Influences of lower-mantle properties on the formation of asthenosphere in oceanic upper mantle

Abstract

Asthenosphere is a venerable concept based on geological intuition of Reginald Daly nearly 100 years ago. There have been various explanations for the existence of the asthenosphere. The concept of a plume-fed asthenosphere has been around for a few years due to the ideas put forth by Yamamoto et al.. Using a two-dimensional Cartesian code based on finite-volume method, we have investigated the influences of lower-mantle physical properties on the formation of a low-viscosity zone in the oceanic upper mantle in regions close to a large mantle upwelling. The rheological law is Newtonian and depends on both temperature and depth. An extended-Boussinesq model is assumed for the energetics and the olivine to spinel, the spinel to perovskite and perovskite to post-perovskite (ppv) phase transitions are considered. We have compared the differences in the behavior of hot upwellings passing through the transition zone in the mid-mantle for a variety of models, starting with constant physical properties in the lower-mantle and culminating with complex models which have the post-perovskite phase transition and depth-dependent coefficient of thermal expansion and thermal conductivity. We found that the formation of the asthenosphere in the upper mantle in the vicinity of large upwellings is facilitated in models where both depth-dependent thermal expansivity and conductivity are included. Models with constant thermal expansivity and thermal conductivity do not produce a hot low-viscosity zone, resembling the asthenosphere. We have also studied the influences of a cylindrical model and found similar results as the Cartesian model with the important difference that upper-mantle temperatures were much cooler than the Cartesian model by about 600 to 700 K. Our findings argue for the potentially important role played by lower-mantle material properties on the development of a plume-fed asthenosphere in the oceanic upper mantle.

Keywords

oceanic asthenosphere / lower mantle / thermal expansivity / thermal conductivity / phase transition

References

[1] Ammann M. W., Brodholt J. P., Wookey J., . First-Principles Constraints on Diffusion in Lower Mantle Minerals and a Weak D” Layer. Nature, 2010, 465(7297): 462-465.

[2] Bina C. R., Helffrich G.. Phase Transitions Clapeyron Slopes and Transition Zone Seismic Discontinuity Topography. J. Geophys. Res., 1994, 99(B8): 15853-15860.

[3] Bottinga Y., Allegre C. J.. Thermal Aspects of Seafloor Spreading and the Nature of the Oceanic Crust. Tectonophysics, 1973, 18(1–2): 1-17.

[4] Čadek O., van der Berg A. P.. Radial Profiles of Temperature and Viscosity in the Earth’s Mantle Inferred from the Geoid and Lateral Seismic Structure. Earth Planet. Sci. Lett., 1998, 164(3–4): 607-615.

[5] Cao Q., Wang P., van der Hilst R. D., . Imaging the Upper Mantle Transition Zone with a Generalized Radon Transform of SS Precursors. Phys. Earth Planet. Inter., 2010, 180(1–2): 80-91.

[6] Cao, Q., van der Hilst, R. D., de Hoop, M. V., et al., 2010b. Complex Plume Dynamics in the Transition Zone underneath the Hawaii Hotspot: Seismic Imaging Results. AGU Fall Meeting

[7] Chopelas A., Boehler R.. Thermal Expansivity in the Lower Mantle. Geophys. Res. Lett., 1992, 19(19): 1983-1986.

[8] Daly R. A.. Igneous Rocks and Their Origin, 1914, New York: McGraw-Hill 563

[9] Davies G. F.. Dynamic Earth, 1999, Cambridge: Cambridge University Press 458

[10] de Koker N.. Thermal Conductivity of MgO Periclase at High Pressure: Implications for the D” Region. Earth Planet. Sci. Lett., 2010, 292(3–4): 392-398.

[11] Dixon J. E., Dixon T. H., Bell D. R., . Lateral Variation in Upper Mantle Viscosity: Role of Water. Earth Planet. Sci. Lett., 2004, 222(2): 451-467.

[12] Elsasser W. M.. Runcorn S. K.. Convection and Stress Propagation in the Upper Mantle. The Application of Modern Physics to the Earth and Planetary Interiors, 1969, New York: Wiley 223 246

[13] Forte A. M., Mitrovica J. X.. Deep-Mantle High-Viscosity Flow and Thermochemical Structure Inferred from Seismic and Geodynamic Data. Nature, 2001, 410(6832): 1049-1056.

