Inferring radial models of mantle viscosity from gravity (GRACE) data and an evolutionary algorithm

Physics of the Earth and Planetary Interiors

Volumn 176, Issue 1-2, 2009, Pages 19-32

  Soldati, G ^a   Boschi, L ^b   Deschamps, F ^b   Giardini, D ^b  

^a ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA   (Italy)

^b ETH ZURICH   (Switzerland)

Author keywords

Gravity; Inverse theory; Mantle rheology; Tomography; Viscous flow

Indexed keywords

CONVECTIVE FLOW; DENSITY ANOMALIES; DENSITY STRUCTURES; DEPTH RANGE; DETERMINISTIC GLOBAL OPTIMIZATION; EARTH'S GRAVITY FIELDS; EARTH'S SURFACE; GRAVITY; GRAVITY ANOMALIES; GRAVITY DATA; GRAVITY RECOVERY AND CLIMATE EXPERIMENTS; INVERSE THEORY; LATERAL VARIATIONS; MANTLE RHEOLOGY; MANTLE STRUCTURE; MANTLE VISCOSITY; NONUNIQUENESS; OPTIMIZATION METHOD; RADIAL PROFILES; SCALE LENGTH; SCALING FACTORS; SEISMIC OBSERVATION; SEISMIC VELOCITIES; SOLUTION SPACE; SYMMETRIC MODEL; SYNTHETIC TESTS; THERMAL ORIGINS; TOMOGRAPHIC; TRANSITION ZONES; TRAVEL TIME; UNIFORM VISCOSITY; WAVE FORMS;

EARTH (PLANET); ELASTICITY; EVOLUTIONARY ALGORITHMS; FLUID DYNAMICS; GLOBAL OPTIMIZATION; INVERSE PROBLEMS; PHASE TRANSITIONS; PLASTICITY; RHEOLOGY; SATELLITE OBSERVATORIES; SEISMIC WAVES; SEISMOLOGY; SET THEORY; STATISTICAL TESTS; STRUCTURAL OPTIMIZATION; THREE DIMENSIONAL; TOMOGRAPHY; VISCOUS FLOW;

VISCOSITY;

ALGORITHM; DATA INVERSION; GRAVITY ANOMALY; GRAVITY FIELD; HETEROGENEITY; INVERSE PROBLEM; MANTLE CONVECTION; NUMERICAL MODEL; OPTIMIZATION; RADIAL FLOW; RHEOLOGY; SEISMIC TOMOGRAPHY; TRANSITION ZONE; VELOCITY STRUCTURE; VISCOSITY; VISCOUS FLOW;

EID: 68549094345     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2009.03.013     Document Type: Article

References (99)

