The role of ground penetrating radar and …...The role of ground penetrating radar and geostatistics in reservoir description ROSEMARY KNIGHT and PAULETTE TERCIER, University of British

The role of ground penetrating radar and geostatistics in reservoir description

ROSEMARY KNIGHT and PAULETTE TERCIER, University of British ColumbiaHARRY JOL, University of Wisconsin - EAU CLAIRE

Interpreters are routinely requiredto develop a continuous model ofthe subsurface through the integra-tion of available data. One of theissues commonly encountered ishow best to “fill in” the regionbetween data points, or describe theregion at a scale less than the scaleof the sampling. We take this oppor-tunity, as part of the Near-SurfaceGeophysics issue, to describe re-search currently underway that canassist in the development of geo-logic models. A near-surface geo-physical method, ground penetrat-ing radar (GPR), provides highresolution images of near-surfacesedimentary packages that can beused to obtain an improved under-standing of both the large-scale andsub-meter scale architecture foundin a variety of depositional environ-ments. In addition, the GPR imagescan be analyzed to obtain a geosta-tistical representation of the deposi-tional environment that could beused in generating stochastic mod-els of the subsurface.

In this paper we present GPRimages from selected deltaic, coastal,and fluvial environments and showboth the detailed sedimentology thatis imaged and the information that isboth captured and lost through thegeostatistical characterization.

GPR images of selected deposition-al environments. GPR studies ofboth modern and ancient systemscan provide a large amount of infor-mation that can improve the under-standing of the lithologic variationand internal structure of ancientreservoirs. A number of recent stud-ies have used 2-D and 3-D GPR datato characterize sedimentary units anddifferent depositional environments.

In a GPR survey, electromagnet-ic energy in the frequency range 1-1000 MHz is transmitted into theground. Changes in the dielectricproperties of the subsurface causereflections of energy which aredetected on the surface. The result ofa GPR survey, the radar image, is amap of reflections marking interfacesacross which there are changes indielectric properties. GPR data arecommonly collected by using a sin-gle transmitter antenna and a singlereceiver antenna and moving thesetwo, at a constant offset, along thesurvey line. Station spacing (i.e.,trace spacing on the final GPR sec-tion) is usually on the order of tensof centimeters to a meter, dependingon the survey’s objective.

GPR data provide remarkablygood images of coarse sedimentarypackages. An excellent example ofGPR data collected over a deltaic

environment is shown in Figure 1.These data were collected in theBrigham City Sand and Gravel Com-pany pit floor and show the late Pleis-tocene Box Elder Creek delta. A pic-ture of a nearby outcrop is shown onthe cover of this issue. This is a clas-sic Gilbert-type fan-foreset delta dom-inated by steeply inclined beds ofsand and gravel. The dipping reflec-tions seen in the GPR data exhibit ahigh degree of continuity and areinterpreted as steeply dipping strata.As GPR records changes in the dielec-tric properties of the subsurface, it ismost likely in this environment thatwe are seeing the boundaries acrosswhich there are changes in grain size.

Figure 2 is an example of GPRdata collected over a sandy coastalbarrier spit, a regressive modern bar-rier spit at Willapa Bay, Washingtonwhich is 38 km long and up to 5 kmwide. The dipping reflections in thissection, are interpreted as beach-face/upper shoreface beds indicatinga shingle-like accretionary deposi-tional pattern. In the strike profileshown in Figure 3, these same bound-aries are seen as a subhorizontal,nearly continuous bedding pattern.

Figure 4 shows an example ofGPR data from a Late Pleistocenebraided fluvial deposit from theEmbarras Airfield, northeastern

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Figure 1. GPR data collected over the Box Elder Creek delta (modified from “Ground-penetrating radar investiga-tion of a Lake Bonneville delta, Provo level, Brigham City, Utah” by Smith and Jol, Geology, 1992). The steeplyinclined beds of sand and gravel in this classic Gilbert type fan foreset delta are seen in the GPR profile. The datainside the blue lines were used in the geostatistical analysis of the GPR section.

