REPORT OF INVESTIGATIONS 9666 

April 2006 

APPLICATIONS OF GROUND-BASED RADAR TO MINE SLOPE 

MONITORING 

Edward L. McHugh, Jami Dwyer, David G. Long, and Charles Sabine 

Department of Health and Human Services 

Centers for Disease Control and Prevention 

National Institute for Occupational Safety and Health 
Cover: Haul truck passing below a failing slope in a Wyoming coal mine. Note that the arcuate failure surface 

reaches almost to the top of the slope. 
REPORT OF INVESTIGATIONS 9666 

APPLICATIONS OF GROUND-BASED RADAR TO MINE SLOPE 

MONITORING 

Edward L. McHugh, Jami Dwyer, David G. Long, and Charles Sabine 

DEPARTMENT OF HEALTH AND HUMAN SERVICES 

CENTERS FOR DISEASE CONTROL AND PREVENTION 

NATIONAL INSTITUTE FOR OCCUPATIONAL SAFETY AND HEALTH 

April 2006 
ii

ORDERING INFORMATION 

Copies of National Institute for Occupational Safety and Health (NIOSH) documents 

and information about occupational safety and health 

are available from 

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4676 Columbia Parkway 

Cincinnati, OH 45226-1998 

 FAX: 513-533-8573 

 Telephone: 1-800-35-NIOSH 

 e-mail pubstaft@cdc.gov

 Web site: www.cdc.gov/niosh

DHHS (NIOSH) Publication No. 2006-116 

This document is in the public domain and may be freely copied or reprinted. 

Disclaimer: 

The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the 

National Institute for Occupational Safety and Health (NIOSH), nor does mention of any company or product 

constitute endorsement by NIOSH. 
iii

TABLE OF CONTENTS 

Page 

Abstract ............................................................................................................................ 1 

Introduction.......................................................................................................................... 2 

 Factors limiting slope stability ............................................................................................. 2 

 Standard highwall monitoring ............................................................................................... 2 

 Displacement monitoring using radar ...................................................................................... 3 

Radar technology ................................................................................................................... 3 

 History........................................................................................................................... 4 

 Imaging radar interferometry ................................................................................................ 5

 Differential interferometry............................................................................................ 6 

 Ground-based differential radar...................................................................................... 6 

 Static differential radar ................................................................................................ 6 

 SAR interferometry .................................................................................................... 7 

 Two-dimensional scanning interferometry ......................................................................... 7 

 Tracking mining hazards with radar........................................................................................ 8 

 Background.............................................................................................................. 9 

 Theory and methods ................................................................................................... 9 

 Field experiments ...................................................................................................... 10 

 Results and analysis.................................................................................................... 12 

Conclusions.......................................................................................................................... 16 

References ........................................................................................................................... 21 

Appendixes 

 A: The science of radar...................................................................................................... 20 

 B: Data tables on field experiments using radar to detect mining hazards .......................................... 27 

FIGURES 

Page 

1.—Highway failure at stone operation crushed dozer and fatally injured dozer operator............................. 3 

2.—Geometry of imaging radar system showing azimuth, look direction, and footprint............................... 6 

3.—Aircraft carrying the YINSAR system. .................................................................................... 8 

4.—Geometry of a system using two receiving antennas for elevation modeling ....................................... 10 

5.—Two-dimensional scanning radar configuration .......................................................................... 10 

6.—One-dimensional scanning radar configuration ........................................................................... 10 

7.—Site of YINSAR slope monitoring experiments .......................................................................... 11 

8.—Radar view of slope with man climbing. .................................................................................. 11 

9.—Baseline of slope with no displacement, test 1............................................................................ 13 

10.—Rock thrown onto slope at about 6 sec, test 2........................................................................... 13

11.—Man ascending slope, test 3 ................................................................................................ 14 

12.—Man descending slope, test 4............................................................................................... 14 

13.—Range interferometric phase image from test 4 showing data analysis segments.................................. 15 

14.—Interferometric phase image from 13 to 26 sec (test 4) showing data source for time/displacement 

 analysis....................................................................................................................... 16 

15.—Displacement on slope at a range of 32 m from radar, test 4......................................................... 16 

16.—Phase profiles along range from bottom to top of slope during three intervals, test 4 ........................... 17 

17.—Diagrammatic radar signatures possible for different failure types using two-dimensional radar 

 configuration ................................................................................................................. 17 
iv

TABLES

Page 

1.—Radar wavelengths and frequencies used in remote sensing............................................................ 4 

2.—Summary statistics for segments of test 4 data ........................................................................... 15

B1.—Phase data for a segment of test 4 ........................................................................................ 27 

B2.—Range interferometric phase profile data, test 4........................................................................ 32

UNIT OF MEASURE ABREVIATIONS USED IN THIS REPORT 

 cm centimeter 

 db decibel 

 GHz gigahertz 

 hr hour 

 Hz hertz 

 kHz kilohertz 

 km kilometer 

m meter 

MHz megahertz 

min minute 

mm millimeter 

mm/hr millimeter per hour 

sec second
1

APPLICATIONS OF GROUND-BASED RADAR TO MINE SLOPE 

MONITORING 

Edward L. McHugh,1 Jami Dwyer, 2 David G. Long,3 and Charles Sabine4

ABSTRACT 

Slope failure accidents were responsible for about 12% of U.S. surface mine fatalities between 1995 and 2003. Small 

surface movements on a mine highwall may be precursors of failure that, if detected, could provide sufficient warning to 

enable workers and machinery to be withdrawn to safety. Radar interferometry offers the necessary precision to detect these 

movements. Radar has some advantages over other methods in its ability to cover large surface areas for true twodimensional monitoring day and night under almost any weather condition. Radar’s active transmit/receive mode of 

operation provides for more direct sampling than do passive optical methods that depend on solar illumination. 

Improvements in microprocessor speeds and capacities have led to the development of a number of small, portable, groundbased systems; such systems are now being deployed at several locations around the world. As part of an ongoing study of 

monitoring technologies, researchers from the National Institute for Occupational Safety and Health and Brigham Young 

University, Provo, UT, cooperated to assess the feasibility of using interferometric radar to monitor mine slope stability. 

Field tests of a device incorporating prototype equipment were successful in that small, centimeter-scale displacements on 

rock slopes were detected. 

 

1

Physical scientist, Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA.

2

Mining engineer, Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA. 

3

Director, Center for Remote Sensing, Brigham Young University, Provo, UT. 4

Geopix, Sparks, NV. 
2 

INTRODUCTION 

 Some instability can be expected at any surface mining operation, but the unexpected movement of ground endangers 

lives and destroys property. Unstable slopes are hazardous for miners who work on or beneath them, and large-scale failures 

have the potential to cause catastrophic loss of life. Between 1995 and 2003, 42 miners died in slope failure accidents at 

surface mines in the United States. Rocks falling from highwalls above the victims caused 24 of these deaths. While small 

rockfalls can cause fatal injuries to workers on foot away from the protection of large machinery, shovel operators and 

drillers suffered the greatest number of fatalities in massive highwall failures. 

 A research project was begun at the Spokane Research Laboratory, National Institute for Occupational Safety and Health 

(NIOSH), to improve recognition of slope stability hazards at surface mines. A principal objective of the project is to 

improve means for detecting conditions in open-pit mines that could lead to catastrophic slope failure. One approach taken 

was to assess the application of remote-sensing technologies to mine slope safety. Remote sensing is the science of deriving 

information about a site by using instruments to collect measurements from a distance without making direct contact with the 

objects being studied. 

 Three aspects of remote-sensing technology—hyperspectral imaging, interferometric radar, and photographic image 

analysis—are being evaluated as tools to help recognize potential hazards at mine sites. These technologies have been 

developed mainly as airborne or satellite instruments, but their spatial resolution and sampling intervals are not sufficient for 

addressing local ground control problems in surface mines. Only recently have increased microprocessor speeds, data 

storage capacities, and signal processing capabilities led to the development of smaller, portable, ground-based systems. 

Adaptation of these technologies to simplified ground-based instruments could provide a cost-effective means to reduce 

injuries from catastrophic failure of mine slopes. 

 This paper summarizes developments in the application of ground-based radar to slope stability monitoring and presents 

information on NIOSH-sponsored experiments recently completed. Field tests of a hyperspectral imager were conducted to 

assess its value for improving geologic maps of potentially unstable alteration zones on mine slopes (McHugh and others, 

2001). Computerized monitoring methods using images from digital and video cameras are being assessed for application to 

mine slope surveillance (McHugh and Girard, 2002). 

FACTORS LIMITING SLOPE STABILITY 

 Mine slopes are designed with an engineered factor of safety to control the risk of injury and damage to miners and 

equipment from rock falls and slope failures. Geologic structures, rock mass properties, and hydrologic conditions are 

elements to be considered in designing a safe and efficient mining operation. The need to control costs commonly results in 

pit walls being made as steep as practical to minimize waste removal and surface disturbance, and to maximize ore 

recovery. However, steeper walls normally mean a greater potential for slope instability. 

 Blasting practices can be adapted to minimize unnecessary fracturing of the highwall. Groundwater, surface water, and 

precipitation runoff can be controlled to abate their deleterious effects on stability. Benches and berms are normally used to 

stop rocks before they can fall far enough to present a significant hazard. Mechanical rockfall catchment systems or 

secondary supports may used where feasible to stabilize slopes as needed in particular locations. 

 However, even carefully designed and constructed slopes may fail (figure 1) because of unidentified geologic structures, 

unexpected weather conditions, or seismic activity. For this reason, regular examination and systematic monitoring of slopes 

for early warning signs of failure are the most important means of protecting exposed mine workers. 

STANDARD HIGHWALL MONITORING 

 Conventional modern monitoring methods depend on regular benchmark surveys that commonly use reflecting prisms at 

specific locations as well as visual inspections. These techniques may be augmented by detailed recording of movement at 
3

known problem sites using extensometers, tension-crack 

monitors, or other instruments. Additional instruments can be 

used as part of a comprehensive system to register subsurface 

rock mass displacement, groundwater parameters, and blast 

vibration levels. Aside from visual inspection, these methods 

provide displacement information only for a single site, or at 

best, a discrete number of sites. If the monitored sites are too 

widely separated or if displacement occurs between sites, 

early indications of a pending slope failure might go 

unnoticed. In addition, these monitoring tools are difficult to 

install at many quarries and surface coal mines where steep 

highwalls and lack of benches limit access to areas above the 

working floor. As mining progresses and monitoring 

different sections of the pit walls becomes necessary, 

relocating monitoring devices is not only costly and time 

consuming, but can also be dangerous on unstable slopes. 