1. Anderson D.L., and Bass J.D. Transition region of the Earth's upper mantle. Nature 320 (1986) 321-328
2. Anderson D.L. Theory of the Earth (1989), Blackwell, Boston
3. Anderson D.L. The case for irreversible chemical stratification of the mantle. Int. Geol. Rev. 44 (2002) 97-116
4. Becker, T.W., Boschi, L., 2002. A comparison of tomographic and geodynamic mantle models, Geochem. Geophys. Geosyst. 3, 2001GC000168.
5. Bercovici D., and Karato S. Whole-mantle convection and the transition-zone water filter. Nature 438 (2003) 39-44
6. Bolfan-Casanova N. Water in the Earth's mantle. Miner. Mag. 69 (2005) 229-257
7. Boschi, L., Becker, T.W., Steinberger, B., 2007. Mantle plumes: dynamic models and seismic images, Geochem. Geophys. Geosyst. 8, Q10006, doi:10.1029/2007GC001733.
8. Bullen K.E. An Introduction to the Theory of Seismology (1947), Cambridge University Press, Cambridge
9. Bunge, H.P., Hagelberg, C.R., Travis, B.J., 2003. Mantle circulation models with variational data assimilation: inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophys. J. Int. 152 (2), 280-301, doi:10.1046/j.1365-246X.2003.01823.x.
10. Cadek O., Yuen D.A., and Cizkova C. Mantle viscosity inferred from geoid and seismic tomography by genetic algorithms: results for layered mantle flow. Phys. Earth Planet. Inter. 107 (1998) 307-326
11. Cammarano F., Goes S., Vacher P., and Giardini D. Inferring upper mantle temperatures from seismic velocities. Phys. Earth Planet. Inter. 138 (2003) 197-222
12. Charbonneau, P., Knapp, B., 1995. A User's guide to PIKAIA 1.0, NCAR Technical Note 418+IA. National Center for Atmospheric Research, Boulder.
13. Corrieu V., Thoraval C., and Ricard Y. Mantle dynamics and geoid Green functions. Geophys. J. Int. 120 2 (1995) 516-523
14. Dal Forno G., Gasperini P., and Boschi E. Linear or nonlinear rheology in the mantle: a 3D finite-element approach to postglacial rebound modeling. J. Geodyn. 39 (2005) 183-195
15. Deschamps F., Snieder R., and Trampert J. The relative density-to-shear velocity scaling in the uppermost mantle. Phys. Earth Planet. Inter. 124 (2001) 193-211
16. Deschamps F., Trampert J., and Snieder R. Anomalies of temperature and iron in the uppermost mantle inferred from gravity data and tomographic models. Phys. Earth Planet. Inter. 129 (2002) 245-264
17. Duffy T.S., and Anderson D.L. Seismic velocities in mantle minerals and the mineralogy of the upper mantle. J. Geophys. Res. 94 (-1912) 1895
18. Dziewonski A.M., and Anderson D.L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25 (1981) 297-356
19. Forte A.M., and Peltier W.R. Plate tectonics and aspherical Earth structure: the importance of poloidal-toroidal coupling. J. Geophys. Res. 92 (1987) 3645-3679
20. Forte A.M., and Peltier W.R. Viscous flow models of global geophysical observables: 1. Forward problems. J. Geophys. Res. 96 (1991) 20131-20159
21. Forte A.M., Dziewonski A.M., and Woodward R.L. Aspherical structure of the mantle, tectonic plate motions, nonhydrostatic geoid and topography of the core-mantle boundary. In: Le MouEl J.-L., Smylie D.R., and Herring T. (Eds). Dynamics of Earth's Deep Interior and Earth Rotation (1993), Am. Geophys. Union, Washington, DC 135-166
22. Forte A.M., Woodward R.L., and Dziewonski A.M. Joint inversions of seismic and geodynamic data for models of threedimensional mantle heterogeneity. J. Geophys. Res. 99 (1994) 21857-21877
23. Forte A.M., and Peltier W.R. The kinematics and dynamics of poloidal-toroidal coupling in mantle flow: the importance of surface plates and lateral viscosity variations. Adv. Geophys. 36 (1994) 1-119
24. Forte A.M., Mitrovica J.X., and Woodward R.L. Seismic-geodynamic determination of the origin of excess ellipticity of the core-mantle boundary. Geophys. Res. Lett. 22 (1995) 1013-1016
25. Forte A.M., and Mitrovica J.X. New inferences of mantle viscosity from joint inversion of long-wavelength mantle convection and post-glacial rebound data. Geophys. Res. Lett. 23 (1996) 1147-1150
