3-d characterization of a clastic reservoir analog: from 3-d gpr

GEOPHYSICS, VOL. 66, NO. 4 (JULY-AUGUST 2001); P. 1026–1037, 16 FIGS., 2 TABLES.

3-D characterization of a clastic reservoir analog: From 3-D GPR datato a 3-D fluid permeability model

R. B. Szerbiak∗, G. A. McMechan∗, R. Corbeanu∗, C. Forster‡,and S. H. Snelgrove‡

ABSTRACT

A three-dimensional (3-D) 100 MHz ground-pene-trating radar (GPR) data volume is the basis of in-situ characterization of a fluvial reservoir analog in theFerron Sandstone of east-central Utah. We use the GPRreflection times to image the bounding surfaces via 3-Dvelocity estimation and depth migration, and we usethe 3-D amplitude distribution to generate a geostatis-tical model of the dimensions, orientations, and geome-tries of the internal structures from the surface down to∼12 m depth. Each sedimentological element is assigneda realistic fluid permeability distribution by kriging withthe 3-D correlation structures derived from the GPRdata and which are constrained by the permeabilities

measured in cores and in plugs extracted from the adja-cent cliff face.

The 3-D GPR image shows that GPR facies changescan be interpreted to locate sedimentological bound-ing surfaces, even when the surfaces do not corre-spond to strong GPR reflections. The site contains twomain sedimentary regimes. The upper ∼5 m containtrough cross-bedded sandstone with average perme-ability of ∼40 md and maximum correlation lengths∼(5.5–12.5) × (3.5–8.0) × (0.2–1.5) m. The lower∼7 m contain scour and fill fluvial deposits with aver-age permeability varying from ∼30 md to ∼15 md asclay content increases, and maximum correlation lengths∼(4.0–12.5) × (3.0–10.0) × (0.5–1.0) m. These represen-tations are suitable for input to fluid flow modeling.

INTRODUCTION

The study of reservoir analogs (at sites where reservoir envi-ronments outcrop at the earth’s surface) has progressed fromone- to two- to three-dimensional (3-D) models of depositionalsystems (Miall and Tyler, 1991; Flint and Bryant, 1993). Thelong-term goal of such studies is the building of accurate 3-Dmodels of the internal structures of reservoirs for reliable sim-ulations of fluid flow for evaluation of production strategies(Tomutsa et al., 1991; Tyler et al., 1992; Fisher et al., 1993a,b). Inthe past, development of 3-D models has typically involved in-terpolation between outcrops or wells based on geometrical orstatistical descriptions of the facies (Allen, 1979; Gundeso andEgeland, 1990; Haldorsen and Damsleth, 1990; Falt et al., 1991)because direct information was not available.

Characterization of reservoir analogs can benefit substan-tially by direct imaging of internal structure by ground-penetrating radar (GPR) (Baker, 1991; Gawthorpe et al., 1993;Bridge et al., 1995). Although most GPR data collected over

Manuscript received by the Editor November 29, 1999; revised manuscript received October 24, 2000.∗The University of Texas at Dallas, Center for Lithospheric Studies, Post Office Box 830688, Richardson, Texas 75083-0688, United States. E-mail:[email protected].‡University of Utah, Department of Geology and Geophysics, 719 Browning Building, Salt Lake City, Utah 84112-0111, United States.c© 2001 Society of Exploration Geophysicists. All rights reserved.

reservoir analogs are 2-D lines (Alexander et al., 1994; Bristow,1995; Aigner et al., 1996; Rea and Knight, 1998), a few full3-D surveys have been acquired (Beres et al., 1995; McMechanet al., 1997). These surveys reveal the dimensions, orientations,geometries, and connectivity of the internal sedimentologicalelements at the scale of meters or less. Three-dimensional GPRrequires 3-D velocity analysis and migration, similar to thoseperformed in 3-D seismic data processing.

When tied to measurements of petrophysical properties(such as fluid permeability) at control points (such as wells oroutcrops), the reservoir elements imaged by GPR can be as-signed realistic petrophysical properties. The goal of the studyreported below is to construct a 3-D permeability model fromGPR data and measured permeabilities, constrained by a va-riety of other measurements. Detailed analyses of the sedi-mentological data, cores, borehole and lab measurements, andflow simulations are beyond the scope of this paper and arepresented elsewhere, although many of these are implict in theresults presented here. Thurmond et al. (1997), McMechan and

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3-D Reservoir Analog Characterization 1027

FIG. 1. Location of the Coyote Basin reservoir analog site.

