Edits

content/geophysical_surveys/gpr/data.rst

@@ -1,65 +1,61 @@
 .. _gpr_csem_data:
 
+
 Data
 ====
 
-Measured Response
------------------
+.. figure:: images/GPR_schematic_example.jpg
+    :align: right
+    :figwidth: 55%
 
-During GPR surveys, a source antenna (Tx) is used to send a pulse of radiowaves (10 MHz to 2.6 GHz) into the ground. As the radiowaves propagate through the Earth, they are distorted as a result of the Earth’s electromagnetic properties. At boundaries where the subsurface electromagnetic properties change abruptly, radiowave signals undergo transmission, reflection and/or refraction. Distorted radiowave signals are then measured by the receiver antenna (Rx).
+    Schematic of a zero-offset GPR setup.
 
-The receiver antenna acts as a transducer and converts incoming radiowave signals into electrical current. Like the primary current within the transmitter antenna, the current induced within the receiver antenna is also a wavelet. The 
 
+During GPR surveys, a source antenna (Tx) is used to send a pulse of radiowaves (10 MHz to 2.6 GHz) into the ground. As the radiowave signal propagates through the Earth, it is distorted as a result of the Earth’s electromagnetic properties. At boundaries where the subsurface electromagnetic properties change abruptly, radiowave signals undergo transmission, reflection and/or refraction. Distorted radiowave signals are then measured by the receiver antenna (Rx).
 
+**What is measured:** Receiver antennas are sensitive to the electric fields carried by radiowave signals and act as transducers, converting incoming GPR signals into electrical current. The induced current produces a corresponding voltage which is then recorded. Ultimately GPR receivers measure the amplitude and polarization of incoming radiowave signals as a function of time. The change in amplitude and polarization of radiowave signals occurs as they are distorted by propagating through the Earth. Because the raw data are eventually normalized, the units are not particularly important.
 
-Processing
-----------
+**Measurement duration:** Radiowave signals for GPR propagate through the Earth at velocities comparable to the speed of light (c :math:`\approx 3.0 \times 10^8` m/s) and travel relatively short distances (metres to 10s of metres). As a result, the total travel times for GPR signals as they propagate from the transmitter antenna to the receiver antenna are very short. The time series collected for a single GPR shot typically lasts up to a few hundred nanoseconds after the signal is generated. However for GPR surveys meant to image very near to the surface (resulting in shorter travel times), data are collected for a shorter period after the transmitter emits the GPR signal.
 
-Gain Correction
-***************
+Because GPR measurements for a single shot are so short, they can be repeated many times for the same trasmitter-receiver pair at the same location (sounding). This allows the quality of GPR data to be improved by stacking (link).
 
-.. figure:: images/GPR_gain_time_function.png
-	:align: right
-	:figwidth: 40%
-
-	Example gain function which corrects for a loss in signal strength at later times.
 
+Visualization
+-------------
 
-Signals measured at earlier times are much stronger than signals which are measured at later times.
-This may be due to scattering, attenuation, geometric spreading or reflection/transmission events.
-As a result, it may not be easy to distinguish important features in the data at later times.
-To account for this, the raw data :math:`d_{raw}(t)` for each reading is multiplied by a gain function :math:`g(t)` as follows:
+2D Visualization: Radargram
+***************************
 
-.. math::
-	d(t) = g(t) \times d_{raw}(t)
+.. figure:: images/GPR_radargram_example.jpg
+    :align: right
+    :figwidth: 55%
 
+    Radargram showing hyperbolic signatures from two buried pipes.
 
-where :math:`d(t)` is the data represented in the radargram.
-The gain function itself is a positive function which increases in magnitude as a function of time.
-Thus a larger gain is applied to raw data at later times.
-An example of the gain function is shown on the right.
-As we can see, the gain function increases in value exponentially to account for the exponential loss in return signal strength over time.
-However, the gain function is generally bounded by a maximum value.
+To gain insight regarding buried structures, GPR measurements are performed at multiple locations using a particular survey configuration; notable survey configurations were discussed here (link). For common offset and common midpoint surveys, data are typically collected along one or more 2D profiles. By amalgamating the data, we can generate a radargram for each profile.
 