[14] Goncharov A. F., Struzhkin V. V., Montoya J. A., . Effect of Composition, Structure, and Spin State on the Thermal Conductivity of the Earth’s Lower Mantle. Phys. Earth Planet. Inter., 2010, 180(3–4): 148-153.

[15] Hansen U., Yuen D. A., Kroening S. E., . Dynamical Consequences of Depth-Dependent Thermal Expansivity and Viscosity on Mantle Circulations and Thermal Structure. Phys. Earth Planet. Inter., 1993, 77(3–4): 205-223.

[16] Hanyk L., Moser J., Yuen D. A., . Time-Domain Approach for the Transient Responses in Stratified Viscoelastic Earth Models. Geophys. Res. Lett., 1995, 22(10): 1285-1288.

[17] Hernlund J. W., Thomas C., Tackley P. J.. A Doubling of the Post-Perovskite Phase Boundary and Structure of the Earth’s Lowermost Mantle. Nature, 2005, 434(7035): 882-886.

[18] Hofmeister A. M.. Pressure Dependence of Thermal Transport Properties. Proc. Natl. Acad. Sci., 2007, 104(22): 9192-9197.

[19] Hofmeister A. M.. Inference of High Thermal Transport in the Lower Mantle from Laser-Flash Experiments and the Damped Harmonic Oscillator Model. Phys. Earth Planet. Inter., 2008, 170(3–4): 201-206.

[20] Hoink T., Lenardic A.. Three-Dimensional Mantle Convection Simulations with a Low-Viscosity Asthenosphere and the Relationship between Heat Flow and the Horizontal Length Scale of Convection. Geophys. Res. Lett., 2008, 35 10 L10304

[21] Huettig C.. Scaling Laws for Internally Heated Mantle Convection: [Dissertation], 2008, Muenster: Westfaelischen Wilhelms-Universitaet

[22] Huettig C., Stemmer K.. Finite Volume Discretization for Dynamic Viscosities on Voronoi Grids. Phys. Earth Planet. Inter., 2008, 171(1–4): 137-146.

[23] Hunt S. A., Weidner D. J., Li L., . Weakening of Calcium Iridate during Its Transformation from Perovskite to Post-Perovskite. Nature Geosci., 2009, 2(11): 794-797.

[24] Karato S. I.. Does Partial Melting Reduce the Creep Strength of the Upper Mantle?. Nature, 1986, 319(6051): 309-310.

[25] Karato S. I.. Insights into the Nature of Plume-Asthenosphere from Central Pacific Geophysical Anomalies. Earth Planet. Sci. Lett., 2008, 274(1–2): 234-240.

[26] Karato S. I.. The Influence of Anisotropic Diffusion on the High-Temperature Creep of a Polycrystalline Aggregate. Phys. Earth Planet. Inter., 2010, 183(3–4): 468-472.

[27] Katsura T., Yokoshi S., Kawabe K., . P-V-T Relations of MgSiO₃ Perovskite Determined by In Situ X-Ray Diffraction Using a Large-Volume High-Pressure Apparatus. Geophys. Res. Lett., 2009, 36 L01305

[28] Kawai K., Tsuchiya T.. Temperature Profile in the Lowermost Mantle from Seismological and Mineral Physics Joint Modeling. Proc. Natl. Acad. Sci., 2009, 106(52): 22119-22123.

[29] King S. D.. On Topography and Geoid from 2-D Stagnant-Lid Convection Calculations. Geochem., Geophys., Geosyst., 2009, 10 Q03002

[30] King S. D., Lee C., Van-Keken P. E., . A Community Benchmark for 2D Cartesian Compressible Convection in the Earth’s Mantle. Geophys. J. Int., 2010, 180(1): 73-87.

[31] Leitch A. M., Yuen D. A., Sewell G.. Mantle Convection with Internal Heating and Pressure-Dependent Thermal Expansivity. Earth Planet. Sci. Lett., 1991, 102(2): 213-232.

[32] Maruyama S.. Plume Tectonics. J. Geol. Soc. Japan, 1994, 100: 24-49.