FIG. 2. Photomosaic of the cliff face at Coyote Basin with interpreted flow units (5, 4, 3, 2, and 1) separated by bounding surfaces (E,D, C, B, and A). F is the present topographic surface. CBn are the locations of pseudohole sections at the cliff face used for depthcontrol and for measuring stratigraphic sections and gamma-ray profiles; extracting core plugs for porosity, fluid permeability, andelectrical property measurements; and for cutting thin sections used in petrography analyses.

1028 Szerbiak et al.

Soegaard (1998), Wang (2000), and Corbeanu et al. (2001) con-tain much of the auxiliary data and some preliminary results.

SITE DESCRIPTION

The field site of the fluvial reservoir analog used in this paperis in the SC3 member of the Ferron Sandstone, which lies withinthe Mancos Shale at the southwestern edge of the San RafaelSwell in east-central Utah (Figure 1). The Ferron Sandstonewas chosen because it has been used extensively in the pastfor reservoir studies and for industry training classes. The par-ticular site chosen (Coyote Basin) has excellent stratigraphiccontrol, outstanding surface and cliff face exposures, and anenvironment that is amenable to acquisition of GPR data (ac-cess to a mesa top with a planar surface with little vegetationadjacent to a cliff). Previous reconnaisance in other parts ofthe Ferron (McMechan et al., 1997) showed the ability of thisenvironment to provide high-resolution images with featuresat scales that can be extrapolated with control from 1-D and2-D sedimentary data, obtained in boreholes, cliff faces, andsurface mapping, into three-dimensions. GPR velocity and at-tenuation are influenced by variations in sand/clay content andporosity, knowledge of which is essential for building reservoirmodels used in fluid flow simulations. Thus, the Coyote Basinsite provides a good test data set.

The upper ∼12 m at Coyote Basin consist of a fluvial sand-stone which scours into the underlying flood plain mudstoneand coal. There are five architectural elements in the sand-stone, identified as units 1 through 5 in ascending stratigraphicorder (Figure 2). Unit 5 lies in the upper 5 m of the com-plex and units 1–4 lie in the lower 7 m. Surfaces A throughE separate the architectural elements with intermittent mud-stone intraclast conglomerates along the erosional basal scours.The A/B surface separates the flood plain mudstone fromthe overlying channel sandstone. The E surface separates themedium-large grained trough cross-bedded sandstone in unit 5from the fine-grained parallel-laminated lenticular sandstonein unit 4. Units 1–4 are interpreted as scour and fill depositsformed during flood cycles, and unit 5 is interpreted to bea channel sandstone deposited in a flow environment char-acterized by uniform and steady discharge (Thurmond et al.,1997).

DATA AQUISITION AND PREPROCESSING

In the summers of 1996 and 1997, 3-D, 2-D, and boreholeGPR data were acquired, four boreholes were cored to a depthof ∼15 m each, and five cliff-face pseudohole profiles werelocated along the southeast edge of the site (Figures 2, 3).Pseudohole profiles consist of measurements made verticallydown the cliff face to simulate data that would be acquiredfrom a cored hole at that location. Thirty-three one-inch diam-eter cylindrical plugs were extracted from the cores (orthogo-nal to the borehole axes) and from the cliff-face pseudoholes.Bulk porosity and minipermeameter data were measured fromthe plugs and the continuous cores. Laboratory measurementson the plug samples provided quantitative information on thepetrophysical and electrical properties of the rocks. Petro-graphic analysis of thin sections provided quantitative miner-alogy information for dielectric constant modeling, parameters

for GPR data modeling, and porosity and sand/clay ratio datafor the reservoir analog. Electrical property analyses (dielec-tric permittivity and electrical conductivity) (McMechan andSoegaard, 1998) provided GPR velocity control and dispersioninformation as a function of fluid saturation.

