### Glossary

Term Description
Amplitude preservation frequency The Nyquist-Shannon theorem ensures that the spectral content of the original signal is preserved. If the amplitude of the signal peak is to be preserved, a higher minimal sampling rate is required. Maximum amplitudes values are often used for further analysis.

f_(Ampl)=f*12

Bandwidth Frequency range of the transmitted GPR signal measured at a decay of 3 dB below the maximum value.
Crossline Distance between profiles.

Other terms:
• X-Line
• Profile separation
Depth estimation Predicting the depth that can be reached with a GPR system is very difficult.The formulas do not account for the frequency dependency.
The maximum depth can be calculated:

z = 35/sigma

Another way to calculate the exploration depth is:

z = (15.9*sqrt(epsilon_r))/sigma

Both formulas are valid for a signal attenuation α > 0.1 dB/m and a conductivity σ > 1 mS/m.
In most circumstances both values are too high when compared with the effective penetration depth on site. These formulas are valid for pulsed systems only.
Dielectric constant

epsilon_r

Other terms:
• RDP
• Relative dielectric permittivity
Footprint Theoretical model to estimate the area covered by the antenna at a specific depth, length A is perpendicular, length B is parallel to the antenna:

A = lambda/4 + z/(sqrt(epsilon_r-1))

B = A/2

Fresnelzone Measure for the horizontal resolution (1/4 of the wavelength) of the signal (so called first fresnelzone) that can be achieved with a given antenna frequency and in a specified material:

r = sqrt((lambda z) / 2 + lambda^2/16)

Frequency The centre frequency f of the antenna is normally specified in MHz. For standard GPR antennas the bandwidth of the antenna is approximately equal to the centre frequency.
Inline Distance between two consecutive traces along the measurement line.

Other terms:
• Station interval
• Step size
• Trace distance
Loss tangent The loss tangent is the ratio of the total energy loss to the total energy storage.

tan delta=(17.8*sigma) / (epsilon_r*f)

Measurement conditions Determination of the central frequency of an antenna is very much depending on the coupling. Hence it is important to know in wich material the specified antenna frequency was determined.
If the frequencies are determined in air the actual frequency content of the data can be up to 20 % higher compared to normal ground conditions.
NM Abbreviation for Noise-Modulated system. This is a different approach using a special modulated signal that is emitted and finally cross-sorrelated with the response to generate a conventional trace. The speed is similar to an RTS the system and pemits to record the complete trace with one "pulse".
Nyquist frequency The Nyquist frequency is the maximum recordable frequency that can be recorded at a given sampling rate. All higher frequencies are aliased.

f_(Nyquist)=1/(2*delta t)

Offset Distance between transmitter and receiver of an antenna (Tx-Rx distance). This value is necessary for different advanced processing steps like NMO.
Parallel broadside Survey configuration with a transmitter (Tx) and receiver (Rx) antenna parallel to each other with their main radiation direction perpendicular to the survey direction.

Other terms:
• HH
Penetration depth This is another, more sophisticated estimate of the maximum depth of the system. For a ground-coupled antenna and a point reflector the frequency dependent signal decay (S) with depth for the material is estimated (see graph). The detection limit for a conventional normal system is indicated by (dN) and the one for a modern high performance, low-noise system by (dH). The intersections on the graph give an estimate of the maximum depth.
Perpendicular broadside Normal survey configuration with a transmitter (Tx) and receiver (Rx) antenna parallel to each other with their main radiation direction parallel to the survey direction.

Other terms:
• VV
Profile Display of consecutive traces measured along a continuous survey path.

Other terms:
• B-Scan
• Cross-Section
• Linescan
• Section
Q-Estimation Change of the shape of the radar pulse as it propagates through the material. This is an effect of freuqency dependant attenuation of electromagnetic waves. This effect is almost linear with frequency:

Q=(sigma)/(2*pi*f)+1

Range Length of the recording window, specified in nanoseconds.
Required sampling interval According to Textronix 10 samples per cycle are required. The highest frequency value can be approximated by double the antenna frequency. Hence the required sampling interval can be estimated by:

deltat_(required) = 100000/(2*f)

Required spatial accuracy If full 3D GPR data shall be recorded the accuracy with which the position should be maintained and recorded is:

deltax = 5/f

Required spatial interval If full 3D GPR data shall be recorded a minimum spatial sampling interval (horizontal distance between traces) is required:

Deltax = lambda/4

RTS Abbreviation for real-time sampling. The advances in electronics permit recording of much more than a single sample per transmitted pulse. The gain in speed is significant and is used for stacking of the data, resulting in a significant higher S/N ratio. Together with a modified recording system the bandwidth of the signal is enlarged at the same time. RTS might be called differently by each manufacturer.

Other terms:
• HDR
• Hyper stacking
Sample Individual eletrical value recorded in the system.

Other terms:
• value
Sampling interval

deltat

SFCW Abbreviation for stepped-frequency continuous wave.

Other terms:
• CWFM
• FMCW
Signal attenuation Reduction of the signal amplitude by the material:

alpha = 1.69*(sigma/sqrt(epsilon_r))

Speed of light c = 0.3 m/ns
Time- or Depth-slice Other terms:
• C-Scan
• Cross-section
• Horizontal slice
• Plan view
Trace Recording of individual samples at a single point representing the variation of the returned signal with time.

Other terms:
• A-Scan
• Scan
• Wiggle
Velocity Propagation speed of the electromagnetic wave for non-magnetic materials in the ground:

v = c / sqrt(epsilon_r)

Wavelength Distance between three consecutive zero-crossing of the wave, measured in the material to be investigated:

lambda = c / (f*sqrt(epsilon_r))

Many of the provided formulas are simplified alghorithms for complex and frequency dependent variables. Nevertheless the formulas give realistic estimations.

References:

A.P. Annan: Ground Penetrating Radar. Principles: Workshop Notes, Sensors & Software Inc., 1992

A.P. Annan: Ground Penetrating Radar. Principles, Procedures and Applications, Sensors & Software Inc., 2003

A.P. Annan, S.W. Cosway: Simplified GPR Beam Model for Survey Design, Extended abstract of 62nd Annual International Meeting of the Society of Exploration Geophysicists, New Orleans, 1992

L.B. Conyers: Ground-Penetrating Radar for Archaeology, Alta Mira Press, Walnut Creek, 2004

J.D. Daniels: Ground Penetrating Radar, IEE, London 2004

M. Dossi, E. Forte, M. Pipan: Minimum threshold for the sampling rate to prevent amplitude distortions in aliasing-free GPR surveys. 17th International Conference on Ground Penetrating Radar (GPR), 2018

M. Grasmueck, R. Weger, H. Horstmeyer: Full-resolution 3D GPR Imaging, Geophysics 70,1, K12-K19, 2005

O. Yilmaz: Seismic Data Processing. Investigations in Geophysics, SEG, Tulsa, 1987