[33] Matyska C., Yuen D. A.. Lower Mantle Dynamics with the Post-Perovskite Phase Change, Radiative Thermal Conductivity, Termperature and Depth-Dependent Viscosity. Phys. Earth Planet. Inter., 2006, 154(2): 196-207.

[34] Matyska, C., Yuen, D. A., 2007. Lower Mantle Material Properties and Convection Models of Multiscale Plumes. In: Fougler, G. T., Jurdy, D. M., eds., Plates, Plumes and Planetary Processes. Geological Society of America Special Paper, 137–163

[35] Mitrovica J. X., Forte A. M.. A New Inference of Mantle Viscosity Based upon Joint Inversion of Convection and Glacial Isostatic Adjustment Data. Earth Planet. Sci. Lett., 2004, 225(1–2): 177-189.

[36] Moresi L. N., Solomatov V. S.. Numerical Investigations of 2D Convection with Extremely Large Viscosity Variations. Phys. Fluids, 1995, 7: 2154-2162.

[37] Nakagawa T., Tackley P. J.. Effects of a Perovskite-Post Perovskite Phase Change near Core-Mantle Boundary in Compressible Mantle Convection. Geophys. Res. Lett., 2004, 31 16 L16611

[38] Nakagawa T., Tackley P. J., Deschamps F., . The Influence of MORB and Harzburgite Composition on Thermo-chemical Mantle Convection in a 3-D Spherical Shell with Self-Consistently Calculated Mineral Physics. Earth Planet. Sci. Lett., 2010, 296(3–4): 403-412.

[39] O’Farrell K. A., Lowman J. P.. Emulating the Thermal Structure of Spherical Shell Convection in Plane-Layer Geometry Mantle Convection Models. Phys. Earth Planet. Inter., 2010, 182(1–2): 73-84.

[40] Oganov A. R., Ono S.. Theoretical and Experimental Evidence for a Post-Perovskite Phase of MgSiO3 in Earth’s D” Layer. Nature, 2004, 430(6998): 445-448.

[41] Oganov A. R., Ono S.. The High Pressure Phase of Alumina and Implications for Earth’s D” Layer. Proc. Natl. Acad. Sci., 2005, 102(31): 10828-10831.

[42] Ohta K.. Electrical and Thermal Conductivity of the Earth’s Lower Mantle: [Dissertation], 2010, Tokyo: Tokyo Institute of Technology

[43] Oldenbur D. W., Brune J. N.. Ridge Transform Fault Spreading Pattern in Freezing Wax. Science, 1972, 178(4058): 301-304.

[44] Parmentier E. M.. Schubert G., Bercovici D.. The Dynamics and Convective Evolution of the Oceanic Upper Mantle. Treatise on Geophysics, 2007, Cambridge: Cambridge University Press 305 324

[45] Poirier J. P.. Introduction to the Physics of the Earth’s Interior, 1991, Cambridge: Cambridge University Press

[46] Ricard Y., Bai W. M.. Inferring Viscosity and the 3-D Density Structure of the Mantle from Geoid, Topography and Plate Velocities. Geophys. J. Int., 1991, 105(3): 561-571.

[47] Richards, M. A., Yang, W. S., Baumgardner, J. R., et al., 2001. Role of a Low-Viscosity Zone in Stabilizing Plate Tectonics: Implications for Comparative Terrestrial Planetology. Geochem., Geophys., Geosyst., 2(8), doi: 10.1029/2000GC000115

[48] Richter F.. Finite Amplitude Convection through a Phase Boundary. Geophys. J. R. Astron. Soc., 1973, 35(1–3): 265-276.

[49] Schenk O., Gartner K., Fichtner W.. Efficient Sparse LU Factorization with Left-Right Looking Strategy on Shared Memory Multiprocessors. BIT, 2000, 40(1): 158-176.

[50] Schubert G., Froidevaux C., Yuen D. A.. Oceanic Lithosphere and Asthenosphere: Thermal and Mechanical Structure. J. Geophys. Res., 1976, 81(20): 3525-3540.

