Directory UMM :Data Elmu:jurnal:J-a:Journal Of Applied Geophysics:Vol43.Issue2-4.2000:

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www.elsevier.nlrlocaterjappgeo

Maximizing the information return from ground penetrating radar

Gary R. Olhoeft

)

Department of Geophysics, Colorado School of Mines, Golden, CO 80401-1887 USA Received 2 February 1999; received in revised form 23 April 1999; accepted 24 May 1999

Abstract

Ground penetrating radar data is not always easy to acquire, and sometimes the acquisition may be constrained by equipment availability, weather, legal or logistical constraints, safety or access considerations. Examples of these include archaeological or geotechnical sites about to be excavated, contaminated lands undergoing remediation, hazardous areas such as unexploded ordnance lands or active volcanoes, and difficult to visit locations such as Antarctica or the surface of Mars. These situations may result in only one chance at acquiring data. Thus, the data need to be acquired, processed and modeled with the aim of maximizing the information return for the time, cost and hazard risked. This process begins by properly setting up the survey with the expectation of the site conditions but allowing for flexibility and serendipity in the unknown. Not only are radar data acquired, but also calibration, orientation, location and other required parameters describing the equipment and survey are recorded. All of these parameters are used in the processing and modeling of the data. The final results will be not just a radar image as a pseudo-cross-section, but a corrected geometric cross-section, interpreted electrical and magnetic properties of the ground, location, orientation, size and shape of subsurface objects, and composition of the ground and objects as inferred density, porosity, fluid saturation, and other relevant material occurrence properties.q₂₀₀₀

Keywords: Acquisition; Processing; Modeling; Interpretation; Display; Utility detection

1. Introduction

For most of the history of ground penetrating radar, the instruments have been used to acquire data that have been presented as distorted im-ages or pseudo-cross-sections of the subsurface ŽMorey, 1974; Olhoeft, 1988 . Such images of-. ten solve problems such as the horizontal loca-tion of some change or thing buried, without any further necessity of processing. However, many problems pose questions requiring an-swers with more detailed information, such as

)_Fax:_q_{1-303-273-3478; e-mail: [email protected]}

what is the depth to a buried utility pipe and its size, orientation, and composition? What are the depth, size, shape and orientation of the unex-ploded ordnance? What is the density of com-paction of soil in the bridge approach? How is the fluid saturation of contaminant perched on this clay layer changing with time as the site is remediated? These questions require quantita-tive answers only obtained by properly acquir-ing the radar data, processacquir-ing and modelacquir-ing the data, and interpreting the results, including a display in terms the person dealing with the problem can understand. The physical processes and the equations to describe them have been

Ž .

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known for a long time. Only in the past decade have they been applied to answer some of the questions above, but they are still not routinely applied.

2. Locating a buried pipe

Fig. 1 illustrates a portion of a radar pseudo-section acquired with a GSSI SIR-10Aq radar

Ž 1_.

system using a 900-MHz in air center fre-quency bistatic bow-tie antenna over a 90-cm

Ž diameter steel pipe buried 37 cm deep surface

. Ž

to top of pipe near Yuma, AZ Olhoeft et al., .

1994 . The radar reflection from the pipe is the result of electromagnetic wave propagation de-scribed by the radar equation and geometry through, among other things, the Fresnel reflec-tion coefficient in amplitude, Snell’s law in angle, and the Stokes scattering matrix in

polar-Ž

ization Balanis, 1989; Powers, 1995; Smith, .

1997 . The location and orientation of the pipe were known, so the electric fields of the anten-nas were set horizontal, parallel to each other, parallel to the long axis of the pipe, and to traverse perpendicular across the pipe, maximiz-ing the couplmaximiz-ing with respect to polarization.

Ž Across the top of the image are marks small

white vertical bars used to locate the antenna and later correct for variations of towing speed. Each mark indicates passage of the center of the antenna past a flag in a series spaced 1 m apart along the antenna traverse path. The vertical black line running through the middle of the image is the location of the single scan wiggle trace plotted to the right. The two way travel time vertical scale is also shown as an equiva-lent depth assuming a relative dielectric permit-tivity of four. The horizontal line across the top of the image currently displays nothing and will

Most GPR antennas are ground-loaded, lowering their center frequency when in contact with the ground by an amount determined by the antenna design and the electro-magnetic properties of the ground.

Fig. 1. Raw radar data acquired with a GSSI SIR-10Aq

Ž .

using a bistatic 900 MHz in air center frequency antenna towed across a 90-cm diameter pipe buried 37 cm deep.

be explained in later figures when it shows features in the data.

The data in the radar image exhibit several problems. The image is horizontally distorted

by uneven towing speed uneven spacing of the .

marks across the top and vertically by an un-known velocity of wave propagation. There is horizontal banding running across the image from less than optimal coupling of the antenna to the ground and unwanted oscillatory ringing of the antenna. There are five vertical lines coming up from the bottom of the image caused by radio frequency interference from nearby

portable radios or cell phones see Appendix .

