1. PTYS 554 Evolution of Planetary Surfaces Gravity and Topography II

2. PYTS 554 – Gravity and Topography II 2 l Gravity and Topography I n Shapes of planets, rotation and oblateness n Center of mass/figure offsets, fossil figures etc… n Hypsometry and geoids l Gravity and Topography II n Crustal isostacy vs. flexure vs. dynamic support n Gravity anomalies n Mapping crustal thickness n Topographic statistics on planetary surfaces

3. PYTS 554 – Gravity and Topography II 3 l Gravity measured in Gals n 1 gal = 1 cm s -2 n Earth’s gravity ranges from 976 (polar) to 983 (equatorial) gal n Sum of centrifugal and gravitational accelerations give expected gravity n Gravity anomalies (deviations from expect gravity) are measured in mgal l Gravitational anomalies n Only really addressable with orbiters n Surface resolution roughly similar to altitude n Anomalies cause along-track acceleration and deceleration n Changes in velocity cause doppler shift in tracking signal n Convert Earth line-of-sight velocity changes to change in g n Downward continue to surface to get surface anomaly n What about the far side of the Moon? Measuring Gravity with Spacecraft

4. PYTS 554 – Gravity and Topography II 4 l Flybys of Ganymede revealed gravity anomalies n Explainable with distributed mass excesses/deficits n Deficits in bright terrain, excess in dark terrain l Non-unique solutions show the value of an orbiter! Palguta et al., 2009

5. PYTS 554 – Gravity and Topography II 5 l Before we can start interpreting gravity anomalies we need to make sure we’re comparing apples to apples… Corrections to Observations l Free-Air correction n Assume there’s nothing but vacuum between observer and reference ellipsoid n Just a distance correction

6. PYTS 554 – Gravity and Topography II 6 l Bouguer correction n Assume there’s a constant density plate between observer and reference ellipsoid n Remove the gravitation attraction due to the mass of the plate n If you do a Bouguer correction you must follow up with a free-air correction Ref. Ellipsoid Ref. Ellipsoid Bouguer Free-Air

7. PYTS 554 – Gravity and Topography II 7 l Terrain correction n Not commonly done except in very mountainous regions n Divide terrain into radial sectors n Use DEM to find h at distance r 1 to r 2 l Eötvös correction n Vertical component of the coriolis force (for moving observers) l Tidal correction n Effects of Moons/Sun on local planetary shapes l Other corrections n Local-geology specific effects of density anomalies e.g. magma chambers etc...

8. PYTS 554 – Gravity and Topography II 8 l Start with g obs at P and Q l Do terrain correction first n If needed g obs – Δg T l Then remove bouguer plate g obs – Δg T – Δg B l Then do free-air correction g obs – Δg T – Δg B – Δg FA l The remove expected g o g obs – Δg T – Δg B – Δg FA – g o l This is the gravity anomaly n Often, for spacecraft data, only the free-air correction is made l Now we can compare gravity values from place to place

9. PYTS 554 – Gravity and Topography II 9 l Airy Isostasy n Compensation achieved by mountains having roots that displace denser mantle material n gH 1 ρ u = gr 1 (ρ s – ρ u ) l Pratt Isostasy n Compensation achieved by density variations in the lithosphere n gD ρ u = gh 1 ρ 1 = gh 2 ρ 2 etc.. l Vening Meinesz n Flexural Model that displaces mantle material n Combines flexure with Airy isostasy l Simple view of mountains n Supported by lithospheric strength n Large positive free-air anomaly n Bouguer correction should get rid of this l Anomalies due to mountains are much weaker than expected though n Due to compensation Effects of Compensation

10. PYTS 554 – Gravity and Topography II 10 Uncompensated Strong positive free-air anomaly Zero or weak negative Bouguer anomaly Compensated Weak positive free-air anomaly Strong negative Bouguer anomaly

11. PYTS 554 – Gravity and Topography II 11 l +ve free air l 0 free air l -ve free-air 0 Bouguer +ve Bouguer -ve Bouguer +ve Bouguer

12. PYTS 554 – Gravity and Topography II 12 l Two ways to interpret Bouguer anomalies n Mass excesses/deficits in the near surface n Constant density crust that varies in thickness wPlay off density contrast with mantle against the mean crustal thickness Interpretation of Anomalies