[51] Schubert G., Turcotte D. L., Olson P.. Mantle Convection in the Earth and Planets, 2001, Cambridge: Cambridge University Press 940

[52] Spiegelman M., Katz R. F.. A Semi-Lagrangian Crank-Nicolson Algorithm for the Numerical Solution of Advection-Diffusion Problems. Geochem., Geophys., Geosyst., 2006, 7 Q04014

[53] Stein C., Hansen U.. Plate Motions and the Viscosity Structure of the MZantle—Insights from Numerical Modelling. Earth Planet. Sci. Lett., 2008, 272(1–2): 29-40.

[54] Steinbach V., Yuen D. A.. The Effects of Temperature-Dependent Viscosity on Mantle Convection with the Two Major Phase Transitions. Phys. Earth Planet. Inter., 1995, 90(1–2): 13-36.

[55] Tang X. L., Dong J. J.. Lattice Thermal Conductivity of MgO at Conditions of Earth’s Interior. Proc. Natl. Acad. Sci. USA, 2010, 107(10): 4539-4543.

[56] Tateno S., Hirose K., Sata N., . Determination of Post-Perovskite Phase Transition Boundary up to 4 400 K and Implications for Thermal Structure in D” Layer. Earth Planet. Sci. Lett., 2009, 277(1–2): 130-136.

[57] Tosi N., Sabadini R., Marotta A. M., . Simultaneous Inversion for the Earth’s Mantle Viscosity and Ice Mass Imbalance in Antarctica and Greenland. J. Geophys. Res., 2005, 110 B07402

[58] Tosi N., Yuen D. A., Cadek O.. Dynamical Consequences in the Lower Mantle with the Post-Perovskite Phase Change and Strongly Depth-Dependent Thermodynamic and Transport Properties. Earth Planet. Sci. Lett., 2010, 298(1–2): 229-243.

[59] van Bemmelen R. W., Berlage H. P.. Versuch Einer Mathematischen Behandlung Geotektonischer Bewegungen Unter Besonderer Beruecksichtigung der Undationstheorie. Gerlands. Beitr. Z. Geophys., 1934, 43(1–2): 19-55.

[60] Walte N. P., Heidelbach F., Miyajima N., . Transformation Textures in Post-Perovskite: Understanding Mantle Flow in the D” Layer of the Earth. Geophys. Res. Lett., 2009, 36 L04302

[61] Wentzcovitch R. M., Justo J. F., Wu Z., . Anomalous Compressibility of Ferropericlase throughout the Iron Spin Cross-over. Proc. Natl. Acad. Sci. USA, 2009, 106(21): 8447-8452.

[62] Wentzcovitch R. M., Yu Y. G., Wu Z. Q.. Thermodynamic Properties and Phase Relations in Mantle Minerals Investigated by First Priniciples Quasiharmonic Theory. Reviews in Mineralogy and Geochemistry, 2010, 71: 59-98.

[63] Xu Y. S., Shankland T. J., Linhardt S., . Thermal Diffusivity and Conductivity of Olivine, Wadsleyite and Ringwoodite to 20 GPa and 1 373 K. Phys. Earth. Planet. Inter., 2004, 143–144: 321-336.

[64] Yamamoto M., Morgan J. P., Morgan W. J.. Global Plume-Fed Asthenosphere Flow—I: Motivation and Model Development. GSA Special Papers, 2007, 430: 165-188.

[65] Yamazaki, D., Karato, S., 2007. Lattice Preferred Orientation of Lower Mantle Materials and Seismic Anisotropy in the D” Layer. In: Hirose, K., Brodholt, J., Lay, T., et al., eds., Post-Perovskite: The Last Mantle Phase Transition. AGU Monograph, 174: 69–78

[66] Yoshino T., Yamazaki D.. Grain Growth Kinetics of CaIrO3 Perovskite and Post-Perovskite, with Implications for Rheology of D” Layer. Earth Planet. Sci. Lett., 2007, 255(3–4): 485-493.

[67] Yu Y., Wu Z., Wentzcovitch R. M.. α-β-γ Transformations in Mg₂SiO₄ in Earth’s Transition Zone. Earth Planet. Sci. Lett., 2008, 273: 115-122.

[68] Yuen D. A., Cadek O., van Keken P., . Boschi E., Morelli A., Ekstrom G., . Combined Results from Mineral Physics, Tomography and Mantle Convection and Their Implications on Global Geodynamics. Seismic Modelling of the Earth’s Structure, 1996, Bologna: Editrice Compositori 463 505