A . Nonetheless, about a third of the way down from the top, a reflection caused by a layer in the geology may be seen to run horizontally across the image, broken in the middle by the trench created to bury the pipe, and exhibiting

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the characteristic ‘‘hyperbola’’ scattering shape caused by the metal pipe. If the problem were utility location, then the problem is solved at this point by noting the presence of a metallic reflector at the horizontal position of the top of the hyperbola. By rotating the antenna electric field orientation while centered above the pipe location indicated by the hyperbola, the az-imuthal strike orientation of the pipe may also be quickly determined from the change in polar-ization response. By measuring the change in polarization with different antenna geometries Žoften called HH, VV and HV polarizations;

van Zyl and Ulaby, 1990 and solving for the Stokes–Mueller polarization matrices, both the strike and dip of the pipe may be determined. For the remainder of this example, polarization will be ignored as the data acquisition was setup to be maximally coupled between the antenna electric field and the long axis of the pipe.

3. Estimating the pipe depth and size

However, if more information is required, the first processing step will be to remove the arti-facts in the data. In Fig. 2, the time zero has been set at the first energy of arrival. Time zero is a function of the system timing, cable lengths, and antenna positioning. The horizontal black line is positioned at time zero and also shows the position of the line plotted across the top of the image, which now shows the uneven mark locations. The average of all the scans has been

accumulated and removed background re-.

moval to eliminate the antenna ringing and horizontal banding across the image. The back-ground removal also removes other horizontal features such as flat lying geology and the surface of the Earth, so time zero had to be located first.

Ž In Fig. 3, a median gradient filter Paeth,

1990; Pratt, 1991; Weeks et al., 1993 has been applied to remove the radio frequency interfer-ence from nearby wireless phone and portable

Ž .

radio transmissions see Appendix A . In Fig. 4,

Fig. 2. The data of Fig. 1 with time zero determined and

Ž .

the average scan removed background removal .

an image processing contrast enhancement

Ž .

stretch Pratt, 1991; Zuiderveld, 1994 has been applied to bring out details in the image. This last step loses all the absolute amplitude

infor-Ž .

mation that will be recovered later and en-Ž

hances not only geological details note the appearance of several small hyperbolas caused

. Ž

by rocks but also noise the radio frequency interference as diagonals across the bottom of the image from the computer inside the

SIR-.

10Aq control box . These steps are done to improve the ability to clearly see the tails of the pipe hyperbola, to be used in determining veloc-ity and size of the pipe.

In Fig. 5, the image has changed size and shape slightly as a spline rubber sheeting

pro-Ž .

cess Bochicchio, 1988 is used with the loca-tions of the marks to correct the horizontal geometry of the image. This allows the scans numbered across the bottom of the image to

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Fig. 3. The data of Fig. 2 with a median gradient filter applied to remove radio noise.

also be labelled as horizontal traverse distance in meters. This may also be done in 3D to correct for topographic relief, but requires the vertical time scale first be converted to a depth scale. The survey in this case is across flat ground. In the process of doing the rubber sheeting, it was found that some scans were missing in making a uniformly spaced image, so an interpolation was used to fill in, with the locations of the filling indicated across the top

of the plot as small spikes two on the left half . and seven on the right half of the image . This interpolative filling is just to make a better looking image.

In Fig. 6, a mathematical function has been fitted to the hyperbola shape in the data. The function is a slice from a conic section that is often called ‘‘hyperbola’’. In the earlier figures, note the hyperbola contains considerable varia-tion in amplitude along its locus as well as some

deviation from the ideal hyperbola shape. These are caused by geological heterogeneity and may be used to describe that heterogeneity. These are also causes of problems in attempting to refocus the hyperbola by synthetic aperture, phase unwrapping, or migration processing ŽYilmaz, 1987; Figs. 43 and 44 of Powers,

1995; Ghiglia and Pritt, 1998 . The slopes of the asymptotes on either side are controlled by the velocity of propagation and thus calibrate the dielectric permittivity between the antenna and the pipe, and give a calibration and conversion of the two-way travel time into depth. The radius of curvature at the peak of the hyperbola

and the lengths of the asymptotes by taking .

into account the antenna pattern give the size of the object causing it. The ellipse drawn within the hyperbola indicates the size of the object, assuming the object is a circular cylinder with axis perpendicular to the plane of the data

im-Fig. 4. The data of im-Fig. 3 with an image processing histogram contrast stretch applied.

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Fig. 5. The data of Fig. 5 after spline rubber sheeting to the marks along horizontal traverse and in fill interpola-tion.

age. The circle is distorted into an ellipse by vertical exaggeration, as no correction has been performed to make the vertical and horizontal axes the same scale dimension. Also indicated in Fig. 6 is the position of the near-field of the antenna, as the hyperbola shape is fit with a far-field ray tracing model assumption. At this point, the data processing and hyperbola fitting indicate a pipe centered 2.78 m from the begin-ning of the traverse, at a depth of 0.34 m in a soil with relative dielectric permittivity of 4.0, and with a diameter of 0.41 m. These numbers can be further refined.

In Fig. 7, an image processing hyperbola mask has been applied to the data to collapse or

focus the hyperbola using a process similar to .

migration; Yilmaz, 1987 . The image now shows only the scattering cross-section of the visible radius of curvature of the pipe. By looking at

other hyperbolas in the image such as those .

from the rocks , their over or under migration Ž

focusing residual hyperbolic shapes pointed up-.

wards or downwards indicates the variability of the velocity and hence dielectric permittivity throughout the section.

