1. Last Time: Ground Penetrating Radar Radar reflections image variations in Dielectric constant  r ( = relative permittivity )  3-40 for most Earth materials;  higher when H 2 O &/or clay present Radar attenuation similar to seismic: where:  higher for clay, silt, briny pore fluids Velocity is not estimated (rather depth is approx. from ~ V )  (but can be estimated from diffraction moveout!!!) Standard “processing” includes static corrections for elevation, filtering, AGC Geology 5660/6660 Applied Geophysics 03 Mar 2014 © A.R. Lowry 2014 For Fri 7 Mar: Burger 349-378 (§6.1-6.4)

2. Introduction to Gravity Gravity, Magnetic, & DC Electrical methods are all examples of the Laplace equation of the form:  2 u = f (sources), where u is a potential, is the gradient operator Notation : Here, the arrow denotes a vector quantity; the carat denotes a unit direction vector. Hence, the gradient operator is just a vector form of slope… Because Laplace’ eqn always incorporates a potential u, we call these “Potential Field Methods”. → ^

3. Gravity We define the gravitational field as And by Laplace’ equation, (1) given a single body of total mass M ; here G is universal gravitational constant = 6.672x10 -11 Integrating equation (1), we have (2) Nm 2 kg 2

4. IF the body with mass M is spherical with constant density, equation (2) has a solution given by: Here r is distance from the center of mass; is the direction vector pointing toward the center. Newton’s Law of gravitation: So expresses the acceleration of m due to M ! has units of acceleration  Gal in cgs (= 0.01 m/s 2 ) On the Earth’s surface, m/s 2

5. HOWEVER,  is not radially symmetric in the Earth… so is not constant! Gravity methods look for anomalies, or perturbations, from a reference value of at the Earth’s surface: 00 11 g ref g obs

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

7. Gravity Measurements: I. Absolute Gravity : Measure the total field  time of a falling body prism vacuum laser ~2m Must measure time to ~10 -11 s; distance to ~10 -9 m for 1  gal accuracy! Nevertheless this is the most accurate ground-based technique (to ~3  gal) Disadvantages: unwieldy; requires a long occupation time to measure

8. Gravity Measurements: II. Relative Gravity : Measures difference in at two locations. Pendulum : difference in period T : Errors in timing of period T  ~0.1 mgal Mass on a spring : M  g = k  l or  g = k  l / M Worden and Lacoste-Romberg are of this type (“zero-length” spring of L-R yields errors around 6  gal) l mass M length l spring constant k

9. Gravity Measurements: III. Satellite Gravity : Measure (from space) the height of an equipotential surface (called the geoid, N ) relative to a reference ellipsoid.

10. Gravity Measurements: Ocean Altimetry : Measure height of the ocean surface using radar or laser (e.g., JASON) Satellite Ranging : Satellite orbits follow the geoid Measure orbits by ranging from the ground to the satellite or ranging between two satellites (e.g., GRACE) N III. Satellite Gravity : Measure (from space) the height of an equipotential surface (called the geoid, N ) relative to a reference ellipsoid

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

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