Variation of traction and strain rate with lithospheric...
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0 50 100 150 200 250 300 Lithosphere thickness (km) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Log (Strain rate ratio) 0.01 asth 10 craton 0.01 asth 100 craton 0.01 asth 1000 craton 0.1 asth 10 craton 0.1 asth 100 craton 0.1 asth 1000 craton 1 asth 10 craton 1 asth 100 craton 1 asth 1000 craton -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -3 -2 -1 0 1 2 3 Variation of traction and strain rate with lithospheric thickness: An insight into understanding cratonic stability Jyotirmoy Paul*, Attreyee Ghosh Indian Institute of Science, Bangalore 560012, *[email protected] We try to understand the deformation patterns at the base of the litho- sphere for different viscosity structures. Here, we numerically estimate the relation between traction and strain rates at the base of the lithosphere. A similar kind of study by Conrad and Lithgow-Bertelloni (2006) used rigid boundary conditions at the surface and showed that traction magnitude in- creased with the increased thickness of the lithosphere if lateral viscosity variation was introduced. In another study, Cooper and Conrad (2009), using an analytical model, showed an exponentially increasing trend for normalized strain rates with lithosphere thickness. As our work focuses on cratons, emphasis is given on the strain rates beneath them. INTRODUCTION MANTLE FLOW MODELLING STRESS STRAIN RELATION 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ 120˚ 120˚ 150˚ 150˚ 180˚ 180˚ -150˚ -150˚ -120˚ -120˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ 120˚ 120˚ 150˚ 150˚ 180˚ 180˚ -150˚ -150˚ -120˚ -120˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ 120˚ 120˚ 150˚ 150˚ 180˚ 180˚ -150˚ -150˚ -120˚ -120˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ -90˚ -90˚ -60˚ -60˚ -30˚ -30˚ 0˚ 0˚ 30˚ 30˚ 60˚ 60˚ 90˚ 90˚ -8 -6 -4 -2 0 2 4 6 75 km Assumptions: 1. Anelastic, viscous, incompressible 2. Boussinesq approxi- mation Boundary Conditions: Free slip at the surface and the core-mantle boundary Density Anomaly: Derived from SMEAN2 to- mography, with high ve- locity region removed under continentes till 300 km (Fig 1) Method: 3 dimensional full spherical finite ele- ment code CitcomS Figure 1: Velocity anomaly derived from SMEAN2 tomography. (a composite model comprised of S40RTS (Ritsema et al., 2011), GyPSuM-S (Sim- mons et al., 2010), and SAVANI (Auer et al., 2014) using the methods of Becker and Boschi (2002)). High velocity regions under continents are re- moved till 300 km to impose neutrally buoyant cratons. Viscosity Structure Relative viscosity (RV) 30 0.1 1 1 50 0 100 300 410 670 CMB Depth (km) Figure 2: Radial Model: 5 layers of different rheological strengths. Reference viscosity of the upper mantle (10 21 Pa-s) is multiplied by relative viscosities in each of these layers, which are 30, 0.1, 1, 1, and 50 respectively. Laterally varying viscosity (LVV) models: Cratons from 3SMAC (Nataf and Ricard, 1996) are introduced till 300 km depth. Craton viscosity varies be- tween 10 to 1000 times the relative viscosities of each layer. Temperature de- pendence of the viscosity is calculated as η = η 0 exp[E(T 0 - T)] till 300 km. As- thenosphere viscosity varies between 10 19 Pa-s and 10 21 Pa-s. TRACTION AT THE BASE OF THE LITHOSPHERE DEFORMATION AT THE BASE OF THE LITHOSPHERE Figure 4: Models of different viscosity combi- nations show variation in traction magnitude at variable base of the lithoshere. Viscosity combinations are mentioned at the top left corner of each figure. First number is the vis- cosity of asthenosphere w.r.t upper mantle vis- cosity and second one is the viscosity contrast of cratons w.r.t their surroundings. Models with high asthenosphere viscosity have signifi- cantly higher traction than those having weaker asthenosphere. Also traction magni- tude increases under the highly viscous cra- tons. Figure 7: The maps showing slowest defor- mation at the variable base of lithosphere for models of different viscosity combina- tions. Viscosity combinations are men- tioned at the top left corner of each figure. Stronger the asthenosphere, lower is the amount of deformation under the cratons. Fastest deforming areas are the mid oceanic ridges. 