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Alberta. The short, discontinuousreflections in the GPR section areinterpreted as cut and fill structures,caused by changes in stream course.The boundaries often observed inGPR profiles probably representbounding discontinuities which mayinclude contacts between beds andsedimentary structures, channelscours, and the base and top of strati-graphic units.

These examples illustrate thevalue of GPR studies in imaging theinternal structure of modern andancient deposits. This allows us to bet-ter understand the nature of the spa-tial heterogeneity that is found at allscales in these types of environments.

Geostatistics from GPR data. Indeveloping a model of the subsur-face, an approach commonly taken isto describe the spatial variabilityusing geostatistics. In the same waythat geostatistical analysis of datafrom analog outcrops is presentlyused in generating stochastic modelsof the subsurface, we suggest thatanalog GPR sections can also be usedas a means of characterizing small-scale heterogeneity. When we usegeostatistical methods to analyze theGPR images, we obtain a geostatisti-cal representation of the image in theform of a semivariogram. It is infor-mative to see what informationabout the internal structure in theGPR images is actually captured inthe geostatistical representation.

Geostatistics is a mathematicalframework that allows us to describethe spatial relationship between datavalues in a region. In our work weuse the semivariogram, a plot whichillustrates the way in which the dif-ference between data values is relat-ed to the distance between the datavalues.

Let us consider some parameterof interest z, where the value of zvaries throughout a region of thesubsurface. To construct our experi-mental semivariogram, that willdescribe the way in which z variesthroughout this region, we select twolocations, separated by a distance hand we compute the differencebetween z at these two locations. Wedo this for all data pairs separated byh and then repeat this exercise for hequal to many other distances. Thesemivariogram is a plot of semivari-ogram function γ (defined in theAppendix) versus h, and is a way ofshowing the difference between datapoints as the distance between themincreases. In our geostatistical analy-

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Figure 2. GPR data collected over the Willapa Bay coastal barrier spit (modifiedfrom “A detailed ground penetrating radar investigation of a coastal barrierspit, Long Beach, Washington, U.S.A.” by Jol et al., 1994 SAGEEP Proceedings.)The dipping reflections are interpreted as beachface/upper shoreface beds indi-cating a shingle-like accretionary depositional pattern. The data inside the bluelines were used in the geostatistical analysis of the GPR section.

Figure 3. GPR strike profile of the Willapa Bay coastal barrier spit (modi-fied from Jol et al.). The beachface/upper shoreface beds are seen as sub-horizontal, laterally continuous reflectors.The data inside the blue lineswere used in the geostatistical analysis of the GPR section.

Figure 4. GPR profile of a braided fluvial deposit from the Embarras Airfield,northeastern Alberta (modified from “Ground penetrating radar: high resolu-tion stratigraphic analysis of coastal and fluvial environments” by Jol et al., pre-sented at the GCSSEPM Foundation 17th Annual Conference, 1996). The short,discontinuous reflections are interpreted as cut and fill structures. The datainside the blue lines were used in the geostatistical analysis of the GPR section.

sis of the GPR data, we use theamplitude values recorded in theradar traces to construct the experi-mental variogram using the programGSLIB.

Let us first consider the GPRimage in Figure 1 from the deltaicenvironment. It is clear that we areseeing in this image features that arelaterally continuous over manymeters in the down dip direction. Ourgeostatistical analysis first indicatesthat the direction of maximum conti-nuity is at a dip of 20°, and we con-struct our experimental variogram inthis direction. The result, Figure 5, isa classic example of a variogram. Thedata points in the experimental vari-ogram (the circles in the figure) are fitusing a standard variogram model(shown as a solid line). Unlike manygeostatistical studies where the lackof data points makes it very difficultto accurately define and interpret thevariogram, the large number of datapoints in the GPR data gives us a“text book” example of a variogram.As seen in Figure 5, the semivari-ogram function γ increases as the dis-tance between data points increases,and levels off when the distancebecomes so large that the data valuesare no longer correlated. For this dataset we find this distance to be 53 m.When we refer back to the GPR imagewe can see that our geostatisticalanalysis of the GPR image from thedeltaic environment has capturedwhat is seen as the dominant featurein this data set, and interpret the 53 mas a measure of the continuity of theinclined strata/ reflections.