13. PYTS 554 – Gravity and Topography II 13 l Assume this… n Topography is compensated n Crustal density is constant l Bouguer anomalies depend on n Density difference between crust and mantle n Thickness of crust wNegative anomalies mean thicker crust wPositive anomalies mean thinner crust l Choose a mean crustal thickness or a crust/mantle density difference -ve Bouguer +ve Bouguer

14. PYTS 554 – Gravity and Topography II 14 l Craters <200km diameter n Negative Bouguer anomalies n Mass deficit due to excavated bowl and low density of fall-back rubble l Mountains n Positive free-air anomalies n Support by a rigid lithosphere l Mascons n First extra-terrestrial gravity discovery n Very strong positive anomalies n Uplift of denser mantle material beneath large impact basins n Later flooding with basalt l Bulls eye pattern – multiring basins n Only the center ring was flooded with mare lavas  Flexure l South pole Aitken Basin n Appears fully compensated n Older Lunar gravity Free-Air

15. PYTS 554 – Gravity and Topography II 15 l Crustal thickness maps show lunar crustal dichotomy Zuber et al., 1994

16. PYTS 554 – Gravity and Topography II 16 l Tharsis n Large free-air anomaly indicates it is uncompensated n But it’s too big and old to last like this n Flexurally supported? l Crustal thickness n Assume Bouguer anomalies caused by thickness variations in a constant density crust n Need to choose a mean crustal thickness n Isidis basin sets a lower limit Mars Gravity Zuber et al., 2000 Free Air

17. PYTS 554 – Gravity and Topography II 17 l Crustal thickness of different areas l But many features are uncompensated…. n So Bouguer anomaly doesn’t translate directly into crustal thickness Zuber et al., 2000

18. PYTS 554 – Gravity and Topography II 18 l Tharsis n Site of large +ve free-air anomaly n Surrounded by –ve anomaly ‘moat’ n Indicates at least some support by flexure of the lithosphere (~Vening Meinesz) Wieczorek, 2007 -ve free- air +ve free- air 0 free- air

19. PYTS 554 – Gravity and Topography II 19 l A common occurrence with large impact basins n Lunar mascons (near-side basins holding the mare basalts) n Utopia basin on Mars Initially isostatic +ve Bouguer 0 free-air Sediment/lava fill basin Now flexurally supported +ve Bouguer +ve free-air

20. PYTS 554 – Gravity and Topography II 20 l Crustal density is not always uniform l Smaller scale anomalies reveal buried flood channels n -ve free-air anomalies indicate fill with less dense material Actual free-air anomaly Predicted free-air anomaly Zuber et al., 2000

21. PYTS 554 – Gravity and Topography II 21 l South polar layered deposits of Mars n Large inner solar system ice sheet containing some dust… l Gravity data indicate density of 1220 kg m -3 n Water-ice with 15% dust Zuber et al., 2007

22. PYTS 554 – Gravity and Topography II 22 l Martian seasonal cap incorporate about 25% of the atmosphere n About ~7x10 15 Kg n Causes periodic flattening of the gravity field Smith and Zuber, 2005 Time variable gravity

23. PYTS 554 – Gravity and Topography II 23 l Large planets: Slower cooling, thinner lithospheres l Small free-air anomalies n Topography supported isostatically or dynamically

24. PYTS 554 – Gravity and Topography II 24 l Small planets: Faster cooling, thicker lithospheres l Large free-air anomalies n Topography supported by flexure of thick lithosphere

25. PYTS 554 – Gravity and Topography II 25 l Time for this? l Small scale topography characterized statistically n ‘Roughness’ is very scale dependant

26. PYTS 554 – Gravity and Topography II 26 RMS height vs profile length RMS deviation vs. lag RMS slope vs. lag Fourier power spectrum Commonly used 1D measures of roughness

27. PYTS 554 – Gravity and Topography II 27 l Decorrelation length, l n Where the autocovarience falls to half the its initial value the topography is ‘decorrelated’ Commonly used 1D measures of roughness Aharonson et al., 2001 where

28. PYTS 554 – Gravity and Topography II 28 l Median slope within a local area Commonly used 2D measures of roughness Aharonson et al., 2001

29. PYTS 554 – Gravity and Topography II 29 l Interquartile scale of elevations n The range of elevations that contains half the measurements Commonly used 2D measures of roughness Aharonson et al., 2001

30. PYTS 554 – Gravity and Topography II 30 l Spectral descriptions n Fourier power spectra