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.

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 5660/6660Applied Geophysics

7 Mar 2014

© A.R. Lowry 2014For Mon 17 Mar: Burger 349-378 (§6.1-6.4)

€

∇2u =r

∇ •r g = −4πGM

€

rg = −4πG ρdV

Vol

∫∫∫

€

rg = ˆ r

GM

r 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 109 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 5660/6660Applied Geophysics

7 Mar 2014

© A.R. Lowry 2014For Mon 17 Mar: Burger 349-378 (§6.1-6.4)

Global Free-Air Gravity Field from GRACE

Example:

Image from UT-CSR/NASA

GRACE designed for time-variable gravity, mostly hydrosphere

GRACE Mass Trend 2003-2010: (Jacob et al., Nature, 2012)

Total mass trend Corrected for solid Earth(i.e., hydrology + cryosphere)

Image from UT-CSR/NASA

GRACE-derived mass trend over Greenland shows melting and accumulation; net loss is 222±9 km3/yr!

Contributionsto global sealevel 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

CARI (GPS)

But GRACE gives solid Earth info too!

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are needed to see this picture.

Example: Free Air Gravity from Satellite Ocean Altimetry

(Note altimeters wereactually intended to findout more about sea levelchange!)