-.. figure:: images/GPR_gain_signal.png
-	:align: center
-	:figwidth: 100%
-
-	(Left) Single trace before gain correction. (Right) Single trace after gain correction.
+The horizontal axis (distance) is used to represent the location of the receiver relative to the transmitter for a particular sounding. The vertical axis shows the total travel times of measured signals. By assuming some a-priori knowledge of the radiowave velocity, the vertical axis is sometimes represented by an approximate depth. The gray-scale denotes the amplitude of the returning signal at each time and location.
 
+3D Visualization
+****************
 
-The strength of returning signals is also much weaker at distances further away from the source.
-Because of this, gain corrections may be applied based on Tx-Rx distance.
-This is not necessary for common offset surveys, but may be important in common midpoint or transillumination surveys.
+GPR data can be visualized in 3D if it is collected along multiple profile lines. Below we see two examples. On the bottom left, we see an example from the Furggwanghorn (link) case history. Here, each 2D profile is plotted separately. On the bottom right, we see GPR data collected over several buried storage tanks. These data were interpolated. The image shown is of several horizontal slices.
+
+.. figure:: images/3Dvisual.png
+    :align: center
+    :figwidth: 100%
+
+    (Left) Multiple radargrams collected over a glacier. (Right) Interpolated radargram data over a set of buried storage tanks.
+
+Processing
+----------
+
+Before raw data can be represented as a final radargram image, several processing steps are usually required. These are summarized below:
 
 
 Stacking
 ********
 
-GPR signals travel at velocities close to the speed of light (c = :math:`3.00 \times 10^8` m/s).
-As a result, the total travel times for GPR signals are on the order of 100s of nanoseconds.
-Because of this, it is easy to repeat the same GPR shot many times over a short interval.
-
 Stacking describes the process of averaging a set of repeated GPR shots in order to reduce noise and improve interpretation.
 Essentially, stacking acts as a way of improving the signal to noise ratio for GPR data collected at a certain location.
 An example of this is demonstrated below.
@@ -72,10 +68,6 @@ As we can see, the more readings we stack, the clearer we see coherent GPR signa
 
 	Example of how averaging multiple traces from the same Tx-Rx pair can improve the signal to noise ratio. This results in an improved image of the returning signal.
 
-
-
-
-
 Smoothing
 *********
 
@@ -94,12 +86,47 @@ We can see that as more data points in time are used for the average, the more e
 
 	Example of smoothing a trace by using a moving average.
 
+Gain Correction
+***************
+
+.. figure:: images/GPR_gain_time_function.png
+	:align: right
+	:figwidth: 40%
+
+	Example gain function which corrects for a loss in signal strength at later times.
+
+
+Signals measured at earlier times are much stronger than signals which are measured at later times.
+This may be due to scattering, attenuation, geometric spreading or reflection/transmission events.
+As a result, it may not be easy to distinguish important features in the data at later times.
+To account for this, the raw data :math:`d_{raw}(t)` for each reading is multiplied by a gain function :math:`g(t)` as follows:
+
+.. math::
+	d(t) = g(t) \times d_{raw}(t)
+
+
+where :math:`d(t)` is the data represented in the radargram.
+The gain function itself is a positive function which increases in magnitude as a function of time.
+Thus a larger gain is applied to raw data at later times.
+An example of the gain function is shown on the right.
+As we can see, the gain function increases in value exponentially to account for the exponential loss in return signal strength over time.
+However, the gain function is generally bounded by a maximum value.
+
+.. figure:: images/GPR_gain_signal.png
+	:align: center
+	:figwidth: 100%
+
+	(Left) Single trace before gain correction. (Right) Single trace after gain correction.
+
+
+The strength of returning signals is also much weaker at distances further away from the source.
+Because of this, gain corrections may be applied based on Tx-Rx distance.
+This is not necessary for common offset surveys, but may be important in common midpoint or transillumination surveys.
+
 
 
 
 
-Visualization
--------------
 
 
 

content/geophysical_surveys/gpr/survey.rst

@@ -20,54 +20,22 @@ Transmitter and Receiver Antennas
 Transmitter Antennas
 --------------------
 
-GPR transmitter antennas generally consist of an open circuit which carries an oscillating current of short duration, otherwise known as a wavelet. The current wavelet carried within the antenna is responsible for generating the pulse radiowaves; which is also a wavelet signal. If the transmitter antenna is small, then it may be treated as an electrical current dipole (link). GPR transmitter antennas operate at very high frequencies (10 :math:`\!^6` - 10 :math:`\!^9` Hz). Ultimately the characteristics of the GPR signal depends on its frequency content and the shape of the transmitter antenna.
+.. figure:: ./images/OpenCircuit.png
+		:align: right
+		:figwidth: 35%
+
+		Basic open circuit.
 