0 0.5 1 1.5 2 2.5 Traction (in MPa) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 log (Normalized strain rate) 0.01 asth 0.1 asth 1 asth Best fit line, r= -0.68 Figure 9: Left:Traction and normalized strain rates at the base of the lithosphere. Different colour dots represent viscosities of asthenosphere with respect to the upper mantle viscosi- ty. Tractions are high under cratons but deformation at their base is very slow. Right: An un- biased viscosity can be obtained if absolute basal traction (T) is divided by this strain rate, η = T*h/δv, where h is the thickness of lithosphere and δv is velocity drop at lithosphere-asthe- nosphere boundary. If T is a linear function of thickness, for a constant δv, viscosity becomes proportional to h 2 . The calculated viscosity plotted against the square of the thickness of the lithosphere shows a modest linear relationship upto 192 km. .01, 10 .01, 100.01, 1000 .1, 10 .1, 100 .1, 1000 1, 10 1, 100 1, 1000 Model Parameter 0.0001 0.001 0.01 Archean 3 Ga Proterozoic 0.1 Cambrian 1 Critical strain rate (Ec) T c =1/3 (0.33) T c =1/13.88 (0.072) T c =1/21.39 (0.0468) T c =1/16.67 (0.06) Figure 10: If a craton has to survive n times the age of an oceanic lithosphere, it has to have at least 1/n times the strain rates of the oceanic lithosphere. Critical strain rate (Ec) calculated from different models is plotted against different viscosity combinations. Tc is the normalized time that gives an idea about how long a craton can survive compared to an average oceanic lithosphere. If critical strain rate (Ec) is more than the normalized time (Tc) of a particular age, then cratons will be destroyed after that age. 1. Traction at the base of lithosphere depends on three factors: Lithosphere thickness, asthe- nosphere viscosiy and craton viscosity. 2. Cratons have maximum stress magnitude at their base, but the strain rate magnitude at their base is minimum. This is potential reason for their long term stablity. 3. Inverse relationship between stress and strain rate is because viscosity is increasing with the square of the thickness of lithosphere. 4. For a craton to become stable it should have a minimum viscosity contrast of 10, 100 and 1000 times the viscosity of its surroundings if asthenosphere viscosity is 10 21 , 10 20 and 10 19 Pa-s respectively. CONCLUSION 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 48 48 48 48 48 48 48 48 48 48 48 96 96 96 96 96 96 96 96 96 96 96 96 144 4144 144 144 144 144 144 144 144 144 144 144 144 192 192 192 192 192 192 192 192 192 192 192 192 192 192 192 240 240 -2 -1 0 1 2 3 log 10 visc 96 km Figure 3: Lateral viscosity varia- tion in the input model of 10 20 Pa-s asthenosphere and cratons of 100 times viscosity contrast. Cratons are highly viscous and MOR are least viscous areas. Litho- sphere thickness is inicated by red contour lines (Conrand and Lithgow-Bertelloni, 2006). SURVIVAL OF CRATONS OVER AGES REFERENCES 1.Conrad, C. P., and C. Lithgow-Bertelloni, Influence of continental roots and asthenosphere on plate mantle coupling, GRL 33(5), 2006. 2. Cooper, C., and C. Conrad, Does the mantle control the maximum thickness of cratons?, Lithosphere, 1(2), 67–72, 2009. 3. Nataf, H.-C., and Y. Ricard, 3smac: an a priori tomographic model of the upper mantle based on geophysical modeling, PEPI 95(1-2), 101–122, 1996. 