GEO 5/6690 Geodynamics 24 Oct 2014

© A.R. Lowry 2014Read for Fri 31 Oct: T&S 105-130

Last Time: Flexural Isostasy

Isostasy is a stress balance resulting in ~consistent pressure at “asthenospheric” depth. Airy isostasy balances vertical stress (in columns) only; flexural isostasy balances vertical + horizontal & is governed by a 4th order PDE:

For a perfectly elastic plate,

and for multiple layers:

For top-loading, the PDE has linear solution (in amplitudes ofsines/cosines) of the form:

€

∇2 D∇ 2w( ) + P∇ 2w + Δρgw = q

€

D =ETe

3

12 1−ν 2( )

€

D = D1 + D2 ⇒ Tetot= Te1

3 +Te2

33

€

WT

r k ( ) = −

ρ 0

Δρ +D

gk 4

HT

r k ( )

Next Journal Article(s) Reading:For Monday Nov 3: Audet & Bürgmann (2011) Dominant role of tectonic inheritance in supercontinent cycles. Nature Geosci. 4 184-187.Important to think about: What are the possible reasons for a directional dependence of Te? Also, read the abstract and conclusions (and look at the figures) of:Kirby & Swain (2014) On the robustness of spectral methods that measure anisotropy in the effective elastic thickness. Geophys. J. Int. 199(1) 391-401.

Problem: What if loads are both surface and internal?

• Total isostatic balance includes surface (topographic) mass plus internal mass variations plus lithospheric stress

• Surface loads are under- compensated by subsurface mass because of flexural strength of the lithosphere

• Internal loads are under- compensated by surface topographic response

If rigidity D and mean profile density of the lithosphere are known,can solve for two unknowns (surface and internal load mass)

from two observations (gravity and topography fields)

Separation of loads is useful for:

• Estimation of lithospheric strength and rheology (parameterized by effective elastic thickness Te)

• Understanding processes of mass redistribution in/on the Earth

Surface loading processes: Internal loading processes:

• Erosion/exhumation• Deposition• Normal faulting (footwall uplift)• Reverse faulting (hanging-wall thrust)• Volcanic construction

• Thermal mass variations• Compositional mass variations• Crustal thickening or thinning by lower crustal flow• Cooled igneous intrusions

Example Applications ofIsostatic Analysis:• Monday’s paper used separation of surface and internal loads for the western US• More commonly, Te is used to model surface processes (e.g., surface response to some “known” load such as basin deposition or erosional mass removal)• And of course Te has implications for strength & rheology

Implications For Mass Flux Processes:

Gravity & Topography reflect a complicated mix of all massflux processes… But if we can separate the loads from their

isostatic response, it narrows the field of candidate processes.

Surface Loads• Erosion• Deposition• Fault Displacement• Volcanic Construction

Subsurface Loads• Thermal Variations• Lithologic Variations• Crustal Thickness (Lower Crustal Flow)

METHOD:Using equations for observed topography h and Bouguer gravity anomaly b plus:

gives 2 eqns in 2 unknowns:

the definition of surface load gravity due to internal mass variation flexure of a thin elastic plate

Then search for Te (& perhaps other parameters) that minimize the difference between observed & predicted coherence

Or equivalently, that minimize correlation of the load fields

Elevation of the Western U.S.Cordillera?

Elevation of the activelyextending Basin and Rangeprovince in the westernUnited States isanomalously high (average~1650 m) given theanomalously thin (30–35km) crust.

Why?

Possible reasons include:• Hot lithosphere due to rifting (stretching) • Hot asthenosphere (e.g., introduced by the Yellowstone hotspot).

Lowry et al. JGR 2000

Surface Load Topography:

• Dominated by normal and thrust fault uplift features, stress-supported rift flank uplift, volcanically constructed topo

• Uncertainties reflect uncertainties in the estimate of Te, uncertainties in reference density structure, measurement error in the original topo and gravity

But mostly instability of the matrix solution for loading!

Crustal MassContribution:

• Used “old” seismic refraction data and estimated mass variations for both crustal thickness variations and internal density variations

• Note we need to know Te to turn mass variation (loading) into elevation!

• Uncertainties reflect interpolation error, uncertainties in seismic velocity structure, errors in regression of seismic velocities to density

Conductive ThermalContribution:

• Note error (neglected crust): Really should be ~30-50% larger.

• Thinning of the thermal boundary layer does contribute to high elevation but only partly explains total elevation

Uncertainties: interpolation error, heat flow measurement error, heat production model, thermal conductivity, coefficient of thermal expansion

Take:

Minus:

Minus:

Minus:

Equals:

Possibility we considered at the time:

Example: Tharsis Rise, Mars:

Martian topography is dominated by (1) a north-south hemispheric “crustal dichotomy” and (2) the Tharsis rise, average elevation 5000 m covering 20% of the planet

The geoid is the shape of the gravity field. The 2000 m geoidanomaly over Tharsis is the largestin the solar system!

The Tharsis Rise Loading Controversy:

Surface topography constructed by volcanism?

Thermal/chemical buoyancy of a single mantle plume?

[e.g., Willemann & Turcotte, 1982;Solomon & Head, 1982]

[e.g., Sleep & Phillips, 1979; Harder& Christensen, 1996; Harder, 2000]

Probably some combination of both!