-**Add image**
+GPR transmitter antennas generally consist of an open circuit which carries an oscillating current of short duration, otherwise known as a wavelet. The current carried within the antenna is responsible for generating a pulse of radiowaves; which is also a wavelet signal. If the transmitter antenna is sufficiently small, then it may be treated as an electrical current dipole (link). GPR transmitter antennas generate signals with very high frequency content (10 :math:`\!^5` - 10 :math:`\!^9` Hz). Ultimately the characteristics of the GPR signal depends on the wavelet, its frequency content and the shape of the transmitter antenna.
 
 
 Receiver Antennas
 -----------------
 
-For GPR, measurements are made by a receiver antenna. Whereas transmitter antennas are transducers which convert electrical current into radiowave signals, receiver antennas are transducers which convert radiowave signals into electrical current. Because GPR receiver antennas are designed to effectively measure radiowave signals generated by the transmitter antenna, GPR systems are designed to use near-identical antennas for the transmitter and receiver.
+For GPR, measurements are made by a receiver antenna. Whereas transmitter antennas are transducers which convert electrical current into radiowave signals, receiver antennas are transducers which convert radiowave signals into electrical current. Because GPR receiver antennas are designed to effectively measure radiowave signals generated by the transmitter antenna, GPR systems are designed to use near-identical antennas for the transmitter and receiver. For some systems, the same antenna is used to transmit and receiver radiowave signals.
 
-.. sidebar:: GPR Antennas
-
-	**Dipole Antenna**
 
-	.. figure:: ./images/AntennaDipole.png
-		:align: center
-
-	**Broadband Dipole Antenna**
-
-	.. figure:: ./images/AntennaBroadband.png
-		:align: center
-
-	**Bow-Tie Antenna**
-
-	.. figure:: ./images/AntennaBowTie.png
-		:align: center
-
-
-Antenna Types
--------------
-
-There are a variety of transmitter antennas used for GPR. Below are several commonly used varieties:
-
-**Dipole Antenna:** Dipole antennas are the most straightforward transmitter used for GPR. Dipole antennas generally consist of two bilateral conductive rods. The efficiency of dipole antennas is strongly dependent on their length. Dipole antennas are most efficient when their total length :math:`L` is a multiple of the half-wavelength of the transmitter's current, i.e.:
-
-.. math::
-	L \approx \frac{n \lambda}{2}
-
-In these cases, the electrical current creates a standing waves in the transmitter antenna. Because of this, dipole antennas for GPR are designed to have a length which works well for a particular set of operating frequencies. Dipole antennas for GPR typically have lengths of 10s of centimetres up to a few metres.
-
-**Broadband Dipole Antenna:** Dipole antennas can be made more broadband by increasing the width of the conductive rods or by using elongated conductive plates. By making the antennas sufficiently broadband, we can more effectively transmit the entire frequency content contained within the source wavelet signal. As a result, broadband dipole antennas are a common choice for GPR applications.
-
-**Bow-Tie Antenna**: Bow-tie antennas consist of two symmetrically oriented flat conductors. Bow-tie antennas were designed to operate at freqencies between 100 MHz and 1 GHz. Thus they are ideal for GPR applications. Boe-tie antennas have become a more popular choice for GPR applications because they are wide-band and thus effective for a wide range of operating frequencies. 
-
-|
-
-
-.. sidebar:: Current Wavelet
+.. sidebar:: Source Wavelet Signals
 
 	.. figure:: images/GPR_wavelet_example.png
 		:align: center
@@ -81,31 +49,70 @@ In these cases, the electrical current creates a standing waves in the transmitt
 