4. Ritsema, J., a. A. Deuss, H. Van Heijst, and J. Woodhouse, S40rts: a degree-40 shear-velocity model for the mantle from new rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements, JGI 184(3), 1223–1236, 2011. ACKNOWLEDGEMENT Fundings covered by IISc GARP and EGU Roland Schlich travel support. Traction and Strain rate calculation: Traction values are calculated at the variable base of lithosphere. Strain rates are cal- culated by dividing traction with the viscosity at that depth. Normalization is done by taking the ratio of any parameter (traction, strain rate or viscosity) at the base of lithosphere in LVV models to that at the same depth in the reference radial model (cf. Conrand and Lithgow-Bertelloni, 2006). Figure 8: Normalized strain rate at the base of the lithosphere. As litho- sphere thickens, normalized strain rate drops monotonically for stronger asthenosphere (10 20 and 10 21 Pa-s). A minor kink is in be- tween 192-240 km depth as viscosi- ty drops in these non cratonic areas. At maximum depth, i.e., at the core of cratons, the normalized strain rate is minimum. Because of very weak rheology, model with as- thenosphere of 10 19 Pa-s shows a jump at around 100 km depth in normalized strain rates. -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -2 -1 0 1 2 3 Log 10 Normalized strain rate -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -3 -2 -1 0 1 2 3 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -2 -1 0 1 2 3 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ -3 -2 -1 0 1 2 3 0.01, 100 0.1, 1000 0.1, 100 0.1, 10 1, 100 Figure 5: Average traction magnitude shows a dependence on asthenospher- ic viscosity, lithosphere thickness and craton viscosity. Each line of different symbol and colour represents the mag- nitude of average tractions obtained from a model of certain viscosity combi- nation presented in the index. A sharp drop of magnitude is observed in be- tween 192-240 km depth because of non-cratonic thick lithosphere. Figure 6: Viscosity and absolute traction roughly holds a linear relationship with a correlation co-efficient of 0.62. Log 10 Normalized strain rate Log 10 Normalized strain rate Log 10 Normalized strain rate Log 10 Normalized strain rate 5. Simmons, N. A., A. M. Forte, L. Boschi, and S. P. Grand, Gypsum: A joint tomographic model of mantle density and seismic wave speeds, JGR: Solid Earth, 115(B12), 2010. 6. Auer, L., L. Boschi, T. Becker, T. Nissen-Meyer, and D. Giardini, Savani: A variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets, JGR: Solid Earth, 119(4), 3006–3034, 2014. 7. Becker, T., and L. Boschi, A comparison of tomographic and geodynamic mantle models, G3, 3(1), 2002. δv % 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0.0 0.5 1.0 1.5 2.0 Traction (in MPa) 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0 1 2 Traction (in MPa) 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0 1 2 Traction (in MPa) 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ -150˚ -120˚ -90˚ -60˚ -30˚ 0˚ -90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚ 0 1 2 3 4 Traction (in MPa) 0.01, 100 0.1, 1000 0.1, 10 1, 100 19 20 21 22 23 24 log viscosity (in Pas) 0 0.5 1 1.5 2 2.5 Traction (in MPa) 0.01 asth 0.1 asth 1 asth Best fit line, r= 0.62 0 50 100 150 200 250 300 Lithosphere Thickness (km) 0 0.5 1 1.5 2 2.5 3 Average absolute basal traction (in MPa) 0.01 asth 10 craton 0.01 asth 100 craton 0.01 asth 1000 craton 0.1 asth 10 craton 0.1 asth 100 craton 0.1 asth 1000 craton 1 asth 10 craton 1 asth 100 craton 1 asth 1000 craton 0.1 asth no craton (ref) 0 2 4 6 8 Thickness 2 (km 2 ) 10 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Calculated viscosity 10 22
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Variation of traction and strain rate with lithospheric thickness:An insight into understanding cratonic stability
Jyotirmoy Paul*, Attreyee GhoshIndian Institute of Science, Bangalore 560012, *[email protected]
We try to understand the deformation patterns at the base of the litho-sphere for di�erent viscosity structures. Here, we numerically estimate the relation between traction and strain rates at the base of the lithosphere. A similar kind of study by Conrad and Lithgow-Bertelloni (2006) used rigid boundary conditions at the surface and showed that traction magnitude in-creased with the increased thickness of the lithosphere if lateral viscosity variation was introduced. In another study, Cooper and Conrad (2009), using an analytical model, showed an exponentially increasing trend for normalized strain rates with lithosphere thickness. As our work focuses on cratons, emphasis is given on the strain rates beneath them.