In the next example, we analyzethe data shown in Figure 2 from thesandy coastal barrier spit. The direc-tion of maximum correlation wasfound to be along depositional dip,at an angle of 3° to the west. In Fig-ure 6 is shown the experimental var-iogram which is modeled to obtain acorrelation length of 24 m. In refer-ring to the GPR image, we concludethat in this case the geostatistics con-tains information about the dipdirection and the continuity of thebeachface/upper shoreface beds.While other more subtle, smallerscale features can be seen in the GPRdata, the reflections from these bedsare such dominant features that ourgeostatistical analysis is only sensi-tive to this structure in the data set.

In the GPR data in Figure 3 we seethe near-horizontal orientation in thebeachface/upper shoreface beds, con-tinuous over most of the section,when imaged in the strike direction.

The experimental variogram obtainedfrom this data set is shown in Figure7, and is found from the modeling tobe dominated by a correlation lengthof 46 m. Again we find that the largescale structure of the beachface/uppershoreface beds is the main feature con-tributing to the semivariogram. Thecontinuity of these beds is found to be

twice as long in the strike direction asin the dip direction. The anisotropypresent in most depositional systemscan be well documented through thecollection and analysis of 3-D GPRdata sets.

Figure 4 shows an example ofGPR data from a braided river. Theexperimental variogram in Figure 8

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Figure 5. Semivariogram obtained through analysis of the GPR data(shown in Figure 1) from the deltaic environment. The data points are thecircles; the model of the semivariogram is the solid line. The geostatisti-cal results give a correlation length of 53 m in a dip direction of 20°. Thisis a measure of the distance over which the inclined strata are continuous.

Figure 6. Semivariogram obtained through analysis of the GPR image of thecoastal barrier spit. The data points are the circles; the model of the semivari-ogram is the solid line. Referring to the GPR data in Figure 2, this variogramwas constructed at an angle of 3° to the west and indicates that the reflectionsfrom the beachface/upper shoreface beds have a correlation length of 24 m.This can be taken as a measure of the spatial continuity of these reflections.

quantifies the spatial heterogeneityseen in this environment. Again, weobtain a very high quality variogramwhich can be modeled with a corre-lation length of 6 m. We find in thisdepositional environment short, dis-continuous reflections, unlike thecoastal environment which tends toproduce continuous features overtens of meters. The length scale of 6m is interpreted as a measure of thescale of the variability associatedwith erosion and deposition of chan-nels and bars. Geostatistical analysisof GPR data appears to be a veryeffective means of describing theobserved structure in the image.

The link between GPR images andmaterial properties. GPR data giveus an excellent way of imaging anddescribing spatial variability in thesubsurface. The critical issue whichmust still be addressed is the rela-tionship between the GPR image andthe properties of the subsurface.Determining this link, between theGPR image and the “geological real-ity” is a key part of our research. Theapproach that we are taking is to con-duct cliff face studies: GPR data arecollected along the top of the cliff andthe imaged section can be seen andsampled. This offers an outstandingopportunity to determine what isreally imaged in the GPR section; i.e.to “ground truth” the GPR data.

In one cliff face experiment wecompared the geostatistical analysisof a photographic image and a GPRimage of a sequence of alternatingcoarse sand, and fine sand and silt.The digital photograph of the facecaptured information about the spa-tial distribution of coarse grained andfine grained beds on the basis of grayscale. There was excellent agreementbetween the variograms from the pho-tograph and the radar data, in deter-mining both the maximum correla-tion direction and the correlationlength. These results led us to con-clude that the GPR data did in factimage the spatial distribution of thesetwo lithologies and could be used toquantify both the correlation directionand length in this sedimentary unit. Inthis example the spatial variation indielectric properties in the subsurfacewas closely related to the spatial vari-ation in grain size; this is very reason-able given what is known about therelationship between dielectric prop-erties and sedimentary properties.

Conclusions. Ground penetratingradar is a high resolution geophysical

technique that can provide outstand-ing image of sedimentary packages.We can use these GPR images ofselected depositional environmentsto further our understanding of bothdepositional processes and the result-ing structure and heterogeneity thatwill exist in the subsurface.

