me: Introduction to Gravity erned by LaPlace’s equation: h solution of the form: we have a spherical body with mass M and constant ( radially symmetric) density, this integral becomes: hod looks for anomalies in gravity g (relative to he gravity expected for a uniform-density ellipsoid hat result from lateral changes in mass density Geology 5660/6660 Applied Geophysics 7 Mar 2014 © A.R. Lowry 2014 r Mon 17 Mar: Burger 349-378 (§6.1-6.4) ∇ 2 u = r ∇ • r g = −4πGM g = −4 πG ρdV Vol ∫∫∫ g = ˆ r GM r 2
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.
Dec 29, 2015
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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!
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Example: Free Air Gravity from Satellite Ocean Altimetry
(Note altimeters wereactually intended to findout more about sea levelchange!)
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