 Point-by-point monitoring of every potential failure block 

on a mine slope is not practical, but a new generation of 

scanning laser rangefinders has partially addressed this under-sampling problem by detecting movement over large areas. 

These instruments can generate digital models of mine slopes without reflector prisms. Displacement can be detected by 

comparing successive scans. Scanning lasers will likely prove to be a practical solution in some mine slope monitoring 

applications, but processing requirements and scan rates have so far made repeat pass intervals too great for effective, timely

slope monitoring. In addition, the range and accuracy of these systems can be impaired by differences in the reflectivity of 

the rock, the angle of the rock face, weather, vegetation, and other factors. 

DISPLACEMENT MONITORING USING RADAR 

 Radar has some advantages over other methods in its ability to cover large areas on the surface for true two-dimensional 

monitoring day and night in almost any weather, and atmospheric dust and/or haze have little effect. Radar’s active 

transmit/receive mode of operation also provides an advantage over passive optical methods that depend on solar or other 

illumination. 

 Although radar technology has been widely used for the last 50 years, only in the last 10 years have advancing computer 

capabilities provided the low-cost processing power needed for interferometric computations. The widespread adoption of 

modern wireless communication devices has resulted in practical integrated circuits for microwave frequencies that can be 

used in task-specific radar applications. To evaluate this technology and to assess the feasibility of using interferometric 

radar to monitor mine slope stability using prototype equipment, a cooperative agreement was established between NIOSH 

and the Center for Remote Sensing at Brigham Young University (BYU), Provo, UT. 

RADAR TECHNOLOGY 

 The term radar is an acronym for Radio Detection and Ranging. It operates in the radio and microwave portions of the 

electromagnetic spectrum at wavelengths ranging from a few millimeters to about a meter. The radar spectrum is itself 

divided into a number of bands having letter designations that were originally adopted for security reasons during World 

War II and that are still used as a shorthand reference (table 1). Radar is an active remote sensing system that provides its 

own energy to illuminate targets of interest and records the return signal reflected from a target. Passive systems, such as 

aerial photography and multispectral sensors, detect solar or thermal radiation reflected or radiated from the ground. 

Because radar systems provide their own energy, they can operate during daylight or at night. Systems with longer 

wavelengths can penetrate clouds to reveal the terrain beneath. 

Figure 1.—Highwall failure at a stone operation crushed dozer 

and fatally injured dozer operator (November 13, 2002). (Photograph courtesy of Mine Safety and Health Administration, 2002.) 
4 

Table 1.—Radar wavelengths and frequencies used in remote sensing. 

Band Wavelength ( λ ), cm Frequency (ν ), GHz 

(109 cycles/sec) 

Common applications 

Ka (0.86 cm) 0.8 to 1.1 40.0 to 26.5 Navigation, weather, synthetic 

vision, altimeters 

K 1.1 to 1.7 26.5 to 18.0 Weather, police, scatterometers, 

Doppler location 

Ku 1.7 to 2.4 18.0 to 12.5 Search, fire control, altimeters, 

scatterometers, precipitation 

X (3.0, 3.2 cm) 2.4 to 3.8 12.5 to 8.0 Navigation, surveillance, SAR, 

weather, police 

C 3.8 to 7.5 8.0 to 4.0 SAR, weather, fire control, altimeters

S 7.5 to 15.0 4.0 to 2.0 Maritime, weather, space, SAR, 

microwave ovens 

L (23.5, 25.0 cm) 15.0 to 30.0 2.0 to 1.0 Early warning, SAR, SEASAT 

P 30.0 to 100.0 1.0 to 0.3 Early warning , SAR, wind profilers 

Bands with wavelengths in parentheses are those most often used in imaging radars. Letter designations were 

adopted during World War II for security reasons. (Adapted from U.S. Dept. of Commerce, 2003, and Skolnik, 1990.)

HISTORY 

 Observers noted the reflection of radio waves from objects in the landscape in the late nineteenth century. The first 

patent for using radar to detect ships was issued in 1904. Research and development took place in the United States, Britain, 

and Germany almost simultaneously during the 1920's and 1930's, with the United States and Britain focusing primarily on 

navigation and detection of aircraft and ships. Significant advances were made in radar development by both Allied and Axis 

countries during World War II. 

 Early radar systems utilized the familiar rotating antenna and circular cathode ray tube display known as a plan position 

indicator (PPI). PPI systems transmitting from the ground to the air encountered a great deal of noise or ground clutter. 

Investigators first tried to eliminate it, but soon realized that the noise was a crude image of the ground terrain. This led to 

airborne PPI's that directed their signals downward toward the ground to provide a continuously updated “map” of the 

surface as a navigation aid. Pilots and navigators used boundaries between contrasting surfaces, such as water and land, or 

large features, such as buildings and cities, to find their way to their destinations. 

 British night-fighter aircraft first used airborne radar to detect enemy aircraft and later as an aid for nighttime or 

inclement-weather bombing. This later application led directly to the development of side-looking airborne radar (SLAR) 

mapping by the military in the early 1950's as a means to acquire images of ground surfaces without flying directly over the 

imaged area. Data were recorded on photographic film as holograms that were converted to images by a set of optical 

lenses. These early imaging radars were real-aperture or “brute force” systems. Advances in antenna design, centimeterwavelength components, and recording devices significantly improved resolution for military reconnaissance. 

 Declassification of SLAR technology led to an explosion of research and development through the 1960's, and imaging 

radar soon became a useful remote-sensing tool. Real-aperture surveys became available commercially in 1969. These early 

systems were simple in design, required little signal processing, and were inexpensive to operate. However, these 

noncoherent SLAR's could not generate high-resolution imagery from data collected at long range. The National 

Aeronautics and Space Administration (NASA) acquired extensive unclassified, multi-polarized, K-band imagery of the 

United States during the late 1960's and early 1970's. Companies such as Westinghouse, Motorola, and 

Goodyear/Aeroservice actively collected radar data in the United States and other countries, including Panama, Brazil, 

Venezuela, Nigeria, and Indonesia. Radar's capability to penetrate clouds in tropical regions led to the first detailed maps of

these areas. 
5

 Synthetic aperture radar (SAR) was being developed concurrently with real-aperture radar in the early 1950's. The 

concept of SAR is generally attributed to Carl Wiley of the Goodyear Aircraft Corp., who found that an artificially long 

antenna could be synthesized using a transported small antenna. For a coherent radar system, a Doppler shift from reflected 

objects occurred as the objects appeared to pass through the radar beam. Spectral analysis of Doppler and phase histories of 

return signals resulted in constant azimuth resolution as a function of range (Curlander and McDonough, 1991). Resolution 

of a radar image improves as wavelength becomes shorter with respect to antenna length. Transporting a relatively small 

antenna to synthesize a long antenna (aperture) permitted the use of longer wavelengths, which are less sensitive to 

atmospheric attenuation, and the acquisition of fine spatial resolution at high altitudes (Campbell, 1996). Advances in signalprocessing techniques over the succeeding decades and the introduction of “chirp” encoding of transmitted pulses led to 

high-resolution images that could be acquired at long ranges. Imaging radar could now be deployed on orbital platforms. 

 With the launch of Landsat 1 in 1972, remote-sensing research was directed away from radar toward reflected radiation 

collected by optical-mechanical scanners in the visible and near-infrared portions of the electromagnetic spectrum. 

Subsequent launches of Landsat 2 in 1975 and Landsat 3 in 1978 provided repeated worldwide coverage of the earth’s 

surface at a resolution of 80 m. 

 After almost a decade of data collection by Landsat, limitations in the imaging data had become apparent. Cloud cover 

was the most serious limitation; vast regions of tropical terrain shrouded in clouds had never been imaged by Landsat. A 

second limitation was the seasonally restricted solar illumination at high latitudes, particularly during long polar nights. 

There was a pressing need to monitor sea ice in shipping lanes on a 24-hour basis, which Landsat could not provide. 

 Radar was recognized as a possible answer to these problems because surface interactions in the microwave portion of 

the electromagnetic spectrum can provide new information that is different from what is observed in the visible and nearinfrared. Oceanographers realized that while color information provided by visible light was important, active radar systems 

could provide additional information on the state of the sea. Seasat, the first SAR imaging radar in space, was launched in 

June 1978 to investigate oceanic phenomena, such as ocean roughness, wave patterns, currents, and pack ice. However, it 

shut down prematurely in October 1978 because of an electrical failure. In the few months it was operational, Seasat proved 

valuable for terrestrial observations as well, despite its small incidence angle that caused severe distortions in mountainous 

areas. Geoscientists found a wealth of structural and geomorphic information in Seasat images that led to renewed interest in 

imaging radar. Seasat was followed by space shuttle imaging radar experiments (SIR-A, SIR-B) and a host of follow-on 

commercial and research radar satellites still currently in operation (Richards and Jia, 1999). 

IMAGING RADAR INTERFEROMETRY 

 Radar interferometry is the use of radar signals traveling two different paths to determine range information from the 

coherent interference between the two signals. Imaging radar interferometry combines images recorded from antennas at 

two different locations to form a spatial baseline. Using the phase difference between the returns to the antennas, 

interferograms can be constructed that record minute differences on a subwavelength scale for corresponding points on the 

image pair. Such interferograms can be used to map topography, measure velocities of objects, and detect temporal change. 

An important application of interferometry in radar is topographic mapping (Zebker and others, 1992; Robertson, 1998; 

Thompson, 2001) where interferometry is combined with SAR to make radar backscatter images and to derive surface 

topography. 

 Spatial baselines are used primarily for topographic mapping. A basic SAR configuration is employed with the beam 

orthogonal to the track. Two receiving antennas are used, usually with one mounted over the other on the fuselage of an 

aircraft or on a satellite. This sort of configuration allows measurement of target height relative to the platform to 

subwavelength accuracy. Simultaneous measurement of short range, look direction, and look angle provides absolute threedimensional locations of each image point (figure 2). From these data, topographic maps or digital elevation models can be 

created, and image artifacts such as foreshortening and layover can be corrected. 

 Topographic mapping can be done with two separate passes and a single receiving antenna or with a single pass and two 

receiving antennas separated by a fixed baseline in the cross-track (range) direction. In two-pass interferometry, the baseline

is defined by the slight difference in the flight paths (in the cross-track direction) of the two passes and requires very precise 

flight path information. Aircraft interferometers are generally dual-antenna, single-pass systems, while dual-pass interferom-
6 

etry is generally reserved for spacecraft where prediction of the 

platform’s motion is more precise. 