26. Forte A.M., and Perry H.K.C. Geodynamic evidence for a chemically depleted continental tectosphere. Science 290 5498 (1940-1944) 1940-1944
27. Forte A.M., and Mitrovica J.X. High Viscosity Deep Mantle Flow and Thermochemical Structure Inferred From Seismic and Geodynamic Data. Nature 410 (2001) 1049-1056
28. Gwinn C.R., Herring T.A., and Shapiro I.I. Geodesy by radio interferometry: studies of the forced nutations of the Earth. 2. Interpretation. J. Geophys. Res. 91 (1986) 4755-4765
29. Hager B.H., and O'Connell R.J. A simple global model of plate dynamics and mantle convection. J. Geophys. Res. 86 (1981) 4843-4867
30. Hager B.H., and Richards M.A. Long-wavelength variations in Earth's geoid: physical models and dynamical implications. Philos. Trans. R. Soc. Lond. A 328 (1989) 309-327
31. Haskell N.A. The motion of a fluid under a surface load 1. Physics 6 (1935) 265-269
32. Huang X., Yousheng X., and Karato S. Water content in the transition zone from electrical conductivity of wadsleyite and ringwoodite. Nature 434 7034 (2005) 746-749
33. Ishii M., and Tromp J. Normal-mode and free-air gravity constraints on lateral variations in velocity and density of Earth's mantle. Science 285 (1999) 1231-1236
34. Jordan T.H. The continental tectosphere. Rev. Geophys. Space Phys. 13 (1975) 112
35. Kaban M.K., Rogozhina I., and Trubitsyn V. Importance of lateral viscosity variations in the whole mantle for modelling of the dynamic geoid and surface velocities. J. Geodyn. 43 (2007) 262-273
36. Karato S.-I. Importance of anelasticity in the interpretation of seismic tomography. Geophys. Res. Lett. 20 (1993) 1623-1626
37. Karato S., Wang Z.C., Liu B., and Fujino K. Plastic deformation of garnets: systematics and implications for the rheology of the mantle transition zone. Earth Planet. Sci. Lett. 130 1-4 (1995) 13-30
38. Karato S.I. Plastic deformation of silicate spinel under transition-zone conditions of the Earths mantle. Nature 395 (1998) 266-269
39. Karato S., and Karki B.B. Origin of lateral heterogeneity of seismic wave velocities and density in the deep mantle. J. Geophys. Res. 106 (2001) 21, 771-21, 783
40. Kaufmann G., and Lambeck K. Glacial isostatic adjustment and the radial viscosity profile from inverse modeling. J. Geophys. Res. 107 (2002) ETG5-1-ETG5-15
41. Kaufmann G., and Wu P. Glacial isostatic adjustment in fennoscandia with a three-dimensional viscosity structure as an inverse problem. Earth Planet. Sci. Lett. 197 1-2 (2002) 1-10
42. Kavner A. Elasticity and strength of hydrous ringwoodite at high pressure. Earth Planet. Sci. Lett. 214 (2003) 645-654
43. Kawakatsu H., and Niu F. Seismic evidence for a 920-km discontinuity in the mantle. Nature 371 (1994) 301-305
44. Kawamoto T., Hervig R.L., and Holloway J.R. Experimental evidence for a hydrous transition zone in the early Earth's mantle. Earth Planet. Sci. Lett. 142 (1996) 587-592
45. Kellogg L.H., Hager B.H., and van der Hilst R.D. Compositional stratification in the deep mantle. Science 283 (1999) 1881-1884
46. Kido M., and Cadek O. Inferences of viscosity from the oceanic geoid: Indication of a low viscosity zone below the 660-km discontinuity. Earth Planet. Sci. Lett. 151 (1997) 125-138
47. Kido M., Yuen D.A., Cadek O., and Nakakuki T. Mantle viscosity derived by genetic algorithm using oceanic geoid and seismic tomography for whole-mantle versus blocked-flow situations. Phys. Earth Planet. Inter. 107 (1998) 307-326
48. King S.D., and Masters G. An inversion for radial viscosity structure using seismic tomography. Geophys. Res. Lett. 19 (1992) 1551-1554
49. King S.D. Radial models of mantle viscosity: results from a generic algorithm. Geophys. J. Int. 122 (1995) 725-734
50. Kohlstedt D.L., Keppler H., and Rubie D.C. The solubility of water in alpha, beta and gamma phases of (Mg,Fe)2SiO4. Contrib. Miner. Petrol. 123 (1996) 345-357
