping the Moho with seismic surface waves: a review, resolution analysis, and recommended inversion strategies. Tectonophysics 309:377–394CrossRefGoogle Scholar
  37. Lekic V, Romanowicz B (2011) Inferring upper-mantle structure by full waveform tomography with the spectral element method. Geophys J Int 185:799–831CrossRefGoogle Scholar
  38. Mather KA, Pearson DG, McKenzie D, Kjarsgaard BA, Priestley K (2011) Constraints on the depth and thermal history of cratonic lithosphere from peridotite xenoliths, xenocrysts and seismology. Lithos 125:729–742CrossRefGoogle Scholar
  39. Mercier JP, Bostock MG, Audet P, Gaherty JB, Garnero EJ, Revenaugh J (2008) The teleseismic signature of fossil subduction: northwestern Canada. J Geophys Res-Sol Ea 113(B4)Google Scholar
  40. Mooney WD, Brocher TM (1987) Coincident seismic reflection/refraction studies of the continental lithosphere: a global review. Rev Geophys 25:723–742CrossRefGoogle Scholar
  41. Mosegaard K, Singh SC, Snyder DB, Wagner H (1997) Monte Carlo analysis of seismic reflections from the Moho and the W-reflector. J Geophys Res 102:2983–2997CrossRefGoogle Scholar
  42. Németh B, Clowes RM, Hajnal Z (2005) Lithospheric structure of the trans-Hudson Orogen from seismic refraction–wide-angle reflection studies. Can J Earth Sci 42:435–456CrossRefGoogle Scholar
  43. Nettleton, LL (1976). Gravity and magnetics in oil prospecting. McGraw-Hill CompaniesGoogle Scholar
  44. Nolet G (1987) Seismic wave propagation and seismic tomography, in Seismic tomography. Springer Netherlands: 1–23Google Scholar
  45. Nolet G (1990) Partitioned waveform inversion and two-dimensional structure under the network of autonomously recording seismographs. J Geophys Res 95:8499–8512CrossRefGoogle Scholar
  46. O'Driscoll LJ, Humphreys ED, Schmandt B (2011) Time corrections to teleseismic P delays derived from SKS splitting parameters and implications for western US P-wave tomography. Geophys Res Lett 38:19Google Scholar
  47. Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39(4):526–536CrossRefGoogle Scholar
  48. Olugboji, T.M., Lekic V, McDonough, W. (2017) A statistical assessment of seismic models of the US continental crust using Bayesian inversion of ambient noise surface wave dispersion data. TectonicsGoogle Scholar
  49. O'Reilly SY, Griffin WL (2013) Moho vs crust–mantle boundary: evolution of an idea. Tectonophysics 609:535–546CrossRefGoogle Scholar
  50. Parker RL (1973) The rapid calculation of potential anomalies. Geophys J Roy Astr S 31:447–455CrossRefGoogle Scholar
  51. Pawlak A, Eaton DW, Bastow ID, Kendall J-M, Helffrich G, Wookey J, Snyder D (2011) Crustal structure beneath Hudson Bay from ambient-noise tomography: implications for basin formation. Geophys J Int 184:65–82CrossRefGoogle Scholar
  52. Postlethwaite B, Bostock M, Christensen NI, Snyder DB (2014) Seismic velocities and composition of the Canadian crust. Tectonophysics 633:256–267CrossRefGoogle Scholar
  53. Pratt RG, Shin C, Hick GJ (1998) Gauss–Newton and full Newton methods in frequency–space seismic waveform inversion. Geophys J Int 133:341–362CrossRefGoogle Scholar
  54. Priestley K, McKenzie D (2006) The thermal structure of the lithosphere from shear wave velocities. Earth Planet Sc Lett 244:285–301CrossRefGoogle Scholar
  55. Ritsema J, Duess A, van Heijst H, Woodhouse J (2011) S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting functions. Geophys J Int 184:1223–1236CrossRefGoogle Scholar
  56. Rudnick RL, Nyblade AA (1999) The thickness and heat production of Archean lithosphere: constraints from xenolith thermobarometry and surface heat flow. Geo Soc S P 6:3–12Google Scholar
  57. Scales JA, Snieder R (1997) To Bayes or not to Bayes? Geophysics 62(4):1045–1046CrossRefGoogle Scholar
  58. Schaeffer AJ, Lebedev S (2013) Global shear speed structure of the upper mantle and transition zone. Geophys J Int 194:417–449CrossRefGoogle Scholar
  59. Schaeffer A, Lebedev S (2014) Imaging the North American continent using waveform inversion of global and USArray data. Earth Planet Sc Lett 402:26–41CrossRefGoogle Scholar
  60. Schetselaar E, Shamsipour P (2015) Interpretation of borehole gravity data of the Lalor volcanogenic massive sulfide deposit, Snow Lake, Manitoba, Canada. Interpretation 3(3):T145–T154CrossRefGoogle Scholar
  61. Schetselaar EM, Snyder DB (2017) National database of Moho depth estimates estimates from seismic refraction and teleseismic surveys. Geol Survey Canada Open File 8243, 14p