INTRODUCTION MANTLE FLOW MODELLING STRESS STRAIN RELATION
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Assumptions:1. Anelastic, viscous, incompressible2. Boussinesq approxi-mation
Boundary Conditions:Free slip at the surface and the core-mantle boundaryDensity Anomaly:Derived from SMEAN2 to-mography, with high ve-locity region removed under continentes till 300 km (Fig 1)
Method:3 dimensional full spherical �nite ele-ment code CitcomS
Figure 1: Velocity anomaly derived from SMEAN2 tomography. (a composite model comprised of S40RTS (Ritsema et al., 2011), GyPSuM-S (Sim-mons et al., 2010), and SAVANI (Auer et al., 2014) using the methods of Becker and Boschi (2002)). High velocity regions under continents are re-moved till 300 km to impose neutrally buoyant cratons.
Viscosity Structure
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Figure 2: Radial Model: 5 layers of di�erent rheological strengths. Reference viscosity of the upper mantle (1021 Pa-s) is multiplied by relative viscosities in each of these layers, which are 30, 0.1, 1, 1, and 50 respectively.
Laterally varying viscosity (LVV) models: Cratons from 3SMAC (Nataf and Ricard, 1996) are introduced till 300 km depth. Craton viscosity varies be-tween 10 to 1000 times the relative viscosities of each layer. Temperature de-pendence of the viscosity is calculated as η = η0 exp[E(T0 − T)] till 300 km. As-thenosphere viscosity varies between 1019 Pa-s and 1021 Pa-s.
TRACTION AT THE BASE OF THE LITHOSPHERE DEFORMATION AT THE BASE OF THE LITHOSPHERE
Figure 4: Models of di�erent viscosity combi-nations show variation in traction magnitude at variable base of the lithoshere. Viscosity combinations are mentioned at the top left corner of each �gure. First number is the vis-cosity of asthenosphere w.r.t upper mantle vis-cosity and second one is the viscosity contrast of cratons w.r.t their surroundings. Models with high asthenosphere viscosity have signi�-cantly higher traction than those having weaker asthenosphere. Also traction magni-tude increases under the highly viscous cra-tons.
Figure 7: The maps showing slowest defor-mation at the variable base of lithosphere for models of di�erent viscosity combina-tions. Viscosity combinations are men-tioned at the top left corner of each �gure. Stronger the asthenosphere, lower is the amount of deformation under the cratons. Fastest deforming areas are the mid oceanic ridges.
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Figure 9: Left:Traction and normalized strain rates at the base of the lithosphere. Di�erent colour dots represent viscosities of asthenosphere with respect to the upper mantle viscosi-ty. Tractions are high under cratons but deformation at their base is very slow. Right: An un-biased viscosity can be obtained if absolute basal traction (T) is divided by this strain rate, η = T*h/δv, where h is the thickness of lithosphere and δv is velocity drop at lithosphere-asthe-nosphere boundary. If T is a linear function of thickness, for a constant δv, viscosity becomes proportional to h2. The calculated viscosity plotted against the square of the thickness of the lithosphere shows a modest linear relationship upto 192 km.
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Figure 10: If a craton has to survive n times the age of an oceanic lithosphere, it has to have at least 1/n times the strain rates of the oceanic lithosphere. Critical strain rate (Ec) calculated from di�erent models is plotted against di�erent viscosity combinations. Tc is the normalized time that gives an idea about how long a craton can survive compared to an average oceanic lithosphere. If critical strain rate (Ec) is more than the normalized time (Tc) of a particular age, then cratons will be destroyed after that age.
1. Traction at the base of lithosphere depends on three factors: Lithosphere thickness, asthe-nosphere viscosiy and craton viscosity.2. Cratons have maximum stress magnitude at their base, but the strain rate magnitude at their base is minimum. This is potential reason for their long term stablity.3. Inverse relationship between stress and strain rate is because viscosity is increasing with the square of the thickness of lithosphere.4. For a craton to become stable it should have a minimum viscosity contrast of 10, 100 and 1000 times the viscosity of its surroundings if asthenosphere viscosity is 1021, 1020 and 1019 Pa-s respectively.
