1. Geology 6600/7600 Signal Analysis 18 Nov 2015 Last time: Deconvolution in Flexural Isostasy Tharsis loading controversy: Surface loading by volcanic extrusives? Or dynamic uplift from plume buoyancy? Load deconvolution matrix for gravity and topography will be singular if the model predicts the same gravity/topography ratio for surface loading as for internal loading! (For Mars, at load depths ≥ 400 km, l = 2–25) Work-around: empirically limit near-singular amplitudes when observed geoid-topography-ratio is far from model range Using “reasonable” range of densities, crustal thickness, Te, load depths get < 30% of loading (< 50% of topography) from plume buoyancy; “best” model (minimizing load correlation) yields 8% of topo from deep buoyancy © A.R. Lowry 2015

2. Anomalous elevation of the western U.S. Cordillera (Lowry, Ribe & Smith, JGR 2000) Researchers have long noted that elevation of the actively extending Basin and Range province in the western United States is anomalously high (average ~1650 m) given the anomalously thin (30–35 km) crust. Hypotheses include hot lithosphere due to rifting (stretching) and hot asthenosphere introduced by the Yellowstone hotspot.

3. Method: Use gravity & topography to estimate T e and surface & internal loads. For this, we estimate reference density structure from crustal seismic refraction profiles and minimize the correlation of loads to choose T e. Use crustal seismic refraction data plus Christensen & Mooney [1995] velocity-density regression to estimate crustal mass variations. Use heat flow data to estimate lithospheric mass variations resulting from thinning of the thermal boundary layer. Subtract surface load topography, crustal elevation, and lithospheric thermal elevation from raw topography.

4. T e Estimation: T e that minimized correlation of the load fields was permitted to vary spatially. Low T e is found in regions of high heat flow and active extension; high T e in stable lithosphere. Seismicity and deformation tends to focus at transitions from high to low T e.

5. Surface Loads must be solved for as an interim step to T e estimation (i.e., prior to assessing which choice of T e in the flexural relations results in minimum correlation of the surface and internal loads. For Cartesian flexure using Bouguer gravity amplitudes and topography the relations can be written: where  1 &  0 are density at top & bottom ( h ) of the lithosphere respectively, and internal loading is modeled as topography on a surface w I at depth z L in the lithospheric interior with density contrast  L.

6. Surface Load Topography: Dominated by normal and thrust fault uplift features, stress- supported rift flank uplift, volcanically constructed topo (and their included flexural resp) Uncertainties reflect uncertainties in the estimate of T e, uncertainties in reference density structure, uncertainties in depth of loads, measurement error in the original topo and gravity… And singularity, mostly at longest wavelengths! Here, cheated a bit by nulling predicted surface load/flexure at “long” wavelengths.

7. Crustal Mass Contribution: Generally dominated by crustal thickness variations, but “Pratt” style internal density variations are also important (estimated here using Christensen & Mooney (JGR 1995) P -velocity/ density regression relations) Uncertainties reflect interpolation error, uncertainties in seismic velocity structure, errors in regression of seismic velocities to density

8. Thought I’d look…

9. For the thermal contribution to elevation: Collected and interpolated heat flow measurements from existing databases Filtered to remove variations with sources above the Moho Modeled the conductive geotherm (including effects of radiogenic heat production & extensional advection) Integrated the mass variation for assumed coefficient of thermal expansion Note correlation of heat flow and T e despite independent data sets!

10. Conductive Thermal Contribution: Thermal effect of stretching the lithosphere (i.e., thinning the thermal boundary layer) does contribute to high elevation of the northern Basin and Range province, but contribution is small relative to total elevation Uncertainties reflect interpolation error, errors in heat flow measurements, uncertainties in radiogenic heat production, thermal conductivity, coefficient of thermal expansion

11. Take: Minus: Equals: !

12. One Possibility:

13. But wait–We’ve seen elev modeling done (mostly) better in Becker et al. (2014)…