 		Wavelet Bandwidth
 
+
 Transmitter Source Signal
 +++++++++++++++++++++++++
 
-The current which flows through the transmitter antenna can be described as a wavelet. The duration and frequency content of the current wavelet also characterizes the radiowave signal emitted by the transmitter. Some important properties of wavelets are defined as follows:
+The current which flows through the transmitter antenna can be described as a wavelet. The duration and frequency content of the current wavelet also characterizes the duration and frequency content of the radiowave signal emitted by the transmitter. Some important properties of wavelets are defined as follows:
 
 	- **Wavelet**: A wave-like oscillation of short duration.
 	- **Pulse Width**: The time duration of the wavelet.
 	- **Bandwidth**: The range of frequencies present in the source wavelet.
 	- **Central Frequency**: The central frequency corresponding to the bandwidth. Sometimes called the operating frequency.
 	- **Spatial Length (wavelength)**: The physical length of the wavelet signal while it propagates through a medium.
-	
-In general, the pulse width (:math:`\Delta t`) and central frequency (:math:`f_c`) are related by the following equation:
+
+Although GPR transmitters emit a time-dependent pulse of radiowaves, transmitter antennas are defined by their operating frequency. In general, the pulse width (:math:`\Delta t`) and operating frequency (:math:`f_c`) are related by the following equation:
 
 .. math::
 	\Delta t \approx \frac{1}{f_c}
 
-Thus higher frequency radiowave signals are contained within shorter wavelet signals. As we will discuss, the choice in pulse width (operating frequency) is a very important aspect of survey design.
+Thus higher frequency radiowave signals are contained within shorter wavelets. We also expect shorter wavelet signals to have shorter spatial lengths. In order to make shorter pulse lengths however, a larger band of frequencies is required. The previous points are summarized in the image below. As we will discuss in survey design (link), the choice in pulse width (or operating frequency) is very important.
+
+.. figure:: images/GPR_pulse_bandwidth.png
+		:align: center
+		:figwidth: 70%
+
+		Pulse length, frequency content and bandwidth for wavelet signals.
+
+
+.. sidebar:: GPR Antennas
+
+	**Dipole Antenna**
+
+	.. figure:: ./images/AntennaDipole.png
+		:align: center
+
+	**Broadband Dipole Antenna**
+
+	.. figure:: ./images/AntennaBroadband.png
+		:align: center
+
+	**Bow-Tie Antenna**
+
+	.. figure:: ./images/AntennaBowTie.png
+		:align: center
+
+Antenna Types
+-------------
+
+There are a variety of transmitter antennas used for GPR. Below are several commonly used varieties:
+
+**Dipole Antenna:** Dipole antennas are the most straightforward transmitter used for GPR. Dipole antennas generally consist of two bilateral conductive rods. The efficiency of dipole antennas is strongly dependent on their length. Dipole antennas are most efficient when their total length :math:`L` is a multiple of the operating frequency's corresponding half-wavelength, i.e.:
+
+.. math::
+	L \approx \frac{n}{2 f_c} = \frac{n \lambda}{2}
+
+In these cases, the electrical current creates standing waves in the transmitter antenna. Dipole antennas for GPR are designed to have a length which works well for a particular operating frequency. Dipole antennas for GPR typically have lengths of 10s of centimetres up to a few metres.
 
+**Broadband Dipole Antenna:** Dipole antennas can be made more broadband by increasing the width of the conductive rods or by using elongated conductive plates. By making the antennas sufficiently broadband, we can more effectively transmit the entire frequency content contained within the source wavelet signal. This antenna type is best used for operating frequencies below 250 MHz. 
 
+**Bow-Tie Antenna**: Bow-tie antennas consist of two symmetrically oriented flat conductors. Bow-tie antennas were designed to operate at freqencies between 100 MHz and 1 GHz. Bow-tie transmitters are a form of wide-band antenna; which is able to more effectively transmit signals with larger bandwidths compared to dipole antennas. As a result, bow-tie antennas are superior when transmitting short wavelength high frequency radiowave signals.
 
 
 Survey Configurations
 +++++++++++++++++++++
 
-The transmitter-receiver configuration used for a GPR survey is strongly dependent on the application. Below are the most commonly used transmitter-receiver configurations for GPR.
+The transmitter-receiver configuration used for a GPR survey is strongly dependent on the application. This will be discussed in detail in survey design (link). Below are the most commonly used transmitter-receiver configurations for GPR.
 
 Common-Offset and Zero-Offset
 -----------------------------