4. Refining the pipe depth

In Fig. 8, the data scan under the vertical black line at the location of the peak of the hyperbola in Fig. 6 has been extracted and plotted as the dashed line. This is the original raw data scan before all the processing above. The processing was performed to produce a clear image and better fit to the hyperbola. The solid line in the main portion of the plot is a full waveform model generated through the radar

Fig. 6. Hyperbola fitting to estimate permittivity and

hence turn two way travel time into depth and to estimate object size.

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Ž .

Fig. 7. Image processing hyperbola masking migration to focus hyperbolas and to estimate velocity variation throughout the image.

equation for a layered earth Duke, 1990; Pow-.

ers and Olhoeft, 1995 from the estimated per-mittivity and depth of the hyperbola fit, and using the parameters versus depth shown on the right side of the plot. The key to the parameters is across the top.

There are three such sets of parameters, of which one is shown in Fig. 8. This one is for the complex dielectric permittivity in terms of the four Cole–Cole dielectric relaxation parameters ŽOlhoeft and Capron, 1994; Olhoeft, 1998a :. ´r1

is the low frequency limit of the relative dielec-tric permittivity,´r` is the high frequency limit, t´ is the time constant, and a´ is the breadth

parameter for the log-normal Cole–Cole distri-bution of time constants. Values of 4.0, 4.0, 0.0, and 1.0 indicate a real permittivity with no imaginary part and no frequency dependence as

´r1s´r`. The values of y1.0 in the next layer

tell the model to use the properties of a metal. There is a similar set for the complex magnetic permeability, which will be assumed to be that of free space in this model, mr1smr`s1.0. The third set describes the low frequency

limit-Ž

ing electrical conductivity seen in the next .

figure .

The label at the top of the figure tells where the field scan is located. On the top right are the

Ž model frequency using a Ricker wavelet Sheriff,

1984 , and a display gain in decibels. Across the bottom are the time scale, the Offss1.81 indi-cates a 1.81-ns offset from the beginning of data

to locate time zero determined from the previ-.

ous processing and the C_rs1.00 is a coupling ratio to describe changes in the antenna center

Ž frequency as it is loaded by the ground not

used here . In the left half of the main plot, the smaller vertical solid line indicates time zero and the larger vertical solid line indicates the estimated position of the near-field boundary. This model assumes far-field, plane wave prop-agation with vertical incidence at horizontal lay-ering. Thus the air wave between the transmitter

and receiver antennas in the data between the .

two vertical lines in the near-field is not mod-eled. An example of near-field modeling and Ž . requirements may be found in Kirkendall 1998 . The first excursion in the data at the left-most edge of the plot is an internal radar system sync pulse and is also not modeled. Multiples be-tween the antenna and the pipe are modeled. Further details of this full waveform modeling

Ž . are published in Powers and Olhoeft 1995 .

In Fig. 8, the first thing noticed about the model attempted from the estimated parameters

derived by the previous processing time zero, .

permittivity and depth are that the amplitudes are wrong. There is also a lot of high frequency ringing caused by truncation in computing

Fourier transforms which are performed only over the frequency range which contains

signifi-.

cant amplitude in the data . The amplitude com-putation includes the effects of geometric spreading deduced from the processing derived

Ž .

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Fig. 8. Full waveform modeling of the scan directly over the pipe in the previous figures. This figure shows the modeling only using the estimated permittivity and depth from the previous hyperbola fitting.

Fresnel reflection coefficient at the interface, and of the hardware range gain function that was recorded with the data, but it has not yet included the exponential material losses ŽOlhoeft, 1998a . In Fig. 9, on the right, the.

electrical conductivity depth profile has been adjusted to more realistically match the decay

shown in the data thus including part of the .

exponential material losses , and to include the conductivity of the metal pipe. To make the

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zero crossings between the model and the data align better, the original processing depth esti-mate is adjusted from 0.34 to 0.36 m.

5. Estimating the soil density and water con-tent

The main wavelet being reflected by the pipe also has some character beyond that of the ideal Ricker wavelet. In particular, the wavelet has one up-going peak and two down-going peaks, with the ideal Ricker wavelet showing the two down-going peaks to be the same amplitude. However, the recorded data show the two down-going peaks to have different amplitudes.

Ž This is caused by frequency dependence or

dispersion in the electromagnetic properties that control the velocity and attenuation of

propaga-Ž .

tion Olhoeft, 1998a . The Cole–Cole parame-ters in Fig. 10 are adjusted to match this ampli-tude difference, changing the shape of the model wavelet to better fit the recorded data. In the process, the zero crossing match requires

an-other depth adjustment to 0.37 m. The depth to the pipe has now been determined to a high accuracy, and the model result agrees

remark-Ž .

ably well with the known depth 0.37 m to the top of the pipe. The remainder of the wiggles in the field data are caused by radio frequency

noise and should not be modeled this is deter-mined by looking at the texture and patterns in

. the 2D radar image in the earlier figures .