Differential Interferometry 

 Temporal baselines are used for velocity mapping and change 

detection. Differential interferometry compares interferometric 

measurements taken at different times to identify very small 

changes, often smaller than the radar wavelength. The method 

assumes that measurements are made from identical tracks at 

different times, which is possible with orbital platforms, but difficult with aircraft. Aircraft motion due to wind drift, roll, pitch, 

and yaw must be known accurately through precise navigation. 

 Repeat observations by satellites can record velocities as small 

as centimeters per day, which is suitable for mapping ice movement and certain kinds of downslope movement. Repeat observation can also be used for longer-term changes of landscape features. If the topography is known, then surface movement due to 

earthquakes and landslides can be measured, and growth of vegetation can be monitored. 

 Interferometry can also be used to measure ocean surface currents from moving aircraft by aligning the two antennas in 

the along-track (azimuth), rather than the cross-track, direction. In this case, interferometry allows estimation of the 

Doppler shift induced by the moving ocean surface. Azimuth interferometry is sensitive to surface changes in the alongtrack/vertical plane. An aircraft configured with one antenna behind the other can measure temporal changes on the order of 

0.01 to 0.1 sec, which is suitable for measuring velocities on the surface on the order of centimeters per second. This type 

of configuration may be used to monitor ocean surface motion and vehicular traffic. 

 One of the earliest and most spectacular applications of radar interferometry for change detection was accomplished at 

the site of the Landers earthquake of 1992 in the Mojave Desert of California (Massonnet, 1997; Massonnet and others, 

1993, 1994). A sequence of ERS-1 radar satellite images of the Landers area before and after the earthquake revealed interference fringes when topographic effects were removed by means of a digital elevation model. Each cycle of interference 

fringes corresponded to 28 mm of seismic movement. Interference patterns also revealed movement on smaller faults in the 

region, including 7 mm of movement on a fault 100 km from the epicenter of the Landers quake. Similar applications of 

radar satellite data have been used to map and monitor landslides, ice movement, and volcano deformation (Fruneau and 

Achache, 1996), and subsidence caused by the extraction of groundwater, oil and gas, or minerals (Carnec and others, 

1996a, b; Stow, 1996; Dixon, 1995). These pioneering studies have generated enormous interest in the earth sciences 

community because they point to an entirely new way to study the surface of the Earth. 

Ground-Based Differential Radar 

 Slope-monitoring radar to detect hazards needs a much shorter repeat time and greater spatial resolution than airborne 

and satellite systems can provide. Ground-based interferometric radar systems have been designed to monitor displacement 

of unstable slopes both in landslide-prone natural settings and at mine sites. 

Static Differential Radar 

 In 1997, field experiments using a static differential radar configuration were conducted by Malassingne and others 

(2001) to test its potential for use in monitoring active volcanoes. The system used a wide-band radar centered at 26 GHz 

(25 to 27 GHz). Short pulses of a few centimeters were transmitted, and return signals were processed to retain phase data. 

Corner reflectors provide a much stronger back-scatter signal than natural surfaces and, with reflectors, absolute distance 

can be measured to an accuracy of about 1 mm at a range of 1,500 m. Differential measurements at that range had a typical 

accuracy of 0.1 mm. Atmospheric effects were almost completely removed by comparing return signals from two locations 

Figure 2.—Geometry of imaging radar system showing azimuth, look direction, and footprint. 
7

separated by a short distance along the line of sight. 

 Back-scattered responses from natural slopes were used to calculate intercorrelation, from which apparent radial 

displacement could be measured, to monitor sites that were too unstable for the installation of reflectors or where reflectors 

had been destroyed. To measure topographic changes, return signals were compared for data collected before and after an 

interval of time. Decorrelation between the two data sets was a measure of the change that occurred during the interval. 

 The 1997 field experiments compared a 40- by 40-m active rockfall area to a relatively stable bedrock slope. The targets 

were sampled in differential mode at a distance of 1 km from the radar antenna and separated by 40 m along the line of 

sight. The rockfall area showed a substantial decorrelation over the 4 days of the experiment, while the more stable slope 

where changes were minimal showed a high degree of correlation. 

SAR Interferometry 

 Experiments in the use of ground-based SAR interferometry to detect displacement associated with landslide motion 

were conducted by Tarchi and others (2003). The site of the experiments was the Tessina earth slide in the eastern Italian 

Alps. The radar system, called Linear SAR (LISA), consists of continuous-wave stepped-frequency (CW-SF) radar with 

rail-mounted transmitting and receiving antennas. The survey system, as well as other sensors, serves as an early-warning 

system for the safety of residential areas below the slide area. 

 The instruments were mounted at a stable location facing the landslide area at an average distance of 500 m. The radar's 

field of view is about 800 m long and 350 m wide. The rail was mounted on a concrete wall, and electronic components 

were installed in an existing building that also contained robotic survey instruments used to monitor the position of 30 

benchmarks on the slope automatically. 

 The radar operated in the frequency band of 16.70 to 16.78 GHz with steps of 100 kHz for a total of 801 frequency 

points. The synthetic antenna aperture was attained by moving the antennas along a straight rail across 2.4 m at 6-mm steps 

for a total of 401 azimuth points. Acquisition time was about 14 min. The radar system configuration and slope geometry 

resulted in a range resolution of about 2 m and an azimuth resolution of about 2 m at the center of the range. Differential 

interferometry for the system had a theoretical displacement resolution of about 0.5 mm along the radar line of sight, 

equivalent to a phase shift of about 20° at the frequencies used. 

 Repeat pass (zero baseline) data collection over a period of several days yielded data sets to produce about 400 SAR 

images. Pairs of images were used to generate differential interferograms showing displacement over time on the landslide 

surface. Unwrapping the phase shift through successive interferograms over a period of 48 hours yielded a nearly constant 

11.7 mm/hr rate of displacement at one surveyed benchmark. This displacement agreed to within 3 mm with surveyed data 

over the interval. 

 Because the design allows for short repeat times (about four times an hour), changes in dielectric constants are 

negligible. A mask is applied to eliminate pixels where temporal decorrelation has diminished the reliability of the phase 

measurement. The experiments showed that this approach to slope monitoring can produce highly accurate displacement 

information over virtually the entire slope with a 2-m spatial resolution. 

Two-Dimensional Scanning Interferometry 

 A scanning radar system using differential interferometry was designed by researchers at the University of Queensland, 

Australia (2002) specifically for monitoring mine slopes. The system, known as slope stability radar (SSR), uses realaperture, 2° beam-width radar to scan a slope both vertically (height) and horizontally (azimuth). Scanning at a rate of 

10°/sec over a range of ±60° vertically and 340° horizontally, the system continuously monitors the slope face for 

deformation. The return signal phase is recorded for each pixel in the resulting image, and phase unwrapping is used to 

remove the 2π ambiguity (Reeves and others, 1997, p. 123). 

 A commercial trailer-mounted unit is available for lease (Ground Probe Pty., Ltd., S. Brisbane, Australia). It features a 

0.92-m-diameter scanning parabolic dish antenna, mounts, controlling/data-collecting computer, remote area power supply, 
8 

warning siren and lights, CCD camera, communication links, and Internet compatibility. Typical scan repeat time is 15 min. 

The system can operate at a range up to 450 m from the target slope. Line-of-sight displacement can be measured to ±0.2 

mm without the use of reflectors. 

 In operation, the system produces an image that shows spatial deformation relative to a reference image for the entire 

slope scanned. The displacement history of each point in the image can be plotted. Total displacements and rates of change 

on the slope are valuable factors in assessing the risk to operations below and when or if operations should be discontinued. 

TRACKING MINING HAZARDS WITH RADAR 

 A radar system designed and assembled at BYU was configured for a series of experiments to evaluate the approach for 

identifying small-scale displacement on mine slopes. The technology stems from research efforts at BYU to build a low-cost 

interferometric synthetic-aperture radar (InSAR) system that could be deployed in light aircraft and operate at low altitudes 

(Lundgreen and others, 2000). NIOSH funding facilitated field tests of a ground-based version of the radar system to detect 

and measure displacement on mine slopes. Such displacement measurements can be used to track mass movement of failing 

slopes in surface mines and possibly warn of imminent catastrophic collapse. The ground-based approach has the distinct 

advantages of high resolution derived from a smaller radar footprint and a high sampling rate (repeat times in seconds) to 

provide real-time displacement detection. 

 The compact InSAR developed at BYU’s Center for Remote Sensing is intended to make imaging radar inexpensive 

enough for small-scale mapping projects (figure 3). The system was funded in part by a NASA grant (Thompson and others, 

1998) and has been used recently in collaboration with the U.S. Geological Survey to periodically collect images of a landslide area in Colorado. 

Figure 3.—Aircraft carrying the YINSAR system. Inset shows computer and IF/RF subsystems, and 

laptop controller. 

Figure 3.—Aircraft carrying th YINSAR system. Insert shows computer and IF/RF subsystems, and 

laptop controller. 
9

BACKGROUND 

 After developing a series of small, low-cost SAR systems in the mid-1990’s, the design team at BYU began 

development of a novel, non-SAR interferometric radar system designed to detect railroad track hazards resulting from 

rockfalls. This system was designed to be very low cost and short range (Waite, 2000). The intention was to adapt this 

system (by extending its range) to support experiments in highwall stability monitoring. As the track hazards system 

developed, the design proved to have inadequate long-term phase stability and could not be used for the proposed mine slope 

experiments. As a result, development was initiated for a new prototype natural hazards radar system with an improved 

chirp transmitter and a fully coherent oscillator scheme to maximize long-term stability. The original system has since been 

modified by an independent firm for use as a road traffic monitoring system and is now being sold commercially. 

 At the same time, development was begun of an X-band interferometric SAR system (known as YINSAR) for operation 

in a small plane (figure 3). When completed, the YINSAR system was successfully used in a multi-season experiment to 

collect interferometric data over a landslide in Colorado and an archeology site in Utah. Conclusion of the planned flight 

program allowed a reconfiguration of the YINSAR hardware to support the mine slope monitoring experiments. 