  62. Schetselaar E, Bellefleur G, Craven J, Roots E, Cheraghi S, Shamsipour P, Caté A, Mercier-Langevin P, El Goumi N, Enkin R, Salisbury M (2017) Geologically-driven 3-D stochastic modelling of physical rock properties in support of interpreting the seismic response of the Lalor volcanogenic massive sulphide deposit, Snow Lake, Manitoba, Canada. In: Gessner K, Blenkinsop TG, Sorjonen-Ward P (eds) Characterization of Ore-Forming Systems from Geological, Geochemical and Geophysical Studies. Geol Soc Spec Publ 453:23 pagesGoogle Scholar
  63. Schmandt B, Humphreys E (2011) Seismically imaged relict slab from the 55 Ma Siletzia accretion to the northwest United States. Geology 39:175–178CrossRefGoogle Scholar
  64. Schmandt B, Dueker K, Humphreys E, Hansen S (2012) Hot mantle upwelling across the 660 beneath Yellowstone. Earth Planet Sc Lett 331:224–236CrossRefGoogle Scholar
  65. Shen W, Ritzwoller MH, Schulte-Pelkum V (2013) A 3-D model of the crust and uppermost mantle beneath the central and western US by joint inversion of receiver functions and surface wave dispersion. J Geophys Res-Sol Ea 118:262–276CrossRefGoogle Scholar
  66. Sheriff RE, Geldart LP (1995) Exploration seismology. Cambridge University pressGoogle Scholar
  67. Sigloch K (2011) Mantle provinces under North America from multifrequency P wave tomography. Geochem Geophys Geosyst 12:1–27CrossRefGoogle Scholar
  68. Simpson RW, Jachens RC, Blakely R, Saltus RW (1986) A new isostatic residual gravity map of the conterminous United States with a discussion on the significance of isostatic residual anomalies. J Geophys Res-Sol Ea 91(B8):8348–8372CrossRefGoogle Scholar
  69. Snyder DB, Bruneton M (2007) Seismic anisotropy of the Slave craton, NW Canada, from joint interpretation of SKS and Rayleigh waves. Geophys J Int 169:170–188CrossRefGoogle Scholar
  70. Snyder DB, Hillier MJ, Kjarsgaard BA, de Kemp EA, Craven JA (2014) Lithospheric architecture of the Slave craton, northwest Canada, as determined from an interdisciplinary 3-D model. Geochem Geophys Geosyst 15:1895–1910CrossRefGoogle Scholar
  71. Snyder DB, Craven JA, Pilkington M, Hillier MJ (2015) The 3-dimensional construction of the Rae craton, Central Canada. Geochem Geophys Geosyst 16:3555–3574CrossRefGoogle Scholar
  72. Snyder DB, Humphreys E, Pearson GD (2017) Construction and destruction of some north American cratons. Tectonophysics 694:464–485CrossRefGoogle Scholar
  73. Tape C, Liu Q, Maggi A, Tromp J (2009) Adjoint tomography of the southern California crust. Science 325:988–992CrossRefGoogle Scholar
  74. Tesauro M, Kaban MK, Mooney WD, Cloetingh S (2014) NACr14: a 3-D model for the crustal structure of the north American continent. Tectonophysics 631:65–86CrossRefGoogle Scholar
  75. Wheeler JO, Hoffman PF, Card KD, Davidson A, Stanford BV, Okulitch AV, and Roest WR (1997) Geologic map of Canada, Map D1860A, version 1.0, scale 1: 5,000,000. Nat. Resour. Can., Ottawa, Ont., CanadaGoogle Scholar
  76. Wittig N, Pearson DG, Duggen S, Baker JA, Hoernle K (2010) Tracing the metasomatic and magmatic evolution of continental mantle roots with Sr, Nd, Hf and and Pb isotopes: a case study of Middle Atlas (Morocco) peridotite xenoliths. Geochim Cosmochim Ac 74:1417–1435CrossRefGoogle Scholar
  77. Yang Y, Li A, Ritzwoller MH (2008) Crustal and uppermost mantle structure in southern Africa revealed from ambient noise and teleseismic tomography. Geophys J Int 174:235–248CrossRefGoogle Scholar
  78. Yuan H, Dueker K (2005) Teleseismic P-wave tomogram of the Yellowstone plume. Geophys Res Lett 32(7)Google Scholar
  79. Yuan H, Levin V (2014) Stratified seismic anisotropy and the lithosphere-asthenosphere boundary beneath eastern North America. J Geophys Res-Sol Ea 119:3096–3114CrossRefGoogle Scholar
  80. Yuan H, Romanowicz B, Fischer KM, Abt D (2011) 3-D shear wave radially and azimuthally anisotropic velocity model of the north American upper mantle. Geophys J Int 184:1237–1260CrossRefGoogle Scholar
  81. Zelt CA (2011) Traveltime tomography using controlled-source seismic data. In Encyclopedia of solid earth geophysics (pp. 1453–1473). Springer NetherlandsGoogle Scholar
  82. Zelt CA, Smith RB (1992) Seismic traveltime inversion for 2-D crustal velocity structure. Geophys J Int 108:16–34CrossRefGoogle Scholar
  83. Zhu L, Kanamori H (2000) Moho depth variation in Southern California from teleseismic receiver functions. J Geophys Res 105:2,969–2,980CrossRefGoogle Scholar
  84. Zhu H, Bozdag E, Peter D, Tromp J (2012) Structure of the European upper mantle revealed by adjoint tomography. Nat Geosci 5:493–498CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • David B. Snyder
    • 1
    Email author
  • Ernst Schetselaar
    • 1
  • Mark Pilkington
    • 1
  • Andrew J. Schaeffer
    • 2
  1. 1.Natural Resources Canada, Geological Survey of CanadaOttawaCanada
  2. 2.Department Earth and Environmental SciencesUniversity of OttawaOttawaCanada

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