Frequency dependences in geological materi-als are dominantly caused by dielectric relax-ation processes related to the presence of water, and to a lesser extent by magnetic relaxation processes related to the presence of iron bearing minerals, and a variety of scattering processes ŽOlhoeft and Capron, 1994; Olhoeft, 1998a .. Assuming all of the frequency dependence comes from the presence of water, the model fitted Cole–Cole parameters indicate the re-quirement of about 1% or 2% water by volume in the soil between the antennas and the pipe to cause the required dispersion and subsequent change in wavelet shape. The Bruggeman–

Ž Hanai–Sen volumetric mixing formula Sen et

Fig. 10. Further improving the model fit over Fig. 9 by including the effects of a frequency dependent complex dielectric permittivity.

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al., 1981; Olhoeft, 1987 may be used to con-vert the dielectric permittivity into bulk density, giving a volume average density of 1.89 grcm3_,

28% porosity sand equivalent soil between the antennas and the pipe, right over the pipe through the trenching disturbed soil. These val-ues are consistent with laboratory measurements

on soil samples from the site Olhoeft and .

Capron, 1993 and on the measured variation of frequency dependence with moisture content in

soils Kutrubes, 1986; Olhoeft, 1981, 1987; .

Canan, 1999 . These values are typically mea-sured in situ for soils using time domain

reflec-Ž .

tometry O’Connor and Dowding, 1999 , which requires pushing probes into the ground, but have been derived here noninvasively from ground penetrating radar data.

The processing and modeling just performed require a few minutes played like a video game on a 32-bit laptop computer. They have yielded

Ž considerable information about the pipe

loca-. Ž

tion, size and depth and the soil density and .

water content . The processing, modeling, and

Ž .

display figure generation were all done with

Ž .

theGRORADARe software Olhoeft, 1998b .

6. Discussion

The parameters derived by this processing are not necessarily unique, but they are con-strained. The largest constraint is in the quality of the data. The hyperbolic scattering shape peak gives the location of the pipe horizontally and is limited in accuracy by the positioning information available to describe the antenna

Ž .

position, orientation polarization and move-ment. Similarly, the shape of the hyperbola is determined by the accuracy of the positioning, and the degree of distortion caused by geologi-cal heterogeneity, thus limiting the ability to determine dielectric permittivity from the asymptotic slopes. The use of the hyperbola

shape asymptote lengths and radius of curva-.

ture at the peak to determine the size of the

object is constrained by the positioning, hetero-geneity, and the knowledge of the antenna pat-tern in the ground.

In the full waveform modeling, the con-straints are the assumptions about the far-field,

Ž .

vertical or normal incidence, polarization, and dealing with both dielectric and magnetic relax-ation. The model presented here only deals with amplitude of reflection at a scatterer using the Fresnel reflection coefficient, and neglects the angular dependence described by Snell’s law, and the polarization change described by the

Ž .

Stokes matrix van Zyl and Ulaby, 1990 . It also neglects scattering from the sides, not in the

plane of the image not under the antenna

tra-. Ž .

verse Olhoeft, 1994b . Models exist to de-scribe such things, but the computational re-quirements are no longer near real time nor within the ability of most portable computers. If exploited, these would give additional informa-tion such as the strike and dip of the pipe.

There is also much more information that may be derived from a radar dataset in terms of

describing geological heterogeneity Olhoeft, 1991, 1994a; Huffman, 1992; Lucius and

Ol-.

hoeft, 1996 , multipath and waveguide modes of

Ž .

propagation Olhoeft, 1993 , surface versus

vol-Ž .

ume scattering Schaber et al., 1986 ,

polariza-Ž .

tion Roberts and Daniels, 1996 , fluid occur-Ž

rence and behavior Olhoeft, 1986, 1992; Sander, 1994; Sander et al., 1992; Brewster et

al., 1995 , and more that can be found in other papers in the literature as referenced. Such mod-eling may also be very useful in predicting radar system performance prior to acquiring data, such as more optimal detection of plastic land mines

in wet rather than dry soil Powers and Olhoeft, .

1996a , or the relative ability to detect metal or Ž plastic pipes, and fluid leaks from pipes Powers

. and Olhoeft, 1996b .

Appendix A

The Federal Communications Commission has initiated an inquiry into ultra-wideband

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is-sues, which encompass ground penetrating radar and all electromagnetic transmissions above 9 kHz. The following is an illustration of one portion of the problem. A GSSI 500-MHz

cen-Ž .

ter frequency in air short pulse antenna is setup in a 6₌6₌3 m high underground room without exterior walls in the interior of a large

building the Green Center on the Campus of .

the Colorado School of Mines . This is done to reduce the signal levels from the cell repeaters to an analog cell phone in order to investigate the interference both ways between the cell phone and the radar system. With the radar off, the cell phone indicates a signal strength in the room about 1r6 of that outside the building, and has no trouble obtaining service. With the

radar on and the antenna properly coupled to the linoleum tile covered concrete floor, the cell phone cannot acquire service within about 1 m of the radar antenna, but once having acquired service outside that range, has no trouble keep-ing it right up to the cell phone touchkeep-ing the antenna. There is no noticeable change in the quality of the conversation up to contact. At the higher levels outside the building, the cell phone has no problems acquiring service right up to the antenna.