THEORY AND METHODS 

 Experiments were designed to demonstrate that changes in an interferometric radar signal resulting from small changes 

in a rock face could be detected in a mine environment. Interferometry is based on the difference in signal phase between 

two observations and thus requires a coherent (phase-preserving) measurement system. Interferometry is widely used in 

radio astronomy and has become important in radar where the inherent coherence of radar signals can be exploited. With 

YINSAR, two antennas separated by a baseline receive a radar echo from a target surface. The antennas are offset in the 

cross-track (range) direction. The phase difference in the echo from each distance (range) bin measured at each antenna can 

be related via the geometry of the measurement to the height of the surface (Zebker and Goldstein, 1986). 

 Small surface movements on a mine highwall that could be precursors to a failure may provide sufficient warning to 

enable men and machinery to be withdrawn to safety (Fukuzono, 1990; Voight, 1989). Such movements may be less than a 

few centimeters and thus require precision measurement systems. Radar interferometry offers the desired precision and can 

operate at night and through smoke and dust without requiring reflectors on a highwall face. This feature allows workers to 

avoid the hazards they would face while installing reflectors on a potentially unstable highwall. 

 In simple terms, radar measures the path length between the antennas and each resolved portion of the highwall face. 

Changes in the path length will be due to movement on the highwall face. As suggested by the geometry shown in figure 4, 

cross-track interferometry compares distance to the target from each antenna by tracking relative phases of the return signal 

at each antenna to yield height information in the cross-track/vertical plane according to the formulas 

 2 2

1 R = (H − h) + x , (1) 

 2 2

2 R = (H + B − h) + x , (2) 

and ∆R = R2 − R1 (3) 

where R1 and R2 = range from target to receiving antennas 1 and 2, 

 H = height of lower receiving antenna above datum, 

 h = height of target above datum, 

 x = horizontal distance to target, 

 B = distance between receiving antennas, 

and ∆R = difference in range between target and receiving antennas 1 and 2. 

 This simple picture is complicated by a number of factors. Humidity variations in the intervening atmosphere can give 

rise to apparent path length changes. Any variations in the location of the microwave scattering centers within the resolution 

element due to moisture content, freezing, liquid water, snow, etc., can also give rise to path length changes. These effects 

vary with radar operating frequency and configuration. While variation of the microwave scattering center with environ- 
10 

mental conditions is inherent to the problem, the effect can be 

ameliorated by interferometric processing and the operating 

frequency employed. 

 Two approaches to the application of radar interferometry 

for highwall monitoring can be distinguished based on the 

number, characteristics, and movement of the radar antennas. 

One approach uses a single, two-dimensional scanning 

antenna; the second uses dual receiving antennas and onedimensional scanning. The latter can be further separated into 

azimuth and range subclasses based on the relative orientation 

of the two antennas. Both approaches have advantages and 

disadvantages. 

 In the first approach, a single pencil-beam antenna is 

scanned in two dimensions over the highwall face (figure 5). 

At each scan location, a radar signal is transmitted, and the radar echo received and processed. The radar signal phase 

recorded at each scan location is preserved. The face is repeatedly scanned in time. The phase measured at each location is 

compared to the phase of the previous scan (or a time average of previous scans). Differences in phase between scans are 

related to face movement with an estimated correction based on weather conditions. This approach requires a high-precision, 

two-dimensional scanning system and exceptionally phase-stable radar, both conditions that add to the expense of the 

system. This approach forms the basis of the monitoring system developed in Australia (University of Queensland, 2002). 

 The second approach adopted for these experiments uses a fan-beam transmitting antenna to illuminate the entire vertical 

face over a narrow horizontal distance. The face is scanned repeatedly in a horizontal (one-dimensional) sweep (figure 6). 

Two receiving antennas are separated by a short baseline. The radar’s range resolution enables vertical resolution of the 

face. The interferometric phase difference between the receiving antennas (which is due to the small path length difference 

between the target and each antenna) is recorded for each scan position. Since the radar is stationary, the differential 

interferometric phase between scans can be easily computed. The differential phase is very sensitive to changes in the 

surface in the plane of the baseline orientation, e.g., either azimuth (horizontal) or range (vertical). (Note that with three 

receiving antennas, azimuth and range interferometry can be done simultaneously.) However, because the interferometric 

path length for a given scan is nearly the same, the atmospheric effects are similar for both channels, and interference is 

minimized. Furthermore, this approach does not have the stringent long-term phase stability requirements of the pencilbeam, two-dimensional scan design, although two receivers and antennas are required. In addition, since scanning is in a 

single dimension, the scanning system is simpler than a two-dimension system. 

FIELD EXPERIMENTS 

Slope monitoring experiments using the YINSAR apparatus were conducted at a sand-and-gravel operation near Provo, 

UT (figure 7). To simplify the tests, the system used fixed antenna positions without the scanning configuration necessary to 

cover the full face as would be required in an operational system. Due to battery power limitations and because the YINSAR 

hardware is unsuited for long-term outdoor deployment, data were collected only for short periods. 

Figure 4.—Geometry of a system using two receiving antennas 

for elevation modeling. 

Figure 5.—Two-dimensional scanning radar configuration. Figure 6.—One-dimensional scanning radar configuration. 
11

The system operates at 9.9 GHz with a 200-MHz bandwidth, giving it a 60-cm range resolution. While a lower 

operating frequency would make the system less sensitive to environment-induced scattering center variations, the system 

was suitable for a proof-of-concept experiment. The final intermediate frequency is all-digital with the signal digitized at 500 

MHz. The pulse repetition frequency was 1200 Hz while the pulse length varied from 0.1 to 150 microseconds. 

 The system had separate receiving and transmitting antennas (bistatic). The antennas were slotted wave-guide-fed horns 

with beam widths of approximately 12° horizontally and 45° vertically. The two receiving antennas were in a range 

interferometric layout with a vertical separation (baseline) of 60 cm (figure 8). A phase change of 2π radians corresponded 

to 3 cm of surface change. The instrument was set up approximately 30 m from the base of a 35°-gravel slope about 11 m 

high. Test 1 (baseline) was an initial measurement of the undisturbed slope. Test 2 showed the effect of throwing a softballsized rock onto the slope, disturbing the surface and shifting a few other rocks. In test 3, a man climbed up the slope, and in

test 4, the man descended. 

Figure 7.—Site of YINSAR slope monitoring experiments. Gravel pile is about 11 m high and has a slope of about 35°. 

Figure 8.—Radar view of slope with man climbing. Inset shows transmitting antenna (left highlight) and receiving antennas (right highlights). 
12 

RESULTS AND ANALYSIS 

 Processed radar data for the four tests are shown in figures 9 through 12. Magnitude and phase are shown graphically 

for each of the two receiving channels as a function of slant range (distance from the radar) and time. The bottom diagram 

in each figure combines data from the two channels to show the interferometric phase at each range cell as a function of 

time. The radar was not scanned as it would be if the entire slope were to be monitored; the images represent a topographic 

slice along the radar beam from the bottom of the slope to the top over the footprint width of the beam (about 4 m). In 

figure 9, the vertical band near 0 m is the result of the radar interacting with itself, the ground, and the truck; this can be

ignored. The band between 20 and 30 m is the face of the gravel slope. Note that in the later figures, the radar selfinteraction occurs at about 10 m, and the slope face is between 30 and 40 m as a result of a change in radar settings. 

 In the baseline interferometric image (figure 9, bottom), the slope is unchanged over the time of the scan, as shown by 

the uniform vertical bands (with minor phase variations)–elapsed time runs from 0 sec at the top of the image to more than 9 

sec near the bottom. The bands represent the static topography of the slope, as shown by phase differences that result from 

the different path lengths for return signals to the two vertically separated receiving antennas. The phase values here are 

unimportant, but result from interaction of radar frequency and the angle of the slope across the range bins. 

 Figure 10 shows the radar response of a softball-sized rock striking halfway up the slope at about 6 sec. The static 

profiles of the slope before and after the impact demonstrate the sensitivity of the radar to even very small changes in the 

surface. The difference in the profiles shows that a lasting change occurred on the slope. 

 Figure 11 shows the progress of a man climbing the slope as the change in phase moves from nearer to greater range, 

i.e., from the left of the slope bands near the top of the image diagonally toward the right over a period of less than 20 sec.

Figure 12 shows the man descending the slope and the phase change moving closer to the instrument (right to left 

diagonally) with time. Note the difference in static slope profiles, which reveal surface change before (e.g., 5 sec) and after

his passage (30 sec). 

 A closer look at the interferometric phase plot for data shown in figure 12 provides a method for measuring 

displacement detected during the test (figure 13). The value of the interferometric phase is shown in the scale at the right of

figure 13, extending between approximately -3 and +3 radians (±π) and encompassing the range of gray-scale color values 

from 0 to 255. Each pixel in the image array has x and y coordinates and an associated data value (Dv) corresponding to this 

scale. Image processing software (Envi 3.2) from Research Systems, Inc., Boulder, CO,5

 was used to quantify the phase 

scale and radar return data by resolving numeric values pixel by pixel. For the interferometric phase at 0 radians, Dv = 127 

at the middle of the color range. Lighter colors (higher Dv) have a limit of Dv = 255 at a positive interferometric phase of 

+π radians; darker colors (lower Dv) represent a negative phase to Dv = 0 at –π radians. A Dv change of 41 (255 -127/π) 

therefore represents a phase change of one radian, yielding the following relationships: 

 Φ = (Dv – 127)/41 (4) 

and ∆Φ = ∆Dv/41 (5) 

where Φ = phase, radians, 

and ∆Φ = phase change, radians. 

 Phase data are plotted by range in horizontal bands every 0.05 sec down the image (y-axis). Range values (x-axis) are 

grouped in segments averaging 4.3 pixels wide, corresponding to the 60-cm instrument resolution. 

 A section of the radar image (box in figure 13) was enlarged to analyze incremental displacement on the slope. For the 

column of data at 32 m (vertical line in figure 14), Dv was recorded over the interval from 13 to 26 sec, and the difference 

between each succeeding pixel, sampled at 0.05 sec, was computed. This difference represents the interferometric phase 

change over the sample increment. The raw data are provided in table B1. 

 

5

 Mention of specific products and manufacturers does not constitute endorsement by the National Institute for 

Occupational Safety and Health. 
13

 For interferometric radar with separate transmitting and receiving antennas, displacement is related to phase change 

by the formula— 

 ∆d = (∆Φ λ)/2π (6) 

where ∆d = displacement, cm, 

 ∆Φ = phase change, radians, 

and λ = radar wavelength, cm. 