51. Kuo C., and Romanowicz B. On the resolution of density anomalies in the Earth's mantle using spectral fitting of normal mode data. Geophys. J. Int. 150 (2002) 162-179
52. Maehara Y., and Langdon T.G. Superplasticity in ceramics. J. Mater. Sci. 25 (1990) 2275-2286
53. Mathews P., Buffett B.A., and Herring T.A. What do nutations tell us about the Earth's interior?. Eos Trans. 80 46 (1999) 19
54. Mathews, P.M, Herring, T.A., Buffett, B.A., 2002. Modeling of nutation and precession: new nutation series for nonridgid Earth and insights into the Earths interior, J. Geophys. Res., 107, 10.1029/2001JB000390.
55. Meike A. A critical review of investigations into transformation plasticity. In: Boland J.N., and Fitz Gerald J.D. (Eds). Defects and Processes in the Solid State: Geoscience Applications (the McLaren volume) (1993), Elsevier, Developments in Petrology 14
56. Milne G.A., Mitrovica J.X., and Forte A.M. The sensitivity of glacial isostatic adjustment predictions to a low-viscosity layer at the base of the upper mantle. Earth Planet. Sci. Lett. 154 (1997) 265-278
57. Mitrovica J.X., and Peltier W.R. Constraints on mantle viscosity based upon post-glacial uplift data from the Hudson Bay region. Geophys. J. Int. 122 (1995) 353-377
58. Mitrovica J.X., and Forte A.M. The radial profile of mantle viscosity: results from the joint inversion of convection and post-glacial rebound observables. J. Geophys. Res. 102 (1997) 2751-2769
59. Mitrovica J.X., and Forte A.M. A new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data. Earth Planet. Sci. Lett. 225 (2004) 177-189
60. Morelli, A., Dziewonski, A. M., 1987. Topography of the core-mantle boundary and lateral homogeneity of the liquid core, Nature 325, 678-683, doi:10.1038/325678a0.
61. Moucha R., Forte A.M., Mitrovica J.X., and Daradich A. Lateral variations in mantle rheology: implications for convection related surface observables and inferred viscosity models. Geophys. J. Int. 169 1 (2007) 113-135
62. Nataf H.C., and Ricard Y. 3SMAC: an a priori tomographic model for upper mantle based on geophysical modeling. Phys. Earth Planet. Inter. 95 (1996) 101-122
63. Obayashi M., and Fukao Y. P and PcP travel time tomography for the core-mantle boundary. J. Geophys. Res. 102 (1997) 17, 825-17, 841
64. Panasyuk S.V., Hager B.H., and Forte A.M. Understanding the effects of mantle compressibility on geoid kernels. Geophys. J. Int. 124 (1996) 121-133
65. Panasyuk, S.V., 1998. The effect of compressibility, phase transformations, and assumed density structure on mantle viscosity inferred from Earth's gravity, Ph.D. Thesis, Massachusets Institute of Technology.
66. Panasyuk S.V., and Hager B.H. A model of transformational superplasticity of the upper mantle. Geophys. J. Int. 133 (1998) 741-755
67. Panasyuk, S.V., Hager, B.H., 2000. Models of isostatic and dynamic topography, geoid anomalies, and their uncertainties, J. Geophys. Res. 105, No. B12, 28,199-28,211.
68. Paulson A., Zhong S., and Wahr J. Modelling post-glacial rebound with lateral viscosity variations. Geophys. J. Int. 163 1 (2005) 357-371
69. Peltier W.R. Glacial isostatic adjustment II. The inverse problem. Geophys. J. Royal Astron. Soc. 46 (1976) 669-706
70. Peltier W.R. Postglacial variations in the level of the sea: implications for climate dynamics and solid-earth geophysics. Rev. Geophys. 36 (1998) 603-689
71. Peter D., Tape C., Boschi L., and Woodhouse J.H. Surface wave tomography: global membrane waves and adjoint methods. Geophys. J. Int. 171 3 (2007) 1098-1117
72. Poirier J.P. Transformation Plasticity, in Creep of Crystals (1985), Cambridge University Press, Cambridge pp. 213-228
73. Reichenberg I. Evolutionsstrategie: Optimierung technisches Systeme nach Prinzipien der biologischen Evolution (1973), Fromann-Holzboog, Stuttgart-Bad Cannstatt
