Overview: Basics of GPR Radar-wave velocity, attenuation and skin depth Modes of acquisition The Radar-range equation Dielectric properties of materials and relation to porosity Case studies [Archeology, engineering, forensics, glaciology, geophysics, mine-detection] EPS435-GPR_01
Geologic-profiling Mine-detection EPS435-GPR_02
Concrete Inspection Surveys http://www.worksmartinc.net/wlss.php http://www.geomodel.com/ Water-leak EPS435-GPR_03
http://www.geomodel.com/ EPS435-GPR_04
The GPR method is very similar to seismic reflection profiling, although the fundamental physics are completely different. Seismic methods are based on the elastic/acoustic properties of the subsurface material, where GPR is based the electro-magnetic properties. GPR is a EM-method, and uses EM waves to image the shallow subsurface. While seismic data is acquired with frequencies typically ranging between 10 and 200 Hz, GPR is using frequencies >> 100MHz. The speed of radar waves is dependent on the relative dielectric constant (ε r ) and the relative magnetic permeability (μ r ), as well as on the speed of light in free space (c = 0.3 m/ns). From Reynolds, 1997 EPS435-GPR_05
What is the dielectric constant? http://en.wikipedia.org/wiki/dielectric_constant The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. It is the ratio of the amount of stored electrical energy when a potential is applied, relative to the permittivity of a vacuum. It is also called relative permittivity. The dielectric constant is represented as ε r. It is defined as ε r = ε s / ε 0 [EQ 3.01] where ε s is the static permittivity of the material, and ε 0 is vacuum permittivity. Vacuum permittivity is derived from Maxwell s equations by relating the electric field intensity E to the electric flux density D. In vacuum, the permittivity ε is just ε 0, so the dielectric constant is 1. EPS435-GPR_06
The electro-magnetic properties of materials are related to their composition and water content, both of which exert the main control over the speed of radio waves propagation and the attenuation of EM waves in material. It is the contrast in the relative dielectric constant between adjacent layers that gives rise to the reflection of incident electro-magnetic waves. The greater the contrast in the speed (or dielectric constant), the higher the reflection coefficient. The speed of electromagnetic waves is given by: V = c / (A) ½, with A = ½ ε r μ r [(1+P 2 )+1], and c is speed of light. [EQ 3.02] Where ε r is the relative dielectric constant, μ r is the relative magnetic permeability, and P is the loss factor. EPS435-GPR_07
In the last equation, P is the loss factor and P is given by: P = σ / ωε, with σ as electrical conductivity, ω = 2πf, where f is frequency, and ε is the permittivity: ε = ε r ε 0 and ε 0 is permittivity of free space (8.854 10-12 F/m). If P 0, then the electromagnetic speed can be written as : V c / (ε r ) ½, or V 0.3 / (ε r ) ½. [EQ 3.03] The reflection strength (R) is given by: R = (V 1 -V 2 ) / (V 1 + V 2 ), or: R = [(ε r1 ) ½ -(ε r2 ) ½ ] / [(ε r1 ) ½ + (ε r2 ) ½ ] [EQ 3.04] EPS435-GPR_08
Attenuation and Skin depth Attenuation of radar waves can be seen equivalently to attenuation of seismic waves. A main process of attenuation is spherical spreading, loss through reflection/transmission, as well as scattering on objects. Effect from the equipment used (Radar-system effects) are typically available from the manufacturer. From Reynolds, 1997 EPS435-GPR_09
If the peak electric field strength of the radar wave on transmission is E 0 and at a distance x away from it has reduced to E x, the ratio of the two amplitudes is given by: E 0 /E x = exp(-αx), [EQ 3.05] Where α is the attenuation coefficient: με α = ω 1/ 2 2 1/ 2 σ 1 1 2 2 2 + ω ε [EQ 3.06] Within the equation of a, ω=2πf, f is frequency in Hz, μ is magnetic permeability (4π 10-7 H/m), σ is bulk conductivity at given frequency (S/m) and ε is the dielectric permittivity, where ε = ε r 8.85 10-12 F/m and ε r is the bulk relative dielectric constant. Note: this equation is valid for non-magnetic material only! EPS435-GPR_10
In the equation 3.06, the term σ/ωε is equivalent to the loss-factor P. P = σ/ωε. Also, the skin depth (δ) is given as: δ = 1 / α. [EQ 3.07] Skin depth δ is a measure for the depth at which the original amplitude is reduced to 1/e, (or to 37%). From Reynolds, 1997 Variation of skin depth δ as function of resistivity for ε r = 8 (crosses) and 40 (circles), which are the extremes in expected values for ε r in the ground. EPS435-GPR_11
Methods of acquisition: The easiest way of doing GPR measurements is to pull a closely-spaced pair of transmitter and receiver over the ground (image in right). This is equivalent to singlechannel (zero-offset) seismic profiling. From Reynolds, 1997 EPS435-GPR_12
Methods of acquisition: In addition to the zerooffset technique, GPR data are also acquired in WARR-mode, with increasing offset. WARR stands for wideangle reflection and refraction. Similarly, a CMP-mode can be achieved similarly to the seismic method (CMP = Common Mid Point) From Reynolds, 1997 EPS435-GPR_13
Methods of acquisition: GPR is also often used in tomography studies. This can be done in a mine with imaging material between mine-shafts (galleries) or doing cross-hole studies between two bore-holes. From Reynolds, 1997 Tomographic imaging is often used in building or construction damage assessments. EPS435-GPR_14