 Wavelength of the 9.9-GHz YINSAR radar is 3.03 cm. Displacement that occurred from one time increment to the next 

is computed by converting the Dv difference between pixels to phase change, then using the above formula. For example, 

between 18.30 and 18.35 sec, Dv changed from 177 to 9 (∆Dv = -168), corresponding to a phase difference of -4.10 

radians. From the equation, net displacement between those two pixels is ∆d = (-4.10 *3.03)/2π or ∆d = -1.98 cm. 

Negative displacement denotes movement toward the instrument (downslope). 

Figure 9.—Baseline of slope with no displacement, test 1. 

Top: Magnitude and phase of each receiving channel as a 

function of time; bottom: range interferometric phase 

showing self-interference near 0 m and return from slope at 

about 20 to 30 m. 

Figure 10.—Rock thrown onto slope at about 6 sec, test 2. 

Top: Phase of each receiving channel; bottom: interferometric phase. 
14 

 The radar's phase change represents a weighted average of displacements over the footprint of the beam resolution 

element, representing a net effective displacement. Since the return for a small area within the resolution element is 

dominated by the background area, we cannot "see" the small area very well, even if the amount of displacement is large. 

Because we are seeking to detect changes in the average phase for each resolution element over time, detailed phase 

unwrapping is unnecessary. 

 Apparent displacement for each successive time increment along the sample line is shown in figure 15. The trace clearly 

shows an inactive interval prior to the slope disturbance (before), a period of change while the man descends the slope 

(during), and a restabilization of the slope following the traverse (after). Table 2 provdes summary statistics for these 

intervals. Baseline data show that the system configuration tested has about a 0.2-cm displacement resolution (two standard 

deviations above the mean) and a signal-to-noise ratio (variance) of 128. The 3-cm maximum possible displacement 

recorded by this method is determined by the radar wavelength. Measuring cumulative displacement across multiple time 

increments in this simple experiment was not possible because of inherent phase ambiguity in the data for this particular 

setup. 

Figure 11.—Man ascending slope, test 3. Top: Magnitude 

and phase of each receiving channel; bottom: range 

interferometric phase. 

Figure 12.—Man descending slope, test 4. Top: Magnitude and phase of each receiving channel; bottom: 

range interferometric phase.
15

Figure 13.—Range interferometric phase image from test 4 showing data analysis segments. 

Table 2.—Summary statistics for segments of test 4 data. 

Test segment Baseline prior to 

displacement (before) 

Active displacement 

(during) 

Stabilizing in new 

configuration (after) 

Time interval, sec 13.0 thru 17.45 17.50 thru 23.14 23.78 thru 25.59 

Minimum, cm -0.56841 -2.59195 -0.23873 

Maximum, cm 0.30694 2.56922 0.32968 

Range, cm 0.87535 5.16117 0.56841 

Sample variance, cm 0.01120 1.43829 0.01914 

Standard deviation, cm 0.10585 1.19929 0.13834 

Count 83 107 35 

 Phase data in the range direction allowed the slope profiles to be compared during the test interval. The phase at each 

range increment from about 26 to 40 m was computed from Dv for 0.1-sec intervals at about times t = 10, 22, and 28 sec 

(before, during, and after) the man traversed the slope (see figure 13). The results of the analysis are shown in figure 16 

(see table B2). The "before" and "after" data show similar profiles, which can be thought of as baseline data; differences 

reflect a lasting change in slope geometry caused by the man’s passage. The “during” data show distinct interferometric 

phase shifts compared to baseline profiles as a result of active displacement in the radar footprint. 

 Implementation of a scanning mechanism for horizontal sweeps of the slope with a fan-shaped beam would provide 

three-dimensional data to assess the stability of the mine highwall. Processing would allow automated computation of 

displacement, velocities, and acceleration for each point on the slope. Data could be used to generate two-dimensional 

images of the highwall, such as the examples shown diagrammatically in figure 17, to assist in analyzing failure 

mechanisms. Using the same scale as in previous interferometric images (e.g., figure 13), where darker colors indicate 

movement toward the instrument, lighter colors indicate movement away from the instrument, and gray shows no relative 
16 

motion, a scanning system could help define the nature of 

movement on a slope. Rotational failure is shown by motion both 

toward and away from the instrument, while wedge and toppling 

failures are characteristically shown by movement toward the 

instrument. 

CONCLUSIONS 

 Ground-based interferometric radar has the potential to measure displacement over large areas of mine highwalls at an unprecedented resolution. Prototype versions based on technology from 

a number of approaches have been introduced at several locations. Based on our simple experiments, range interferometry 

clearly has the desired sensitivity and thus is a functional 

approach for low-cost slope monitoring. Further development is 

required, however. 

 The objectives for this future work will be to design a practical ground-based interferometric radar instrument for measuring 

small increments of displacement on rock slopes as an aid to an 

assessment of slope stability. Such an instrument would be— 

● Robust and easily transportable. 

● Simple enough to be operated by nonexperts. 

● Reasonably priced. 

● Able to present displacement data with two- or three- 

 dimensional images of a slope. 

● Capable of operating autonomously where continuous moni- 

 toring is required. 

● Able to measure displacement of less than 1 cm. 

● Capable of a spatial resolution approaching 2 m. 

● Able to monitor rock slopes from a range of at least 1 km. 

 Design development to support longer-term experiments will 

need to address such issues as scanning rates, alarm detection 

thresholds, the effects of weather, and methods to prevent 

interference from ordinary mining operations (e.g., movement of 

equipment). In particular, the effects of weather on radar return 

from the surface are critical. Moisture on a rock face will likely 

change the scattering center, which could be interpreted as changes 

on the monitored slope. Detection algorithms must be sufficiently 

sophisticated to provide reliable discrimination between changes in 

atmospheric conditions versus actual displacement. The radar’s 

long-term phase stability and effects of conditions such as snow 

and ice accumulation on benches or water running down the 

highwall face need to be tested. Carefully conducted monitoring of 

real highwall faces with independently verified readings will be 

essential for ultimately validating this technology. 

Figure 14.—Interferometric phase image from 13 to 26 sec 

(test 4) showing data source for time/displacement analysis 

(vertical line). 

Figure 15.—Displacement on slope at a range of 32 m from 

radar, test 4. 
17

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Martinez, A., and A.P. Byrnes. 2001. Modeling Dielectric-Constant Values on Geologic Materials: An Aid to GroundPenetrating Radar Data Collection and Interpretation. Current Research in Earth Sciences, Bull. 247, Part 1, pp. 1-16. 

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Figure 16.—Phase profiles along range from bottom to 

top of slope during three intervals, test 4. 

Figure 17.—Diagrammatic radar signatures possible for different failure types using two-dimensional radar configuration. 
18 

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Canberra, Australia, pp. 119-123. 

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University, Provo, UT, 140 pp. 

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of ERS SAR Interferometry (Zurich, Switzerland). http://www.geo.unizh.ch/rsl/fringe96/papers/

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20 

APPENDIX A: THE SCIENCE OF RADAR 

RADAR EQUATION 

 The radar equation (Skolnik, 1990, p. 1.6) can be written as 

2 2 4 4πR

A

σ

πR

PG P r

rt

t t

r = (A1) 

where Pr = received power at polarization r,

 Pt = transmitted power at polarization t,

 Gt = antenna gain in direction of target at polarization t,

 R = distance between radar and target, 

 Ar = effective receiving area of receiving antenna aperture at polarization r,

and σrt = radar cross-section or the area intercepting that amount of power of polarization t, which, when 

scattered isotropically, produces an echo at polarization r equal to that observed from the target. 

 The radar equation assumes that the transmitting and receiving antennas are at the same location. A radar beam 

illuminates an area of the surface that is larger than the ground resolution cell. It is useful to define an average differential, 

or radar cross-section per unit area, and to consider the average return power. The total average return power is found by 

integrating the radar return from each differential area over the entire illuminated area as follows: 

 ∫ =

Ao

o r

rt

t t

ar ds

πR

A

σ

πR

PG P 2 2 4 4 (A2) 

where Par = total average return power, 

 s = surface integral taken over the irradiated area A0,

and o

rt σ = scattering coefficient. 

 The effective size of the antenna aperture is related to the antenna gain by 

 π

G λ A r

r 4

2

= (A3) 

where λ = wavelength. 

 Therefore, 

 ( ) ∫ =

Ao

o

rt

t t r

ar σ ds

R

PG G

π

λ P 3 4

2

4 . (A4) 

 All parameters of the radar equation (Pt, G, λ) are fixed by the operator, and R is known by the location of the radar 

relative to the target. The scattering coefficient is the only variable in the radar equation that governs the average return 

power strength. In addition to the radar parameters (Pt, G, λ, R), the scattering coefficient is also influenced by surface and 

volume parameters that include slope aspect relative to the radar beam, surface roughness, volume scattering, dielectric 

constant, depression angle, and polarization. 

 Pulse repetition frequency largely determines the maximum range of the radar set. If the period between successive 

pulses is too short, an echo from a distant target may return after the transmitter has emitted another pulse. This would 
21

make it impossible to tell whether the observed pulse is the echo of the pulse just transmitted or the echo of the preceding 

pulse. This produces a situation referred to as “range ambiguity.” The maximum unambiguous rate is the longest range to 

which a transmitted pulse can travel and return to the radar before the next pulse is transmitted. 

SCATTERING MECHANISMS 

 The radar return from natural terrains involves both surface- and volume-scattering mechanisms. The return for snowcovered ground, for example, may include surface scattering from air-snow and snow-ground interfaces and volume 

scattering from the interior of the snow layer. Similar statements can be made for vegetated terrains and heterogeneous 

ground surfaces. 

 Ground surfaces can be modeled mathematically in terms of facets, spheres, cylinders, and dihedral and trihedral corner 

reflectors. Surface-scattering mechanisms arising from these models have been applied to three basic types of surfaces: 

1. Surfaces with horizontal roughness scales greater than the incident radar wavelength, 

2. Surfaces with slopes and roughness scales that are small compared with the incident wavelength, and 

3. Some combination of the above mechanisms. 

 Volume-scattering mechanisms have been studied for two basic types of heterogeneous media: continuous 

heterogeneous media and homogeneous media with discrete scatterers embedded (Moore, 1990; Toomay, 1989). 

