Geology 5660/6660 Applied Geophysics 29 Feb 2016 © A.R. Lowry 2016 Last Time: Ground Penetrating Radar (GPR) Radar = electromagnetic radiation (light) in the MHz (radio) frequency band  Governed by wave equation (  similar to seismic!)  Source & receiver are dipole antennae  Signal is a single pulse  Processing & display analogous to seismic section  High frequency  high resolution (but also)  High attenuation  Images changes in electromagnetic impedance Z For Wed 2 Mar: Burger (§ )

Last Time: Ground Penetrating Radar (GPR) Velocity (usually) is not estimated; emphasis is mostly on the the imaging of structure rather than physical properties. Instead TWTT  depth is approximated from rough ~ V Radar reflections image variations in dielectric constant  r ( = relative permittivity )  3-40 for most Earth materials;  higher when H 2 O &/or clay present Geology 5660/6660 Applied Geophysics 29 Feb 2016 © A.R. Lowry 2016 For Wed 2 Mar: Burger (§ )

For most applications (i.e., near-surface)  1 ≈  2 ≈ 1 ;  (10 -4 –10 -1 ) «  (10 6 –10 10 !), and hence (i.e., we are imaging velocity variations corresponding to changes in dielectric permittivity!) For the water table, R ~ 0.1 Recall seismic waves attenuate as where Q is quality factor; Radar waves attenuate similarly as ; where Attenuation is extremely high for shale, silt, clay, and briny water (which is why GPR rarely penetrates > 10 m!). 

Skin depth, or depth of penetration, is ~ 1/ . Hence main applications are in archaeology, environmental, engineering site investigation… Also used for cavity detection and other very near-surface applications GPR freqs

Frequency-dependence of the attenuation results in dispersion : High frequencies attenuate more rapidly; pulse appears to “broaden” and the phase is delayed: This has “appearance” of a lower velocity medium. GPR freqs

(From a very old cemetery in Alabama…) “Black-box” processing is simplistic so see some of the same features observed in low-level (brute stack) seismic processing:

Assuming a constant velocity can introduce a factor of 2 to 3 scale error in converting velocity to depth! ( But one could reduce velocity scaling error if  were calculated from, e.g., NMO or travel-time amplitude decay)…

V1V1 Alternatively can use moveout on Diffractions : h1h1 h2h2 x The equations are the same as they were for seismic, but since GPR is (usually) zero offset, x s = x g ! Thus rsrs xgxg

Note some data processing steps are similar to seismic but lack some tools (such as refraction velocity analysis). Commonly do static corrections for elevation, filtering, automatic gain control; much less common to migrate.

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’s eqn always incorporates a potential u, we call these “Potential Field Methods”. → ^

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

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