1. Last Time: Introduction to Gravity Governed by LaPlace’s equation: with solution of the form: If we have a spherical body with mass M and constant (or radially symmetric) density, this integral becomes: Method looks for anomalies in gravity  g (relative to the gravity expected for a uniform-density ellipsoid) that result from lateral changes in mass density  Geology 5660/6660 Applied Geophysics 7 Mar 2014 © A.R. Lowry 2014 For Mon 17 Mar: Burger 349-378 (§6.1-6.4)

2. Last Time: Introduction to Gravity (Cont’d) Measurements may be surface-based (i.e., taken with instruments placed on the ground surface) or space-based ; absolute or relative Surface measurements accurate to ~3-6  Gals (for absolute gravimeters or relative measurements by Lacoste-Romberg): i.e., nearly one part in 10 9 of the total acceleration! Satellite measurements (especially GRACE) can be extremely accurate (<0.1  Gal!), but only at very large spatial scales (> 500 km) Time-variable gravity can be useful for understanding dynamical processes (fluid envelopes & solid Earth) Surface-based time-variable g used for environmental/ hydrologic applications Geology 5660/6660 Applied Geophysics 7 Mar 2014 © A.R. Lowry 2014 For Mon 17 Mar: Burger 349-378 (§6.1-6.4)

3. Global Free-Air Gravity Field from GRACE Example: Image from UT-CSR/NASA

4. GRACE designed for time-variable gravity, mostly hydrosphere

5. GRACE Mass Trend 2003-2010: (Jacob et al., Nature, 2012) Total mass trendCorrected for solid Earth (i.e., hydrology + cryosphere)

6. Image from UT-CSR/NASA GRACE-derived mass trend over Greenland shows melting and accumulation; net loss is 222±9 km 3 /yr! Contributions to global sea level change: Greenland: 0.61±0.02 mm/yr Antarctica: 0.45±0.20 mm/yr Continental: 0.41± 0.08 mm/yr Ice total: 1.48 Altimetry: 3.3

7. CARI (GPS) But GRACE gives solid Earth info too!

8. Example: Free Air Gravity from Satellite Ocean Altimetry

9. (Note altimeters were actually intended to find out more about sea level change!)