We find that geostatistical analy-sis of GPR images can be used

to obtain a geostatistical representa-tion of the different depositionalenvironments. This geostatisticalanalysis captures information about the spatial distribution of the domi-nant sedimentological features, butinevitably loses information aboutmuch of the detailed sub-meter scalevariability that can be seen in theimage. Our long-term objective in

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Figure 7. Semivariogram obtained through analysis of the GPR strike pro-file of the coastal barrier spit, shown in Figure 3. The data points are thecircles; the model of the semivariogram is the solid line. When imaged inthis direction the near-horizontal reflections from the beachface/uppershoreface beds are found to have a correlation length of 46 m.

Figure 8. Semivariogram obtained for the GPR profile (Figure 4) of a braid-ed river sand. The data points are the circles; the model of the semivari-ogram is the solid line. The short, discontinuous reflectors, which likelyrepresent the erosion and deposition of channels and bars, have a correla-tion length of 6 m.

this research is to collect and ana-lyze GPR data from a wide variety ofdepositional environments to deter-mine whether there exists a charac-teristic geostatistical “signature”associated with specific environ-ments. The variograms from theGPR data could then be used to helpextrapolate in areas where the depo-sitional environment is known, butthere is a shortage of hard data. Inthis way, GPR studies of near-sur-face, modern and ancient deposits,can assist in the integration of data toobtain a more realistic and accuratemodel of the subsurface.

Suggestions for further reading. Anumber of recent studies have used2-D and 3-D GPR data to character-ize sedimentary units and differentdepositional environments. Someexamples of these are: “Ground pen-etrating radar: high resolution strati-graphic analysis of coastal and flu-vial environments” by Jol et al.(SEPM, 1996); “Response of groundpenetrating radar to bounding sur-faces and lithofacies variations insand barrier sequences” by Baker(Exploration Geophysics, 1991);“Anatomy of a bioclastic grainstonemegashoal (Middle Silurian, south-

ern Ontario) revealed by groundpenetrating radar” by Pratt andMiall (Geology, 1993); and “Use ofground penetrating radar for 3-Dsedimentological characterization ofclastic reservoir analogs” byMcMechan et al. (GEOPHYSICS, 1997).An excellent introduction to geosta-tistics can be found in the book byIsaaks and Srivastava, titled An Intro-duction to Applied Geostatistics(Oxford University Press, 1989).Geostatistical analysis of the GPRdata was completed using softwareprovided in GSLIB Geostatistical Soft-ware Library and User’s Guide byDeutsch and Journel (Oxford Uni-versity Press, 1992). Details of themethodology used to analyze theGPR data are given in “Geostatisticalanalysis of ground penetrating radardata: a means of describing spatialvariation in the subsurface” by Reaand Knight (Water Resources Research,accepted for publication 1997). LE

Acknowledgments: Funding for this researchhas been received from Amoco Canada, Cono-co, Esso Resources, Pan Canadian, Petrel-Robertson, Petro-Canada, Natural Sciencesand Engineering Council of Canada, NorcenEnergy Resources, Western Geophysical, theUniversity of Wisconsin-Eau Claire. and Sen-sors and Software. This work has also been

supported by the U.S. Air Force Office of Sci-entific Research, Air Force Material Com-mand, USAF, under grant number F49620-95-I-0166. The U.S. government is authorizedto reproduce and distribute reprints for gov-ernmental purposes notwithstanding anycopyright notation thereon. The views andconclusions contained herein are those of theauthors and should not be interpreted as nec-essarily representing the official policies orendorsements, either expressed or implied, ofthe Air Force Office of Scientific Research orthe U.S. government. Derald Smith and RickMeyers (University of Calgary) are acknowl-edged for their field support, and we thankBruce Slevinsky of Petro-Canada who initial-ly triggered our interest in geostatistical analy-sis of GPR data for reservoir characterization.

Corresponding author: Rosemary Knight,[email protected]

APPENDIX. The experimental semi-variogram is described by the fol-lowing equation:

where h is the lag, or separation vec-tor, between two data points, z(x)and z(x+h), and N is the number ofdata pairs used in each summation.

γ ( ) z(x ) z(x h)N i i

i

N

hh

h

= − +[ ]( )=

( )

∑12

1

2

2