The cell phone is operating at a frequency near 900 MHz and the radar antenna coupled to the concrete has ay3-dB bandwidth of roughly 300 to 700 MHz. With the radar operating and the antenna stationary, the data in Fig. 11 are

Fig. 11. The right half of this image is in the presence of a cell phone that is turned off. The left half, the cell phone is on and acquiring service, but there is no communication. In the middle, the cell phone is being used for voice communication. The plotted line across the top of the image represents the data under the horizontal black line through the image, showing the change in noise level at 61.6 ns two-way travel time. The plotted lines in the boxes to the right are single wavelet wiggle

Ž .

traces at 806 and 810 scans across the images. At 806 left box the cell phone is on and being used to communicate, and at

Ž .

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obtained. In the image portion of Fig. 11 on the left, the cell phone is on, obtaining service, but

Ž .

not being used in standby . On the right, the cell phone is turned off. In the middle, the cell phone is being used to communicate a voice conversation. The data at the position of the horizontal line across the bottom of the image are plotted across the top of Fig. 11, clearly showing the change in noise amplitude levels with cell phone operation. The change in noise character from top to bottom in the image re-flect the modulation of the range gain, plotted in the right side of Fig. 11. The right two boxes containing wiggle trace plots of single scans are

Ž .

with the cell phone on and in use left and off Žright at vertical cursor positions 806 and 810. scans, respectively.

Under the conditions on the right with the cell phone off, the radar can map the thickness of the concrete, see the rebar in the concrete, and see the sewer pipe beneath the floor. On the left with the cell phone in standby, the radio frequency noise masks the sewer pipe so it cannot be found. In the middle, the active cell phone conversation makes rebar detection marginal and concrete thickness determination is not possible. See http:rrwww.fcc.gov and NOI 98-153 for more information about the issues.

References

Balanis, C.A., 1989. Advanced Engineering Electromag-netics. Wiley, New York, 981 pp.

Bochicchio, R., 1988. Computerized geometric correction of ground penetrating radar images. MSc Thesis, Geo-physical Engineering, Department of Geophysics, Col-orado School of Mines, Golden, CO, 91 pp.

Brewster, M.L., Annan, A.P., Greenhouse, J.P., Kueper, B.H., Olhoeft, G.R., Redman, J.D., Sander, K.A., 1995. Observed migration of a controlled DNAPL release by geophysical methods. Ground Water 33, 977–987. Canan, B., 1999. Dielectric properties of clay–water–

organic mixtures. PhD Thesis, Department of Geo-physics, Colorado School of Mines, Golden, CO, 400 pp.qCD-ROM.

Duke, S.K., 1990. Calibration of ground penetrating radar and calculation of attenuation and dielectric

permittiv-ity versus depth. MSc Thesis, Department of Geo-physics, Colorado School of Mines, Golden, 236 pp. Ghiglia, D.C., Pritt, M.D., 1998. Two-Dimensional Phase

Unwrapping. Wiley, New York, 493 pp.

Huffman, A.C., III, 1992. Characterization of three-dimen-sional geological heterogeneities using ground penetrat-ing radar. MSc Thesis, Department of Geophysics, Colorado School of Mines, Golden, 189 pp.

Kirkendall, B., 1998. A rapid limited 3-dimensional near-field modeling program for ground penetrating radar, MSc Thesis, Department of Geophysics, Colorado School of Mines, Golden, CO, 176 pp.

Kutrubes, D.L., 1986. Dielectric permittivity measure-ments of soils saturated with hazardous fluids, MSc Thesis, Department of Geophysics, Colorado School of Mines, Golden, 300 pp.

Lucius, J.E., Olhoeft, G.R., 1996. Geophysical investiga-tions of heterogeneity and scale at Princeton, Min-nesota, Management Systems Evaluation Area. In:

Ž .

Morganwalp, D.W., Aronson, D.A. Eds. , USGS WRI Report 94-4015. US Geological Survey Toxic Sub-stances Hydrology Program Review. Proc. of the Tech-nical Meeting, Colorado Springs, CO, September 20– 23, 1993, pp. 581–589.

May, B.T., Hron, F., 1978. Synthetic seismic sections of typical petroleum traps. Geophysics 43, 1119–1147. Morey, R.M., 1974. Geophysical surveying system

em-ploying electromagnetic impulses. US Patent 3,806,795, Fig. 2.

O’Connor, K.M., Dowding, C.H., 1999. GeoMeasure-ments by Pulse TDR Cables and Probes. CRC Press, Boca Raton, FL, 432 pp.

Olhoeft, G.R., 1981. Electrical properties of rocks. In:

Ž .

Touloukian, Y.S., Judd, W.R., Roy, R.F. Eds. , Physi-cal Properties of Rocks and Minerals. McGraw–Hill, New York, pp. 257–330.

Olhoeft, G.R., 1986. Direct detection of hydrocarbon and organic chemicals with ground penetrating radar and complex resistivity. Proc. of the NWWArAPI Confer-ence on Petroleum Hydrocarbons and Organic Chemi-cals in Ground Water — Prevention, Detection and Restoration, November 12–14, 1986, Houston. NWWA, Dublin, OH, pp. 284–305.

Olhoeft, G.R., 1987. Electrical properties from 10y3 _to

10q9Hz — physics and chemistry. In: Banavar, J.R.,

Ž .

Koplik, J., Winkler, K.W. Eds. , Physics and Chem-istry of Porous Media II. American Institute of Physics Conf. Proc. 154, Ridgefield, CT, 1986. AIP, New York, pp. 281–298.