 Some general conclusions emerge from modeling studies. For surface scattering with incidence angles less than 30°, the 

expected interaction mechanism is quasi-specular reflection or diffraction from locally smooth facets that are larger than the 

incident radar wavelength. For incidence angles in the 30° to 80° range, any significant radar return is likely to be in the 

form of Bragg scattering, where roughness scales with a horizontal dimension l satisfies the relationship 

 2lsinθ = λ . (A5) 

 Cross-polarized surface backscattering in the range o o 0 ≤θ ≤ 80 arises from scattering by multiple surfaces. The crosspolarized return is usually more than 10 db lower than the like-polarized return from the same surface. 

 Volume scattering from a weakly heterogeneous medium or a medium with sparsely distributed scatterers is likely to 

produce a polarized radar return from a single-scattering process; cross-polarized returns arise from a second-bounce 

mechanism. The cross-polarized return is usually more than 15 db lower than the like-polarized return. In strongly 

heterogeneous media, multiple scattering effects become important, producing cross-polarized signals raised to within 10 db 

of the like-polarized return from the same target. Multiple scattering is much more important in producing a cross-polarized 

component than in producing a like-polarized component. 

INFLUENCES ON RADAR RETURN 

 Factors that influence the strength and character of return radar signals fall into two categories: system parameters and 

target parameters. System parameters include radar polarization, look direction, resolution cell size, wavelength, and 

depression angle. Target parameters include the complex dielectric constant, surface roughness, and surface cover. All of 

these factors are somewhat interdependent, and certain tradeoffs may be necessary to achieve the best possible radar images. 

System Parameters 

Polarization 

 Although early imaging radars used circular polarization, most imaging radars transmit electromagnetic energy with the 

electrical vector in the horizontal plane and can receive return signals in either the horizontal (HH or like-polarized) or 

vertical (HV or cross-polarized) plane. Differences in tonality between like- and cross-polarized returns in radar imagery 

can be used to differentiate geologic and geographic features. 
22 

 Four mechanisms are known to cause cross-polarized radar returns (Campbell, 1996): 

1. Quasi-specular reflection, 

2. Multiple scattering as a result of surface roughness, 

3. Multiple volume scattering due to heterogeneities, especially those embedded within a skin depth of a target surface, and 

4. Physical or geometric anisotropic properties of a target. 

 The first three of these are commonly encountered in remote-sensing applications. Quasi-specular reflection from 

smoothly undulating surfaces predicts essentially no cross-polarized return at near-vertical incidence angles and increasing 

levels of cross-polarization at larger incidence angles. The cross-polarized component is weak compared to the likepolarized return. Cross-polarized returns due to multiple reflections from rough surfaces and from volume scattering predict 

fairly uniform returns at all incidence angles except near-grazing. Multiple volume scattering produces stronger crosspolarized returns than scattering due to surface roughness. Multiple volume scattering from vegetation is also a major cause 

of cross-polarization. Returns from bare ground have little or no cross-polarized component. The difference in strength of 

returns from like- and cross-polarized signals remains fairly constant as incidence angles increase to near-grazing. 

Look Direction 

 Look direction, the direction of the transmitted radar beam, can be crucial to the quality of a radar image. Look 

direction is generally perpendicular to the direction of movement of the radar platform and is commonly oriented 

perpendicular to the structural or topographic “grain” of the terrain being observed. This orientation achieves maximum 

backscatter from features such as mountain slopes and stream banks. Stream channels that are perpendicular to the look 

direction stand out in sharp relief in radar images with the near bank in radar shadow and the opposite bank brightly 

illuminated. Although streams parallel to the look direction may disappear in a radar image, for interferometry, it is 

sometimes useful to look with the grain to avoid layover and shadows. 

Resolution Cell 

 The resolution cell is the region on the ground contributing to the return signal that generates a point on the image at a 

particular instant. The resolution cell is determined by the half-power angular width of the antenna pattern, the time interval

of the transmitted pulse, and, for synthetic aperture radar, the bandwidth of the Doppler filter. All scatterers in a resolution 

cell contribute collectively to the gray tone of a point on an image, but not all scatterers are identifiable unless there is 

significant contrast with the background gray level. A bright roof facing the radar antenna might be identifiable even if it is

smaller than the resolution cell. 

 The characteristic grainy appearance of a radar image results from destructive and constructive interference among the 

reflections from individual surface scattering centers within a resolution cell. These interference effects are random due to 

slight differences in the direction and angle of view even in areas with relatively uniform properties, causing brightness 

variations in adjacent pixels known as speckle. Speckle can be reduced by averaging multiple looks at a piece of ground 

during image acquisition, or by applying a median filter during image processing. However, this filtering will result in a 

loss of spatial resolution in the image. 

 The ground-resolution cell is determined by specific characteristics of the radar system. These include depression angle 

γ , pulse length τ , wavelength λ , antenna length D, and slant range distance S. The size of the resolution cell is determined by range resolution Rr, or resolution in the look direction, and azimuth resolution Ra, or resolution in the direction of 

the flight line. 

 Range resolution is determined by depression angle and pulse length and is theoretically equal to one-half the pulse 

length. Range resolution is given by 

 γ

τ

2cos

c Rr = . (A6) 
23

 Because the radar measures the range distance to features in slant range rather than true horizontal distance 

along the ground, in a slant-range image, features in the near range would appear compressed relative to the far 

range. The cosine of the depression angle converts slant range to ground range resolution. Equation A6 shows the 

inverse relationship between depression angle and ground range resolution; as the angle increases from 0° to 90°, 

the cosine of the angle decreases from 1 to 0. Therefore as the depression angle increases (nearer range) the ground 

resolution cell gets larger, resulting in a decrease in spatial detail. 

 Shortening the pulse length will achieve higher range resolution, but the energy in each transmitted pulse will be 

reduced. A longer pulse will transmit more power to the target and in turn more power will be reflected, resulting in 

increased target information and greater reliability. The trade-off between range resolution and pulse length can be partly 

resolved using frequency modulation, or “chirp.” 

 Instead of a short pulse, a longer pulse can be used with an upward or downward linear sweep of frequencies encoded 

within the transmitted radar pulse. The return signal is stored in memory and processed by Fourier transformation together 

with a reference wave. The result is a unique frequency that places the reflector at a point within the radar pulse. 

 Resolution in the azimuth direction is determined by the width of the radar footprint on the ground. To be resolved, two 

objects must be separated by a distance greater than the beam width on the ground. The trace of the radar beam on the 

ground is fan shaped, so azimuth resolution in the near range will be better than in the far range. The angular beam width is 

proportional to the radar wavelength, so resolution is better at shorter wavelengths than longer. The angular beam width is 

also inversely proportional to the antenna length D. A long antenna creates a narrow beam width, but there is a practical 

limit to the antenna length that can be carried by an aircraft or an orbital platform. For a real-aperture radar, azimuth 

resolution is given by 

 D

S Ra

λ

2

1 = . (A7) 

 Synthetic aperture radar resolves the difference in azimuth resolution between the near and far range by tracking the 

apparent Doppler frequency shift of objects as the radar beam sweeps across them. Any particular target is illuminated by 

the radar beam for a finite time period T and 

 T = L /υ (A8) 

where υ = velocity of platform 

and L = azimuthal dimension of the radar footprint, which can be written as 

 D

S L λ = . (A9) 

 During time period T the apparent motion of a target through the radar beam yields a time-dependent Doppler shift in 

the frequency of the return pulse. This Doppler phase history can then be used to distinguish between targets within the 

same footprint through a process of Fourier analysis and matched filter processing. Thus the target’s illumination is 

equivalent to that from a synthetic aperture of length υ T, which is simply L. The resulting azimuthal resolution can be 

obtained from equation A7 in which D is replaced by L.

 2 2

1

2

1 D

S

D S

L

S Ra = = = λ λ λ . (A10) 

 The azimuthal resolution is therefore independent of platform height and depends only on the size of the antenna. 
24 

Wavelength 

 The wavelength of incident radiation affects the scattered signal by (1) defining the effective surface roughness and (2) 

determining the depth of penetration and consequent volume effects of the ground surface. The relation between wavelength 

and surface roughness is described in the section on "Target Parameters." 

 The depth of surface penetration depends in part on the wavelength of the incident radiation. “Skin depth” defines the 

depth below the surface at which the amplitude of the incident radiation is reduced to 37% of the surface value. This 

quantity is determined by 

 2

1

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = πςη

λ δ (A11) 

where δ = skin depth, 

 λ = wavelength, 

 ς = conductivity, 

 η = 

2

1

⎟

⎠

⎞ ⎜

⎝

⎛

ε

μ , 

 μ = permeability of terrain, 

and ε = permittivity of terrain. 

 Permittivity is strongly dependent on soil moisture. Moist soils allow very little penetration of incident radiation, while 

very dry and permeable soils, such as aeolian sands in hyperarid environments, might allow penetration of L-band radiation 

to several meters. 

Depression Angle 

 Depression angle is usually defined as the angle between the horizontal plane at the antenna and the line of sight to an 

illuminated spot on the ground. The average depression angle refers to the line that marks the midpoint of the radar beam in 

the range direction, while the minimum and maximum depression angles refer to the far-range and near-range lines of sight. 

The depression angle can have a significant effect on the radar image. Too shallow an angle results in excessive radar 

shadow on the back side of mountains and ridges and minimal backscatter; too steep an angle causes foreshortening of 

slopes facing the antenna or layover of steep slopes. Layover occurs where the radar pulse intersects the top of a slope 

before the bottom, causing the slope to appear to lean toward the antenna in the image. Most imaging radars employ a 

depression angle of 30° to 40° for terrestrial observation; scatterometers operate over a broader range (30° to 80°) of 

depression angles.

Target Parameters 

Relative Complex Dielectric Constant 

 The relative complex dielectric constant ε is an electrical property of matter that can strongly affect radar returns. It is 

commonly written as 

 ε = ε′ − jε′′ (A12) 

where ε′ = the real part, often referred to as the relative permittivity, 

and ε′′ = an imaginary part, also known as the loss factor or conductivity. 
25

 The term relative means that ε is normalized to the permittivity of free space εο. Most surface materials have dielectric 

constants between about 3 and 8 (Martinez and Byrnes, 2001). Water has a dielectric constant of 80. Moisture in rocks and 

soils can raise their dielectric constants to about 20. Increasing the dielectric constant of surface materials due to water 

content increases the backscatter coefficient, which in turn increases the tonality of the radar image. 

 The strong polarity of water molecules accounts for its high dielectric constant. Water molecules in soils and vegetation 

oscillate in harmony with the electrical vector of radar waves over a wide range of radar frequencies, greatly enhancing the 

strength of the return signal. Virtually no energy penetrates the surface if even small amounts of water are present. 