Surface GPR data acquisition

A rectangular grid was surveyed on the top of the mesa(Figure 3) adjacent to the cliff face for the 3-D GPR data ac-quisition. Dimensions of the grid are 40.0 m × 16.5 m with a0.5 m grid spacing between both lines and stations on each line.The GPR lines strike approximately N10◦W. The 3-D GPRdata volume consists of 34 north-south lines each of 80 traces,giving a total of 2720 traces. The GPR equipment used was aPulseEKKO IV system (manufactured by Sensors & Software,Inc.), with a transmitter voltage of 1000 V. Half-wave dipoletransmitter and receiver antennas were oriented parallel toeach other and perpendicular to the in-line direction to recordtransversely polarized electric waves. Three-dimensional datasets were recorded at frequencies of 50, 100, and 200 MHz,which provided depth resolutions of ∼1.0, 0.5, and 0.25 m, re-spectively. The maximum depth of penetration was ∼8 m forthe 200 MHz data, and was limited by the clay-rich flood plainsiltstone at ∼12 m depth for the 100 MHz and 50 MHz data.A single common-midpoint (CMP) gather, covering an offsetrange of 26 m, was recorded for each frequency. The CMPsprovided initial velocity control and helped determine the

FIG. 3. Coyote Basin survey map. CBn are the pseudohole pro-file location shown in Figure 1. A–D are cored wells, “+” sym-bols outline the 3-D GPR grid. GPR traces were collected ev-ery 0.5 m in both X and Y directions. Solid lines crossing thesurface are mapped fractures.


optimal source-receiver offsets for acquiring the 3-D common-offset data. Velocities varied from ∼0.125 m/ns near the surfaceto ∼0.06 m/ns in the deeper siltstone, with an average veloc-ity of 0.092 m/ns. Offsets used were 3 m for the 50 MHz and100 MHz data and 2 m for the 200 MHz data. The time sam-pling increment was 800 ps, and the record length was 800 ns.Reflections were recorded from both submeter-scale sedimen-tary structures and larger dimension architectural features. The100 MHz data represented a good compromise between res-olution and depth of penetration, so we concentrate on thesedata in the following sections.

GPR data preprocessing

If the attenuation and dispersion are sufficiently small (es-pecially when electrical conductivity is small), GPR data ap-pear (except for the time scale) somewhat similar in theirkinematic properties to reflection seismic data (Davis and An-nan, 1989). Under these conditions, GPR data processing cantake advantage of some parts of seismic data processing anddisplay/interpretation software (Fisher et al., 1992). Notableexceptions occur when amplitudes are considered (Zeng et al.,2000).

Data preprocesssing consisted of trace editing, time-zero cor-rection, subtraction of the exponential amplitude baseline, airwave subtraction, bandpass filtering to reduce noise, predictivedeconvolution to remove interantenna ringing, and insertionof elevation data into the trace headers (Figure 4). The effec-tive dominant source frequency is less than the nominal systemfrequency because of the antenna-to-ground coupling charac-teristics. Spectral analysis showed that the 100 MHz signals be-came ∼75 MHz, which was the frequency used in simulating theGPR data by finite-difference modeling, as described below.

FIG. 4. Data preprocessing. (a) Raw field data for the line atY = 9.5 m. (b) The same data after all preprocessing.

VELOCITY MODEL BUILDING

An accurate 3-D velocity distribution is a necessary prereq-uisite to reliable 3-D prestack migration. The main informationavailable for the velocity model construction are the observedtwo-way traveltimes picked from the main reflections, and theobserved depths of the corresponding horizons in the coresand at the cliff face. Velocity model building proceeded in twosteps. First, observed reflection times were iteratively fitted atthe depth control points (at the boreholes and the cliff facepseudoholes). Then, these 1-D profiles were extrapolated intothe 3-D volume using a geostatistical model derived from re-flection traveltimes. We now detail each of the steps in turn.

Borehole control: 1-D modeling

Auxiliary data for velocities include CMP gathers, verticalborehole GPR profiles, and lab measurements of the com-plex dielectric permittivity from both borehole and cliff facesamples. We used these auxiliary data to constrain the initialmodel; fine tuning of the 1-D velocity profiles at the boreholeswas done by finite-difference simulation (Xu and McMechan,1997) of the near-hole finite-offset traces extracted from the3-D data volume (Figure 5). In general, the GPR velocity de-creases as the clay fraction increases, in part because clay re-tains both bound and intrapore water. GPR velocity correlateswith fluid permeability since both quantities vary as a functionof lithology (Figures 5d, e). The low fluid permeability of clay(Figures 5c, e) is the basis of the assumption made below thatthe correlation structures obtained from semivariograms of theGPR reflection amplitudes may be used to estimate the spatialvariations of fluid permeability.

The traveltimes of the reflections from the main boundingsurfaces (A/B to E) match reasonably well in the observed andsynthetic data (Figures 5a, b). Neither the primary reflections,nor the other arrivals (which are multiples and offline reflec-tions), are expected to match exactly because the 1-D modelingcannot reproduce the subtleties of 3-D propagation.