Olhoeft, G.R., 1988. Selected bibliography on ground pen-etrating radar. Proceedings of the Symposium on the Applications of Geophysics to Engineering and Envi-ronmental Problems, March 28–31, 1988, Golden, CO, pp. 462–520.

(12)

Olhoeft, G.R., 1991. Quantitative statistical description of subsurface heterogeneities with ground penetrating radar at Bemidji, Minnesota. USGS WRI 91-4034. US Geo-logical Survey Toxic Substance Hydrology Program. Proceedings of the Technical Meeting, Monterey, CA, March 11–15, 1991, pp. 650–653.

Olhoeft, G.R., 1992. Geophysical detection of hydrocarbon and organic chemical contamination. In: Bell, R.S.

ŽEd. , Proceedings on Application of Geophysics to.

Engineering, and Environmental Problems, Oakbrook, IL. Society of Engineering and Mining Exploration Geophysics, Golden, CO, pp. 587–595.

Olhoeft, G.R., 1993. Velocity, attenuation, dispersion and diffraction hole-to-hole radar processing. In: Miller, R.,

ŽEd. , Proceedings of the Fourth Tunnel Detection.

Symposium on Subsurface Exploration Technology. Colorado School of Mines, Golden, CO, 26–29 April 1993. US Army Belvoir Research, Development and Engineering Center, pp. 309–322.

Olhoeft, G.R., 1994. Geophysical observations of geologi-cal, hydrological and geochemical heterogeneity. In:

Ž .

Bell, R.S., Leper, C.M. Eds. , Symp. on the Applica-tion of Geophysics to Engineering and Environmental Problems, March 27–31, 1994, Boston. EEGS, Little-ton, CO, pp. 129–141.

Olhoeft, G.R., 1994. Modeling out-of-plane scattering ef-fects. Proc. of the Fifth Int. Conf. on Ground Penetrat-ing Radar, Kitchener, Ontario, 12–16 June 1994, pp. 133–144.

Olhoeft, G.R., 1998a. Electrical, magnetic and geometric properties that determine ground penetrating radar per-formance. Proc. of GPR 1998, 7th Int. Conf. On Ground Penetrating Radar, May 27–30, 1998. The Univ. of Kansas, Lawrence, KS, USA, pp. 177–182.

Olhoeft, G.R., 1998b. GRORADARe: Acquisition, Process-ing, ModelProcess-ing, and Display of Ground Penetrating

Radar Data, ver. 4.0 software and data distributed on

CD-ROM at GPR 1998 . 7th Int. Conf. On Ground Penetrating Radar, May 27–30, 1998. The Univ. of

Ž .

Kansas, Lawrence, KS, USA http:rrwww.g-p-r.com . Olhoeft, G.R., Capron, D.E., 1993. Laboratory measure-ments of the radio frequency electrical and magnetic properties of soils from near Yuma, Arizona. US Geo-logical Survey Open-File Report 93–701, 214 pp. Olhoeft, G.R., Capron, D.E., 1994. Petrophysical causes of

electromagnetic dispersion. Proc. of the Fifth Int. Conf. on Ground Penetrating Radar, Kitchener, Ontario, 12– 16 June 1994, pp. 145–152.

Olhoeft, G.R., Powers, M.H., Capron, D.E., 1994. Buried object detection with ground penetrating radar. Proc. of

Ž .

Unexploded Ordnance UXO Detection and Range Remediation Conference, Golden, CO, May 17–19, 1994, pp. 207–233.

Paeth, A., 1990. Median finding on a 3₌3 grid. In:

Ž .

Glassner, A.S. Ed. , Graphics Gems. Academic Press, New York, pp. 171–175 and 711–712.

Powers, M.H., 1995. Dispersive ground penetrating radar modeling in 2D. PhD Thesis T-4820, Department of Geophysics, Colorado School of Mines, Golden, 198 pp.

Powers, M.H., Olhoeft, G.R., 1995. GPRMODV2: one-di-mensional full waveform forward modeling of disper-sive ground penetrating radar data, version 2.0. US Geological Survey Open File Report 95–58, 41 pp.q floppy diskette.

Powers, M.H., Olhoeft, G.R., 1996. Computer modeling to transfer GPR UXO detectability knowledge between sites. Proc. UXO Forum 1996 Conference Proceedings, Williamsburg, VA, March 26–29, 1996. Department of Defense Explosives Safety Board, Alexandria, VA, pp. 347–356.

Powers, M.H., Olhoeft, G.R., 1996. Modeling the GPR response of leaking, buried pipes. In: Bell, R.S., Cramer,

Ž .

M.H. Eds. , Proc. of SAGEEP 1996, Keystone, Col-orado. EEGS, Wheat Ridge, CO, pp. 525–534. Pratt, W.K., 1991. Digital Image Processing, 2nd edn.

Wiley, New York, 698 pp.

Roberts, R.L., Daniels, J.J., 1996. Analysis of GPR polar-ization phenomena. Journal of Environmental and

Engi-Ž .

neering Geophysics 1 2 , 139–157.