Conversely, radar energy can penetrate as much as 2 m into hyperarid soils from space-borne platforms, as has been 

demonstrated in the aeolian sands of the Sahel in northern Africa (Schaber and others, 1997). 

Surface Roughness 

 Surface roughness is the terrain property that has the greatest influence on the strength of radar returns. Measured in 

centimeters, roughness refers to textural features that are comparable in size to radar wavelengths. The average height of 

surface irregularities can be taken as a measure of roughness. 

 Three categories of roughness are commonly defined. Smooth surfaces are those in which radar energy is reflected 

forward according to Snell’s law (specular reflection) with virtually no backscatter toward the receiving antenna. Rough 

surfaces result in diffuse, hemispherical scattering in all directions of radar energy with a significant return to the antenna. 

An intermediate category is a mixture of specular and hemispherical reflection. 

 Criteria for roughness depends on the wavelength of the incident radar beam and its depression angle. The Rayleigh 

criterion considers a surface to be smooth if 

 γ

λ

8sin

h < (A13) 

where h = vertical relief in centimeters, 

 λ = radar wavelength in centimeters, 

and γ = depression angle of incident radar. 

 Peake and Oliver (1971) modified the Rayleigh criterion, defining a smooth criterion as 

 γ

λ

25sin

h < (A14) 

and a rough criterion as 

 γ

λ

4.4sin

h < . (A15) 

Surface Cover 

 The backscattering coefficient of bare soil is influenced by soil moisture, random roughness, periodic surface patterns 

(e.g., row tillage), and soil texture. Soil moisture and soil texture are governed chiefly by dielectric properties, or water 

content. Backscattering properties due to roughness and surface patterns depend in part on the wavelength of incident 

radiation. A soil may appear rough at short wavelengths and smooth at longer wavelengths. 
26 

 Vegetation may be viewed as a mixture of leaves, fruit, branches, and stalks embedded in air. Returns from deciduous 

leaves may dominate the total radar return, particularly in the spring when their water content is high. Radar returns from 

vegetation are also dependent on wavelength. Short wavelengths will interact more with tree canopies, leading to strong 

volume scattering from foliage. Long wavelengths tend to penetrate canopies and interact with the ground surface. 
27

APPENDIX B: 

