Jan 2019 How is topography supported Alternatives to isostasy What limits the height of mountains The science of landscapes Earth amp Planetary Surface Processes httpgeosciuchicagoedukitegeos286002019 ID: 1021490
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1. GEOS 28600Lecture 3Wednesday 15 Jan 2019How is topography supported? Alternatives to isostasyWhat limits the height of mountains?The science of landscapes:Earth & Planetary Surface Processeshttp://geosci.uchicago.edu/~kite/geos28600_2019/
2. Key points from todayHow is topography supported? Relationship between topography & gravity at length scales much larger than, comparable to, and much smaller than, the lithospheric thickness.Explanation of Airy isostasyQuantities inferred from topographygravity comparison._______________________________________What limits the height of mountains?Explain the mechanism that limits the height of Tibet and the AltiplanoExplain the process relationship between the height of Tibet and the height of Mt. Everest
3. Airy isostasy (floating)Free-air gravity anomaly is negligibly small for loads small compared to planet radius
4. EXPECTATIONS AND OBSERVATIONS: BOUGUER GRAVITY EQUATION, GRAVITY-TOPOGRAPHY CORRELATION, ADMITTANCE MECHANISMS: AIRY ISOSTASY, FLEXURE (MEMBRANE STRESSES)APPLICATIONS: STRENGTH HEAT FLOW THERMAL HISTORY; INFERENCE OF BURIED OCEANSHow is topography supported?
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6. Following Turcotte & Schubert (2nd edn):
7. Different worlds show similar behavior in gravity-topography ratio (“admittance”)as a function of wavelengthMars2πGρΔzAdmittance is sometimes calculated using “Bouguer gravity”, gravity thathas been corrected for mass of topographyIn this course we only use “free-air gravity” (uncorrected for topography).Moon
8. EXPECTATIONS AND OBSERVATIONS: BOUGUER GRAVITY EQUATION, GRAVITY-TOPOGRAPHY CORRELATION, ADMITTANCE MECHANISMS: AIRY ISOSTASY, FLEXURE (MEMBRANE STRESSES)APPLICATIONS: STRENGTH HEAT FLOW THERMAL HISTORY; INFERENCE OF BURIED OCEANSHow is topography supported?
9. Definition of the lithosphereWatts, in Treatise on Geophysics(1st edn.), 2007elastic lithosphere – supports loads over geologic timeseparate from:seismic lithosphere – permits earthquakesthermal boundary layerlayer that is conductively affectedby the cold boundary condition of the planet’s surface
10. Lithosphere: strength versus depthByerlee’s lawg=3.7 m s-2g=9.8 m s-2g=8.9 m s-2g=1.6 m s-2
11. stiffness (Pa, N m-2)Young’s modulusflexural rigidity (N m)wavelength (m)compensation, cm = [ (kg m s-2)/(kg m-3 × m s-2) ]1/4elastic thickness (m)Poisson’s ratio (0.25 – 0.33, dimensionless)Compensation curvescan be used to constrainDA slightly modified technique is needed for load size comparable to planet radius (‘membrane stresses’)
12. Membrane support example: Tharsis (volcanic province) load on MarsPhillips et al. Science 2001
13. EXPECTATIONS AND OBSERVATIONS: BOUGUER GRAVITY EQUATION, GRAVITY-TOPOGRAPHY CORRELATION, ADMITTANCE MECHANISMS: AIRY ISOSTASY, FLEXURE (MEMBRANE STRESSES)APPLICATIONS: STRENGTH HEAT FLOW THERMAL HISTORY; INFERENCE OF BURIED OCEANSHow is topography supported?
14. Thermal history of Mars Major reductionin Mars’ geothermalheat flow at aroundthe time that the surface was drying out.Ruiz et al., Nature Scientific Reports, 2014Base of elastic lithosphere corresponds to T ~ 550-600 C(McNutt, JGR, 1984)depth(m)thermalconductivity(W m-1 K-1)heat flow (W m-2)surface T(K)
15. INSIGHT mission (landed on Mars 26 Nov 2018)
16. Inferring oceans on EuropaHurford et al. Icarus 2005Billings & Kattenhorn Icarus 2005Elastic thickness issmallIce is soft and warm atshallow depths(From Europa’s overalldensity) water substancepersists to great depthMost of the water isvery warm and likelyliquid
17. Key points: topography versus gravityRelationship between topography & gravity at length scales much larger than, comparable to, and much smaller than, the lithospheric thickness.Explanation of Airy isostasyQuantities inferred from topographygravity comparison.Next : what sets the height of mountains?
18. CRUSTAL FLOW: THE MECHANISM THAT LIMITS THE HEIGHT OF TIBET AND THE ALTIPLANOHOW EROSION CAN LIFT MOUNTAINS: THE PROCESS RELATIONSHIP BETWEEN THE HEIGHT OF TIBET AND THE HEIGHT OF MT. EVERESTWhat limits the height of mountains?
19. Maximum mountain height in solar system contextVolcanic extrusion: MarsWhole-lithosphere breaking? Io, Boosaule Mons
20. AltiplanoTibetWhat limits the height of mountain belts on Earth?
21. Isostasy is not an equilibrium stateLiu & Shen, Tectonics, 1998
22. Crustal flowMcKenzie et al. JGR 2000
23. Gravitational collapse of mountain beltsCopley & McKenzie, Geophys. J. Int. 2007
24. CRUSTAL FLOW: THE MECHANISM THAT LIMITS THE HEIGHT OF TIBET AND THE ALTIPLANOHOW EROSION CAN LIFT MOUNTAINS: THE PROCESS RELATIONSHIP BETWEEN THE HEIGHT OF TIBET AND THE HEIGHT OF MT. EVERESTWhat limits the height of mountains?
25. adapted from Molnar & England 1990 Nature
26. Additional slides
27. FlexurePoisson’s ratiogravity (m/s^2)elastic thickness (m)flexuralparameter
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