Sander, K.A., 1994. Characterization of DNAPL move-ment in saturated porous media using ground penetrat-ing radar. Master of Engineerpenetrat-ing Thesis, ER-4336, Department of Geology and Geological Engineering, Colorado School of Mines, Golden, CO, 258 pp. Sander, K.A., Olhoeft, G.R., Lucius, J.E., 1992. Surface

and borehole radar monitoring of a DNAPL spill in 3D versus frequency, look angle and time. In: Bell, R.S.

ŽEd. , Proc. of the Symposium on the Application of.

Geophysics to Engineering and Environmental Prob-lems, Oakbrook, IL. Society of Engineering and Min-eral Exploration Geophysics, Golden, CO pp. 455–469. Schaber, G.G., McCauley, J.F., Breed, C.S., Olhoeft, G.R., 1986. Shuttle imaging radar: physical controls on signal penetration and subsurface scattering in the eastern Sahara. Institute of Electrical and Electronic Engineers Transactions: Geoscience and Remote Sensing GE-24, 603–623.

Sen, P.N., Scala, C., Cohen, M.H., 1981. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics 46, 781–795.

Sheriff, R.E., 1984. Encyclopedic Dictionary of Explo-ration Geophysics, 2nd edn. Soc. of Explor. Geophys., Tulsa, 323 pp.

Smith, G.S., 1997. An introduction to classical electromag-netic radiation. Cambridge Univ. Press, Cambridge, UK, 653 pp.

(13)

van Zyl, J.J., Ulaby, F.T., 1990. Scattering matrix repre-sentation for simple targets: In: Ulaby, F.T., Elachi, C.

ŽEds. . Radar Polarimetry for Geoscience Applications..

Artech House, Norwood, MA, pp. 17–52.

Weeks, A.R., Kasparis, T., Lane, J.E., 1993. Image en-hancement using linear and non-linear spatial filtering techniques. DSP Applications, November, pp. 35–44.

Yilmaz, O., 1987. Seismic data processing. Soc. Explor. Geophys., Tulsa, pp. 90 and 259.

Zuiderveld, K., 1994. Contrast limited adaptive histogram

Ž .

equalization. In: Heckbert, P.S. Ed. , Graphics Gems IV. Academic Press, New York, pp. 474–485.

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zero crossings between the model and the data

align better, the original processing depth

esti-mate is adjusted from 0.34 to 0.36 m.

5. Estimating the soil density and water

con-tent

The main wavelet being reflected by the pipe

also has some character beyond that of the ideal

Ricker wavelet. In particular, the wavelet has

one up-going peak and two down-going peaks,

with the ideal Ricker wavelet showing the two

down-going peaks to be the same amplitude.

However, the recorded data show the two

down-going peaks to have different amplitudes.

Ž

This is caused by frequency dependence

or

.

dispersion in the electromagnetic properties that

control the velocity and attenuation of

propaga-Ž

.

tion Olhoeft, 1998a . The Cole–Cole

parame-ters in Fig. 10 are adjusted to match this

ampli-tude difference, changing the shape of the model

wavelet to better fit the recorded data. In the

process, the zero crossing match requires

an-other depth adjustment to 0.37 m. The depth to

the pipe has now been determined to a high

accuracy, and the model result agrees

remark-Ž

.

ably well with the known depth 0.37 m to the

top of the pipe. The remainder of the wiggles in

the field data are caused by radio frequency

Ž

noise and should not be modeled this is

deter-mined by looking at the texture and patterns in

.

the 2D radar image in the earlier figures .

Frequency dependences in geological

materi-als are dominantly caused by dielectric

relax-ation processes related to the presence of water,

and to a lesser extent by magnetic relaxation

processes related to the presence of iron bearing

minerals, and a variety of scattering processes

Ž

Olhoeft and Capron, 1994; Olhoeft, 1998a .

.

Assuming all of the frequency dependence

comes from the presence of water, the model

fitted Cole–Cole parameters indicate the

re-quirement of about 1% or 2% water by volume

in the soil between the antennas and the pipe to

cause the required dispersion and subsequent

change in wavelet shape. The Bruggeman–

Ž

Hanai–Sen volumetric mixing formula Sen et

Fig. 10. Further improving the model fit over Fig. 9 by including the effects of a frequency dependent complex dielectric permittivity.

(2)

.

al., 1981; Olhoeft, 1987 may be used to

con-vert the dielectric permittivity into bulk density,

giving a volume average density of 1.89 g

r

cm

_,

28% porosity sand equivalent soil between the

antennas and the pipe, right over the pipe

through the trenching disturbed soil. These

val-ues are consistent with laboratory measurements

Ž

on soil samples from the site

Olhoeft and

.

Capron, 1993 and on the measured variation of

frequency dependence with moisture content in

Ž

soils

Kutrubes, 1986; Olhoeft, 1981, 1987;

.

Canan, 1999 . These values are typically

mea-sured in situ for soils using time domain

reflec-Ž

.

tometry O’Connor and Dowding, 1999 , which

requires pushing probes into the ground, but

have been derived here noninvasively from

ground penetrating radar data.

The processing and modeling just performed

require a few minutes played like a video game

on a 32-bit laptop computer. They have yielded

Ž

considerable information about the pipe

loca-.

Ž

tion, size and depth and the soil density and

.

water content . The processing, modeling, and

Ž

.

display figure generation were all done with

Ž

.

the

GRORADAR

e

software Olhoeft, 1998b .