74. Resovsky J.S., and Ritzwoller M.H. Regularization uncertainty in density models estimated from normal mode data. Geophys. Res. Lett. 26 (1999) 2319-2322
75. Resovsky J.S., and Trampert J. Using probabilistic seismic tomography to test mantle velocity-density relationships. Earth Planet. Sci. Lett. 215 (2003) 121-134
76. Ricard Y., Fleitout L., and Froidevaux C. Geoid heights and lithospheric stresses for a dynamic earth. Ann. Geophys. 2 (1984) 267-286
77. Ricard Y., Vigny C., and Froidevaux C. Mantle heterogeneities, geoid, and plate motion: a Monte Carlo inversion. J. Geophys. Res. 94 (1989) 13, 739-13, 754
78. Ricard Y., and Wuming B. Inferring the mantle viscosity and its three dimensional structure from geoid, topography and plate velocities. Geophys. J. Int. 105 (1991) 561-571
79. Richards M.A., and Hager B.H. Geoid anomalies in a dynamic Earth. J. Geophys. Res. 89 (1984) 5987-6002
80. Richards M.A., and Hager B.H. Effects of lateral viscosity variations on geoid anomalies and topography. J. Geophys. Res. 94 (1989) 10, 299-10, 313
81. Ritsema J., van Heijst H.J., and Woodhouse J.H. Complex shear wave velocity structure imaged beneath Africa and Iceland. Science 286 (1999) 1925-1928
82. Ritsema J., van Heijst H.J., and Woodhouse J.H. Global transition zone tomography. J. Geophys. Res. 109 (2004) Art. No. 02302
83. Romanowicz B. Can we resolve 3D density heterogeneity in the lower mantle?. Geophys. Res. Lett. 28 (2001) 1107-1110
84. Romanowicz, B., 2003. Global mantle tomography: progress status in the past 10 years. Annu. Rev. Earth Planet. Sci. 31,303-31,328 doi:10.1146/annuaearth.31.091602.113555.
85. Sammis C.G., and Dein J.L. On the possibility of transformational superplasticity in the Earth's. mantle. J. Geophys. Res. (1974) 79
86. Simmons, N.A., Forte, A.M., Grand, S.P., 2007. Thermochemical structure and dynamics of the African superplume, Geophys. Res. Lett. 34, L02301 doi:10.1029/2006GL028009.
87. Smyth J.R. Beta-Mg2SiO4: a potential host for water in the mantle. Am. Miner. 72 (1987) 1051-1055
88. Smyth J.R., and Jacobsen S.D. Nominally anhydrous minerals and Earth's deep water cycle. In: van der Lee S., and Jacobsen S.D. (Eds). Earth's Deep Water Cycle, Geophys. Monogr. Ser., vol. 168 (2006), Am. Geophys. Union 1-11
89. Spada G., Sabadini R., and Yuen D.A. Viscoelastic response of a hard transition zone: effects on post-glacial uplifts and rotational signatures. Earth Planet. Sci. Lett. 105 (1991) 453-462
90. Steinberger B., and O'Connell R.J. Changes of the Earth's rotation axis owing to advection of mantle density heterogeneities. Nature 387 (1997) 169-173
91. Tapley, B., Ries, J., Bettadpur, S., Chambers, D., Cheng, M., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., Wang, F., 2005. GGM02-an improved Earth gravity field model from GRACE. J. Geodesy doi:10.1007/s00190-005-0480-z.
92. Tarantola A. Inversion of seismic reflection data in the acoustic approximation. Geophysics 49 (1984) 1259-1266
93. Trampert J., Deschamps F., Resovsky J., and Yuen D. Probabilistic tomography maps chemical heterogeneities throughout the lower mantle. Science 306 (2004) 853-856
94. Tromp J., Tape C., and Liu Q. Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophys. J. Int. 160 (2005) 195-216
95. van der Hilst R.D., and Karason H. Compositional heterogeneity in the bottom 1000 km of Earth's mantle: towards a hybrid convection model. Science 283 (1999) 1885-1888
96. van der Meijde M., Marone F., Giardini D., and van der Lee S. Seismic evidence for water deep in Earth's upper mantle. Science 300 (2003) 1556-1558
97. Wessel P., and Smith W.H.F. Free software helps map and display data. Eos Trans., AGU 725 (1991) 445-446
98. Wu P. Deformation of an incompressible viscoelastic flat earth with power-law creep: a finite element approach. Geophys. J. Int. 108 (1992) 136-142
99. Zhang S., and Christensen U.R. Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle. Geophys. J. Int. 114 (1993) 531-547