DATA TABLES ON FIELD EXPERIMENTS USING RADAR TO DETECT MINING HAZARDS 

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

13.03 459 310 64 -1.54 

13.09 459 311 14 -2.76 -50 -1.22 -0.6 

13.14 459 312 17 -2.68 3 0.07 0.0 

13.19 459 313 15 -2.73 -2 -0.05 0.0 

13.24 459 314 16 -2.71 1 0.02 0.0 

13.30 459 315 37 -2.20 21 0.51 0.2 

13.35 459 316 18 -2.66 -19 -0.46 -0.2 

13.40 459 317 17 -2.68 -1 -0.02 0.0 

13.46 459 318 19 -2.63 2 0.05 0.0 

13.51 459 319 26 -2.46 7 0.17 0.1 

13.56 459 320 18 -2.66 -8 -0.20 -0.1 

13.62 459 321 16 -2.71 -2 -0.05 0.0 

13.67 459 322 20 -2.61 4 0.10 0.0 

13.72 459 323 20 -2.61 0 0.00 0.0 

13.78 459 324 24 -2.51 4 0.10 0.0 

13.83 459 325 29 -2.39 5 0.12 0.1 

13.88 459 326 31 -2.34 2 0.05 0.0 

13.94 459 327 21 -2.59 -10 -0.24 -0.1 

13.99 459 328 28 -2.41 7 0.17 0.1 

14.04 459 329 26 -2.46 -2 -0.05 0.0 

14.10 459 330 29 -2.39 3 0.07 0.0 

14.15 459 331 22 -2.56 -7 -0.17 -0.1 

14.20 459 332 33 -2.29 11 0.27 0.1 

14.26 459 333 28 -2.41 -5 -0.12 -0.1 

14.31 459 334 25 -2.49 -3 -0.07 0.0 

14.36 459 335 26 -2.46 1 0.02 0.0 

14.42 459 336 27 -2.44 1 0.02 0.0 

14.47 459 337 20 -2.61 -7 -0.17 -0.1 

14.52 459 338 27 -2.44 7 0.17 0.1 

14.57 459 339 27 -2.44 0 0.00 0.0 

14.63 459 340 19 -2.63 -8 -0.20 -0.1 

14.68 459 341 20 -2.61 1 0.02 0.0 

14.73 459 342 18 -2.66 -2 -0.05 0.0 

14.79 459 343 21 -2.59 3 0.07 0.0 

14.84 459 344 17 -2.68 -4 -0.10 0.0 

14.89 459 345 26 -2.46 9 0.22 0.1 

14.95 459 346 17 -2.68 -9 -0.22 -0.1 

15.00 459 347 22 -2.56 5 0.12 0.1 

15.05 459 348 24 -2.51 2 0.05 0.0 

15.11 459 349 28 -2.41 4 0.10 0.0 

15.16 459 350 30 -2.37 2 0.05 0.0 
28 

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

15.21 459 351 20 -2.61 -10 -0.24 -0.1 

15.27 459 352 31 -2.34 11 0.27 0.1 

15.32 459 353 21 -2.59 -10 -0.24 -0.1 

15.37 459 354 25 -2.49 4 0.10 0.0 

15.43 459 355 21 -2.59 -4 -0.10 0.0 

15.48 459 356 24 -2.51 3 0.07 0.0 

15.53 459 357 51 -1.85 27 0.66 0.3 

15.59 459 358 21 -2.59 -30 -0.73 -0.3 

15.64 459 359 21 -2.59 0 0.00 0.0 

15.69 459 360 20 -2.61 -1 -0.02 0.0 

15.74 459 361 27 -2.44 7 0.17 0.1 

15.80 459 362 24 -2.51 -3 -0.07 0.0 

15.85 459 363 26 -2.46 2 0.05 0.0 

15.90 459 364 22 -2.56 -4 -0.10 0.0 

15.96 459 365 27 -2.44 5 0.12 0.1 

16.01 459 366 23 -2.54 -4 -0.10 0.0 

16.06 459 367 19 -2.63 -4 -0.10 0.0 

16.12 459 368 27 -2.44 8 0.20 0.1 

16.17 459 369 19 -2.63 -8 -0.20 -0.1 

16.22 459 370 30 -2.37 11 0.27 0.1 

16.28 459 371 25 -2.49 -5 -0.12 -0.1 

16.33 459 372 31 -2.34 6 0.15 0.1 

16.38 459 373 29 -2.39 -2 -0.05 0.0 

16.44 459 374 29 -2.39 0 0.00 0.0 

16.49 459 375 28 -2.41 -1 -0.02 0.0 

16.54 459 376 36 -2.22 8 0.20 0.1 

16.60 459 377 23 -2.54 -13 -0.32 -0.2 

16.65 459 378 29 -2.39 6 0.15 0.1 

16.70 459 379 24 -2.51 -5 -0.12 -0.1 

16.76 459 380 26 -2.46 2 0.05 0.0 

16.81 459 381 28 -2.41 2 0.05 0.0 

16.86 459 382 25 -2.49 -3 -0.07 0.0 

16.92 459 383 27 -2.44 2 0.05 0.0 

16.97 459 384 28 -2.41 1 0.02 0.0 

17.02 459 385 29 -2.39 1 0.02 0.0 

17.07 459 386 30 -2.37 1 0.02 0.0 

17.13 459 387 28 -2.41 -2 -0.05 0.0 

17.18 459 388 23 -2.54 -5 -0.12 -0.1 

17.23 459 389 30 -2.37 7 0.17 0.1 

17.29 459 390 30 -2.37 0 0.00 0.0 

17.34 459 391 31 -2.34 1 0.02 0.0 

17.39 459 392 28 -2.41 -3 -0.07 0.0 

17.45 459 393 25 -2.49 -3 -0.07 0.0 

17.50 459 394 40 -2.12 15 0.37 0.2 

17.55 459 395 34 -2.27 -6 -0.15 -0.1 

17.61 459 396 19 -2.63 -15 -0.37 -0.2 
29

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

17.66 459 397 37 -2.20 18 0.44 0.2 

17.71 459 398 52 -1.83 15 0.37 0.2 

17.77 459 399 35 -2.24 -17 -0.41 -0.2 

17.82 459 400 15 -2.73 -20 -0.49 -0.2 

17.87 459 401 42 -2.07 27 0.66 0.3 

17.93 459 402 10 -2.85 -32 -0.78 -0.4 

17.98 459 403 13 -2.78 3 0.07 0.0 

18.03 459 404 20 -2.61 7 0.17 0.1 

18.09 459 405 126 -0.02 106 2.59 1.2 

18.14 459 406 45 -2.00 -81 -1.98 -0.9 

18.19 459 407 31 -2.34 -14 -0.34 -0.2 

18.24 459 408 223 2.34 192 4.68 2.2 

18.30 459 409 177 1.22 -46 -1.12 -0.5 

18.35 459 410 9 -2.88 -168 -4.10 -1.976 

18.40 459 411 53 -1.80 44 1.07 0.5 

18.46 459 412 14 -2.76 -39 -0.95 -0.5 

18.51 459 413 79 -1.17 65 1.59 0.8 

18.56 459 414 59 -1.66 -20 -0.49 -0.2 

18.62 459 415 35 -2.24 -24 -0.59 -0.3 

18.67 459 416 79 -1.17 44 1.07 0.5 

18.72 459 417 86 -1.00 7 0.17 0.1 

18.78 459 418 77 -1.22 -9 -0.22 -0.1 

18.83 459 419 67 -1.46 -10 -0.24 -0.1 

18.88 459 420 101 -0.63 34 0.83 0.4 

18.94 459 421 54 -1.78 -47 -1.15 -0.5 

18.99 459 422 135 0.20 81 1.98 0.9 

19.04 459 423 44 -2.02 -91 -2.22 -1.1 

19.10 459 424 53 -1.80 9 0.22 0.1 

19.15 459 425 32 -2.32 -21 -0.51 -0.2 

19.20 459 426 51 -1.85 19 0.46 0.2 

19.26 459 427 132 0.12 81 1.98 0.9 

19.31 459 428 97 -0.73 -35 -0.85 -0.4 

19.36 459 429 57 -1.71 -40 -0.98 -0.5 

19.42 459 430 115 -0.29 58 1.41 0.7 

19.47 459 431 20 -2.61 -95 -2.32 -1.1 

19.52 459 432 129 0.05 109 2.66 1.3 

19.57 459 433 4 -3.00 -125 -3.05 -1.5 

19.63 459 434 230 2.51 226 5.51 2.6 

19.68 459 435 30 -2.37 -200 -4.88 -2.3 

19.73 459 436 101 -0.63 71 1.73 0.8 

19.79 459 437 26 -2.46 -75 -1.83 -0.9 

19.84 459 438 177 1.22 151 3.68 1.8 

19.89 459 439 253 3.07 76 1.85 0.9 

19.95 459 440 28 -2.41 -225 -5.49 -2.6 

20.00 459 441 28 -2.41 0 0.00 0.0 

20.05 459 442 240 2.76 212 5.17 2.5 
30 

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

20.11 459 443 77 -1.22 -163 -3.98 -1.9 

20.16 459 444 10 -2.85 -67 -1.63 -0.8 

20.21 459 445 17 -2.68 7 0.17 0.1 

20.27 459 446 27 -2.44 10 0.24 0.1 

20.32 459 447 222 2.32 195 4.76 2.3 

20.37 459 448 230 2.51 8 0.20 0.1 

20.43 459 449 16 -2.71 -214 -5.22 -2.5 

20.48 459 450 15 -2.73 -1 -0.02 0.0 

20.53 459 451 11 -2.83 -4 -0.10 0.0 

20.59 459 452 22 -2.56 11 0.27 0.1 

20.64 459 453 7 -2.93 -15 -0.37 -0.2 

20.69 459 454 28 -2.41 21 0.51 0.2 

20.74 459 455 127 0.00 99 2.41 1.2 

20.80 459 456 56 -1.73 -71 -1.73 -0.8 

20.85 459 457 124 -0.07 68 1.66 0.8 

20.90 459 458 243 2.83 119 2.90 1.4 

20.96 459 459 128 0.02 -115 -2.80 -1.3 

21.01 459 460 47 -1.95 -81 -1.98 -0.9 

21.06 459 461 246 2.90 199 4.85 2.3 

21.12 459 462 18 -2.66 -228 -5.56 -2.7 

21.17 459 463 172 1.10 154 3.76 1.8 

21.22 459 464 176 1.20 4 0.10 0.0 

21.28 459 465 6 -2.95 -170 -4.15 -2.0 

21.33 459 466 127 0.00 121 2.95 1.4 

21.38 459 467 111 -0.39 -16 -0.39 -0.2 

21.44 459 468 210 2.02 99 2.41 1.2 

21.49 459 469 10 -2.85 -200 -4.88 -2.3 

21.54 459 470 231 2.54 221 5.39 2.6 

21.60 459 471 110 -0.41 -121 -2.95 -1.4 

21.65 459 472 180 1.29 70 1.71 0.8 

21.70 459 473 7 -2.93 -173 -4.22 -2.0 

21.76 459 474 132 0.12 125 3.05 1.5 

21.81 459 475 53 -1.80 -79 -1.93 -0.9 

21.86 459 476 37 -2.20 -16 -0.39 -0.2 

21.91 459 477 92 -0.85 55 1.34 0.6 

21.97 459 478 42 -2.07 -50 -1.22 -0.6 

22.02 459 479 46 -1.98 4 0.10 0.0 

22.07 459 480 95 -0.78 49 1.20 0.6 

22.13 459 481 224 2.37 129 3.15 1.5 

22.18 459 482 136 0.22 -88 -2.15 -1.0 

22.23 459 483 240 2.76 104 2.54 1.2 

22.29 459 484 220 2.27 -20 -0.49 -0.2 

22.34 459 485 221 2.29 1 0.02 0.0 

22.39 459 486 130 0.07 -91 -2.22 -1.1 

22.45 459 487 107 -0.49 -23 -0.56 -0.3 

22.50 459 488 237 2.68 130 3.17 1.5 
31

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

22.55 459 489 57 -1.71 -180 -4.39 -2.1 

22.61 459 490 194 1.63 137 3.34 1.6 

22.66 459 491 38 -2.17 -156 -3.80 -1.8 

22.71 459 492 224 2.37 186 4.54 2.2 

22.77 459 493 30 -2.37 -194 -4.73 -2.3 

22.82 459 494 226 2.41 196 4.78 2.3 

22.87 459 495 247 2.93 21 0.51 0.2 

22.93 459 496 103 -0.59 -144 -3.51 -1.7 

22.98 459 497 14 -2.76 -89 -2.17 -1.0 

23.03 459 498 43 -2.05 29 0.71 0.3 

23.09 459 499 22 -2.56 -21 -0.51 -0.2 

23.14 459 500 60 -1.63 38 0.93 0.4 

23.19 459 501 77 -1.22 17 0.41 0.2 

23.24 459 502 60 -1.63 -17 -0.41 -0.2 

23.30 459 503 26 -2.46 -34 -0.83 -0.4 

23.35 459 504 89 -0.93 63 1.54 0.7 

23.40 459 505 41 -2.10 -48 -1.17 -0.6 

23.46 459 506 37 -2.20 -4 -0.10 0.0 

23.51 459 507 44 -2.02 7 0.17 0.1 

23.56 459 508 31 -2.34 -13 -0.32 -0.2 

23.62 459 509 70 -1.39 39 0.95 0.5 

23.67 459 510 33 -2.29 -37 -0.90 -0.4 

23.72 459 511 37 -2.20 4 0.10 0.0 

23.78 459 512 39 -2.15 2 0.05 0.0 

23.83 459 513 18 -2.66 -21 -0.51 -0.2 

23.88 459 514 36 -2.22 18 0.44 0.2 

23.94 459 515 35 -2.24 -1 -0.02 0.0 

23.99 459 516 22 -2.56 -13 -0.32 -0.2 

24.04 459 517 10 -2.85 -12 -0.29 -0.1 

24.10 459 518 17 -2.68 7 0.17 0.1 

24.15 459 519 21 -2.59 4 0.10 0.0 

24.20 459 520 21 -2.59 0 0.00 0.0 

24.26 459 521 24 -2.51 3 0.07 0.0 

24.31 459 522 21 -2.59 -3 -0.07 0.0 

24.36 459 523 31 -2.34 10 0.24 0.1 

24.41 459 524 10 -2.85 -21 -0.51 -0.2 

24.47 459 525 25 -2.49 15 0.37 0.2 

24.52 459 526 19 -2.63 -6 -0.15 -0.1 

24.57 459 527 25 -2.49 6 0.15 0.1 

24.63 459 528 27 -2.44 2 0.05 0.0 

24.68 459 529 21 -2.59 -6 -0.15 -0.1 

24.73 459 530 16 -2.71 -5 -0.12 -0.1 

24.79 459 531 29 -2.39 13 0.32 0.2 

24.84 459 532 13 -2.78 -16 -0.39 -0.2 

24.89 459 533 11 -2.83 -2 -0.05 0.0 

24.95 459 534 32 -2.32 21 0.51 0.2 
32 

Table B1.—Phase data for a segment of test 4; phase = (Dv-127)/41 and ∆Phase = ∆Dv/41

Time, sec Pixel location Data value, Dv Phase, Phase change Displacement, cm 

 x y Radians ∆Dv ∆Radians 

25.00 459 535 25 -2.49 -7 -0.17 -0.1 

25.05 459 536 31 -2.34 6 0.15 0.1 

25.11 459 537 25 -2.49 -6 -0.15 -0.1 

25.16 459 538 25 -2.49 0 0.00 0.0 

25.21 459 539 23 -2.54 -2 -0.05 0.0 

25.27 459 540 37 -2.20 14 0.34 0.2 

25.32 459 541 20 -2.61 -17 -0.41 -0.2 

25.37 459 542 39 -2.15 19 0.46 0.2 

25.43 459 543 28 -2.41 -11 -0.27 -0.1 

25.48 459 544 42 -2.07 14 0.34 0.2 

25.53 459 545 71 -1.37 29 0.71 0.3 

25.59 459 546 32 -2.32 -39 -0.95 -0.5 

Table B2.—Interferogram range profiles, test 4. Phase = (mean dv-127) ÷ 41. Phase in radians. 

 Time, 

sec 

Y axis Range, meters 

 26.4 26.9 27.5 28.2 28.8 29.3 30 30.6 31.1 31.8 32.4 32.9 33.6 34.2 34.7 35.4 36 36.5 37.2 37.8 38.5

X axis 419 423 427 432 436 440 445 449 453 458 462 466 471 475 479 484 488 492 497 501 506

Before 

 10.00 254 131 135 185 135 109 165 121 97 60 17 56 86 127 179 197 138 120 156 202 151 112

 10.48 263 134 72 96 121 132 171 123 96 55 12 49 89 127 179 205 154 107 102 150 169 165

Mean 133 104 141 128 121 168 122 96.5 57.5 14.5 52.5 87.5 127 179 201 146 114 129 176 160 139

Phase 0.13 -0.57 0.33 0.02 -0.16 1.00 -0.12 -0.74 -1.70 -2.74 -1.82 -0.96 0.00 1.27 1.80 0.46 -0.33 0.05 1.20 0.80 0.28

During 

 18.19 408 153 90 102 75 89 155 129 106 51 223 214 128 149 49 98 48 41 124 133 92 132

 22.29 485 153 159 124 144 152 171 188 166 225 221 157 42 138 167 193 182 133 101 113 104 122

Mean 153 125 113 110 121 163 159 136 138 222 186 85 144 108 146 115 87 113 123 98 127

Phase 0.63 -0.06 -0.34 -0.43 -0.16 0.88 0.77 0.22 0.27 2.32 1.43 -1.02 0.40 -0.46 0.45 -0.29 -0.98 -0.35 -0.10 -0.71 0.00

After 

 24.15 520 127 123 126 145 86 108 133 86 86 21 48 79 107 172 83 60 72 95 107 118 101

 28.40 600 162 82 93 195 108 73 152 108 63 15 34 51 87 155 216 90 60 94 108 168 110

 Mean 145 103 110 170 97 90.5 143 97 74.5 18 41 65 97 164 150 75 66 94.5 108 143 106

 Phase 0.43 -0.60 -0.43 1.05 -0.73 -0.89 0.38 -0.73 -1.28 -2.66 -2.10 -1.51 -0.73 0.89 0.55 -1.27 -1.49 -0.79 -0.48 0.39 -0.52
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