6. Discussion

The parameters derived by this processing

are not necessarily unique, but they are

con-strained. The largest constraint is in the quality

of the data. The hyperbolic scattering shape

peak gives the location of the pipe horizontally

and is limited in accuracy by the positioning

information available to describe the antenna

Ž

.

position, orientation

polarization

and

move-ment. Similarly, the shape of the hyperbola is

determined by the accuracy of the positioning,

and the degree of distortion caused by

geologi-cal heterogeneity, thus limiting the ability to

determine

dielectric

permittivity

from

the

asymptotic slopes. The use of the hyperbola

Ž

shape asymptote lengths and radius of

curva-.

ture at the peak to determine the size of the

object is constrained by the positioning,

hetero-geneity, and the knowledge of the antenna

pat-tern in the ground.

In the full waveform modeling, the

con-straints are the assumptions about the far-field,

Ž

.

vertical or normal incidence, polarization, and

dealing with both dielectric and magnetic

relax-ation. The model presented here only deals with

amplitude of reflection at a scatterer using the

Fresnel reflection coefficient, and neglects the

angular dependence described by Snell’s law,

and the polarization change described by the

Ž

.

Stokes matrix van Zyl and Ulaby, 1990 . It also

neglects scattering from the sides, not in the

Ž

plane of the image not under the antenna

tra-. Ž

.

verse

Olhoeft, 1994b . Models exist to

de-scribe such things, but the computational

re-quirements are no longer near real time nor

within the ability of most portable computers. If

exploited, these would give additional

informa-tion such as the strike and dip of the pipe.

There is also much more information that

may be derived from a radar dataset in terms of

Ž

describing geological heterogeneity

Olhoeft,

1991, 1994a; Huffman, 1992; Lucius and

Ol-.

hoeft, 1996 , multipath and waveguide modes of

Ž

.

propagation Olhoeft, 1993 , surface versus

vol-Ž

.

ume scattering Schaber et al., 1986 ,

polariza-Ž

.

tion Roberts and Daniels, 1996 , fluid

occur-Ž

rence and behavior

Olhoeft, 1986, 1992;

Sander, 1994; Sander et al., 1992; Brewster et

.

al., 1995 , and more that can be found in other

papers in the literature as referenced. Such

mod-eling may also be very useful in predicting radar

system performance prior to acquiring data, such

as more optimal detection of plastic land mines

Ž

in wet rather than dry soil Powers and Olhoeft,

.

1996a , or the relative ability to detect metal or

Ž

plastic pipes, and fluid leaks from pipes Powers

.

and Olhoeft, 1996b .

Appendix A

The Federal Communications Commission

has initiated an inquiry into ultra-wideband

(3)

is-sues, which encompass ground penetrating radar

and all electromagnetic transmissions above 9

kHz. The following is an illustration of one

portion of the problem. A GSSI 500-MHz

cen-Ž

.

ter frequency

in air

short pulse antenna is

setup in a 6

₌

6 ₌

3 m high underground room

without exterior walls in the interior of a large

Ž

building the Green Center on the Campus of

.

the Colorado School of Mines . This is done to

reduce the signal levels from the cell repeaters

to an analog cell phone in order to investigate

the interference both ways between the cell

phone and the radar system. With the radar off,

the cell phone indicates a signal strength in the

room about 1

r

6 of that outside the building,

and has no trouble obtaining service. With the

radar on and the antenna properly coupled to the

linoleum tile covered concrete floor, the cell

phone cannot acquire service within about 1 m

of the radar antenna, but once having acquired

service outside that range, has no trouble

keep-ing it right up to the cell phone touchkeep-ing the

antenna. There is no noticeable change in the

quality of the conversation up to contact. At the

higher levels outside the building, the cell phone

has no problems acquiring service right up to

the antenna.

The cell phone is operating at a frequency

near 900 MHz and the radar antenna coupled to

the concrete has a

y

3-dB bandwidth of roughly

300 to 700 MHz. With the radar operating and

the antenna stationary, the data in Fig. 11 are

Ž .

traces at 806 and 810 scans across the images. At 806 left box the cell phone is on and being used to communicate, and at

Ž .

(4)

obtained. In the image portion of Fig. 11 on the

left, the cell phone is on, obtaining service, but

Ž

.

not being used in standby . On the right, the

cell phone is turned off. In the middle, the cell

phone is being used to communicate a voice

conversation. The data at the position of the

horizontal line across the bottom of the image

are plotted across the top of Fig. 11, clearly

showing the change in noise amplitude levels

with cell phone operation. The change in noise

character from top to bottom in the image

re-flect the modulation of the range gain, plotted in

the right side of Fig. 11. The right two boxes

containing wiggle trace plots of single scans are

Ž

.

with the cell phone on and in use left and off

Ž

right at vertical cursor positions 806 and 810

.

scans, respectively.

Under the conditions on the right with the

cell phone off, the radar can map the thickness

of the concrete, see the rebar in the concrete,

and see the sewer pipe beneath the floor. On the

left with the cell phone in standby, the radio

frequency noise masks the sewer pipe so it

cannot be found. In the middle, the active cell

phone

conversation

makes

rebar

detection

marginal and concrete thickness determination

is not possible. See http:

rr

www.fcc.gov and

NOI 98-153 for more information about the

issues.

References