Geostatistical velocity estimation: 3-D model construction

For accurate 3-D Kirchhoff depth migration of the 3-D GPRdata, the 3-D velocity model needs to be able to provide reliabletraveltimes by ray tracing; correct time integrals are desired,but subwavelength details are not necessary. Thus, a smoothvelocity model is both sufficient and also ensures stability ofthe ray trace computations. To achieve this, we used sequentialGaussian simulation (sGs) and kriging (Journel and Huijbregts,1978; Isaaks and Srivastava, 1989; Deutsch and Journel, 1992)to extrapolate the sparse vertical velocity control at the bore-holes into a 3-D volume.

For 3-D velocity estimation, the input data consist of the3-D GPR reflection traveltimes picked for bounding surfacesE and A/B, depth control at the wells and the cliff face, andcomputed interval velocities at the wells. Only surfaces E andA/B were used for depth control because these separate the twomain depositional styles at the site (unit 5 from the topographicsurface to the sedimentological bounding surface E, and units4–1 between bounding surfaces E and A/B).

We estimated the 3-D velocity variations in four steps.First, we constructed 2-D semivariograms (Journel and Hui-jbregts, 1978; Deutsch and Journel, 1992) from the observed


finite-offset reflection times for surfaces E and A/B. A semi-variogram γ (x) is a measure of the spatial correlation of anobserved variable, and is typically fitted with a spherical, Gaus-sian, or exponential model depending on the shape of the γ (x)function. A semivariogram is characterized by three parame-ters: the range is the distance (x) between data pairs whereγ (x) reaches a constant value (beyond which there is no cor-relation), the sill is the value of γ at the range, and the nuggetrepresents the measurement error and is the semivariogramvalue at x = 0 (see Rea and Knight, 1998, and Tercier et al.,2000, for examples from 2-D GPR data). Most real data arefitted using a ‘nested’ (linear) combination of semivariograms,each of which represents the data variability over differentcharacteristic spatial scales. In the second step, we used thesesemivariograms to smoothly interpolate the reflection travel-times and to estimate depths at each GPR midpoint by linearkriging. Third, the time and depth estimates were combinedinto interval velocity estimates at each midpoint for the in-tervals between the topographic surface and surface E, andbetween surfaces E and A/B. Finally, we used 2-D semivari-ograms from the interval velocities to horizontally extrapolatevelocity control from the borehole and pseudoholes. Each ofthese processes and their results are now described in turn.

FIG. 5. (a) Synthetic offset GPR traces (center group) with corresponding field data traces (left and right groups) for boreholeD. The synthetics are produced by finite-difference modeling. All traces are plotted with automatic gain control (AGC) scaling.(b) Core log, (c) clay profile, (d) GPR interval velocity profile, and (e) median fluid (nitrogen) permeability profile for borehole D.(c), (d), and (e) are blocked averages, not the raw measurements.

Two-dimensional semivariograms of the observed 3-D re-flection traveltimes are the basis of the 3-D velocity estima-tion, and were computed from the dense grid of GPR reflectiontraveltimes. Figures 6a and 6b contain the observed two-waytotal traveltimes (smoothed with a 3 × 3 2-D operator) to sur-faces E and A/B, respectively. These smoothed surfaces pre-serve the structural elements of the original time data. Thecorresponding 2-D time semivariogram maps (Deutsch andJournel, 1992) in Figures 7a and 7b display the semivariogramvalues (γ ) at all azimuths. The dominant trend of both mapsis N10◦W on both time surfaces although there is also a sec-ondary N30◦E trend in the East surface reflections (Figure 7a),which correlates with the orientation of the dominant surfacefractures (Figure 3). Goovaerts (1997) points out that the be-havior near the origin of a semivariogram dominates interpo-lation. Small variations at the long lags will have little effecton the interpolation, but these same variations may indicate achange in the geologic process that controls the sampled vari-able. Thus, at Coyote Basin, the geometry of the erosional sur-faces is accurately modeled using only the major and minoraxes of the structure (at azimuths N10◦W and S80◦W).