CONCLUSION
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SURVIVAL OF CRATONS OVER AGES
REFERENCES1.Conrad, C. P., and C. Lithgow-Bertelloni, In�uence of continental roots and asthenosphere on plate mantle coupling, GRL 33(5), 2006.2. Cooper, C., and C. Conrad, Does the mantle control the maximum thickness of cratons?, Lithosphere, 1(2), 67–72, 2009.3. Nataf, H.-C., and Y. Ricard, 3smac: an a priori tomographic model of the upper mantle based on geophysical modeling, PEPI 95(1-2), 101–122, 1996.4. Ritsema, J., a. A. Deuss, H. Van Heijst, and J. Woodhouse, S40rts: a degree-40 shear-velocity model for the mantle from new rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements, JGI 184(3), 1223–1236, 2011.
ACKNOWLEDGEMENTFundings covered by IISc GARP and EGU Roland Schlich travel support.
Traction and Strain rate calculation:
Traction values are calculated at the variable base of lithosphere. Strain rates are cal-culated by dividing traction with the viscosity at that depth. Normalization is done by taking the ratio of any parameter (traction, strain rate or viscosity) at the base of lithosphere in LVV models to that at the same depth in the reference radial model (cf. Conrand and Lithgow-Bertelloni, 2006).
Figure 8: Normalized strain rate at the base of the lithosphere. As litho-sphere thickens, normalized strain rate drops monotonically for stronger asthenosphere (1020 and 1021 Pa-s). A minor kink is in be-tween 192-240 km depth as viscosi-ty drops in these non cratonic areas. At maximum depth, i.e., at the core of cratons, the normalized strain rate is minimum. Because of very weak rheology, model with as-thenosphere of 1019 Pa-s shows a jump at around 100 km depth in normalized strain rates.
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30˚
60˚
90˚−180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
−2 −1 0 1 2 3
Log 10 Normalized strain rate
−180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚−180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
−3 −2 −1 0 1 2 3
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
−2 −1 0 1 2 3
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
−3 −2 −1 0 1 2 3
0.01, 100
0.1, 10000.1, 100
0.1, 10
1, 100
Figure 5: Average traction magnitude shows a dependence on asthenospher-ic viscosity, lithosphere thickness and craton viscosity. Each line of di�erent symbol and colour represents the mag-nitude of average tractions obtained from a model of certain viscosity combi-nation presented in the index. A sharp drop of magnitude is observed in be-tween 192-240 km depth because of non-cratonic thick lithosphere.
Figure 6: Viscosity and absolute traction roughly holds a linear relationship with a correlation co-e�cient of 0.62.
Log 10 Normalized strain rate
Log 10 Normalized strain rateLog 10 Normalized strain rate
Log 10 Normalized strain rate
5. Simmons, N. A., A. M. Forte, L. Boschi, and S. P. Grand, Gypsum: A joint tomographic model of mantle density and seismic wave speeds, JGR: Solid Earth, 115(B12), 2010.6. Auer, L., L. Boschi, T. Becker, T. Nissen-Meyer, and D. Giardini, Savani: A variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets, JGR: Solid Earth, 119(4), 3006–3034, 2014.7. Becker, T., and L. Boschi, A comparison of tomographic and geodynamic mantle models, G3, 3(1), 2002.
δv %
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
0.0 0.5 1.0 1.5 2.0
Traction (in MPa)
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
0 1 2
Traction (in MPa)
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
0 1 2
Traction (in MPa)
0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚ −150˚ −120˚ −90˚ −60˚ −30˚ 0˚
−90˚
−60˚
−30˚
0˚
30˚
60˚
90˚
0 1 2 3 4
Traction (in MPa)
0.01, 100
0.1, 1000
0.1, 10
1, 100
19 20 21 22 23 24log viscosity (in Pas)
0
0.5
1
1.5
2
2.5
Trac
tion
(in M
Pa)
0.01 asth0.1 asth1 asthBest �t line, r= 0.62
0 50 100 150 200 250 300Lithosphere Thickness (km)
0
0.5
1
1.5
2
2.5
3
Ave
rage
abs
olut
e ba
sal t
ract
ion
(in M
Pa)
0.01 asth 10 craton0.01 asth 100 craton0.01 asth 1000 craton0.1 asth 10 craton0.1 asth 100 craton0.1 asth 1000 craton1 asth 10 craton1 asth 100 craton1 asth 1000 craton0.1 asth no craton (ref)
0 2 4 6 8
Thickness 2 (km 2 ) 10 4
0
0.5
1
1.5
2
2.5
3
3.5
4
Calc
ulat
ed v
isco
sity
10 22