Semivariogram models are robust approximations to exper-imental data (Posa, 1989). For Coyote Basin, we used 2-D


semivariograms to accurately model dimensions of geologicalstructures by specifying the major and minor axes of geomet-rical anisotropy. For each unit, we use the same type of model(Gaussian) to fit the experimental semivariograms (Deutschand Journel, 1992) in the directions of both minor and majorcorrelation axes so that a single structure can be specifiedfor the sGs and the kriging interpolation. These models sat-isfy the positive-definiteness property of the covariance matrix(McBratney and Webster, 1986).

FIG. 6. Smoothed two-way total traveltimes for (a) surface Eand (b) surface A/B. Borehole locations A–D are indicatedwith ⊕ symbols.

FIG. 7. Two-dimensional semivariogram maps of total reflec-tion times from (a) surface E and (b) surface A/B. Contours areof maximum semivariogram amplitudes; black arrows indicatemajor correlation trends.

We constructed smoothed total time surfaces by kriging theoutput of an sGs at a random set of 100 control points (similar tothe method of Gomez-Hernandez and Srivastava, 1990). Thisprocess filters the measurement error (of traveltime picking)and provides a smooth, yet accurate, time surface for use in in-terval velocity computations. The dense coverage of traveltimedata provides an accurate correlation function and the resultinginterpolation of traveltimes has negligible loss of information.

FIG. 8. Estimated depths from the topographic datum to (a)surface E and (b) surface A/B. Borehole locations (A–D) andcliff-face pseudohole locations (CB1–CB5) are indicated with⊕ symbols. The horizontal dotted lines in (a) and (b) are theeastern edge of the GPR grid. Depths for Y < 0 are not used inthe velocity model construction.

FIG. 9. Depth averaged interval velocites (a) between datumand surface E and (b) between surfaces E and A/B.


The smoothing process is done geostatistically rather than de-terministically, to produce unbiased estimates.

We simulated the depths to surfaces E and A by extrapo-lating from the fixed depths at the boreholes and the cliff face.This was done by averaging 100 sequential Gaussian depth sim-ulations (Deutsch and Journel, 1992) for each of the two depthsurfaces at 100 random (X, Y) locations within the survey area,and then kriging to interpolate simulated depth values at eachGPR midpoint (Figures 8a, b). The simulations were averagedto reduce the interpoint variance (Bain and Engelhardt, 1992).

The correlation functions we used for the depth inter-polations in Figure 8 are those computed from the reflec-tion traveltimes (Figure 6). Using the time correlation func-tions to estimate depths assumes that the underlying sedi-mentological processes (flow and deposition rates, volumes,and scales) affect the internal structure (and, hence, ve-locity variations) within the units with the same geome-try and scales as the scour surface that supports them.This assumption was necessary since there were insufficentdata to compute an accurate semivariogram from the sparsespatial depth control points alone (Gomez-Hernandez andSrivastava, 1990). The average depth errors between the con-trol points and the smoothed depth simulation on boundingsurfaces E and A/B are 4.32% (20 cm) and 0.6% (7 cm), respec-tively, which are acceptable as they are less than one-quarterwavelength.

We computed the average velocity between each pair ofbounding surfaces at each GPR midpoint from traveltimescorrected for source-receiver offset and from the depths toeach layer. Because of the finite GPR antenna offset, this is aniterative inversion problem, very similar to tomography (Caiand McMechan, 1999). The velocity solution was obtainedby performing 3-D ray tracing and minimizing differencesbetween calculated and observed traveltimes by simplex op-timization. Figures 9a, b show the average vertical velocity ateach midpoint for the intervals from the topographic surface toE and from E to A/B, respectively. Velocity correlation func-tions with N10◦W and S80◦W azimuths are computed from theaverage interval velocities.

The final estimated 3-D velocities were computed by hori-zontally extrapolating velocities from the nine borehole andpseudohole control profiles. At each depth slice, the proce-dure used the same sGs and kriging techniques used for in-terpolation of the bounding surface depths. Semivariogrammodels (Table 1) for the velocity variations in the horizontalplane (Figure 10) were used to interpolate the velocity field at0.5 m depth increments while being constrained by the mea-sured velocities at each depth in the boreholes and the pseudo-holes. The final 3-D velocity field (Figure 11) shows a generalvelocity decrease with depth, a steep gradient near surface E

Table 1. Semivariogram parameters for velocity intervals 1and 2 fitted with a Gaussian model. Sill values were picked tothe nearest 0.025 unit, ranges were picked to the nearest 0.25m, and nugget values were picked to the nearest 0.005 units.

Direction Interval Sill Range (m) Nugget

S80◦W 1 2.200 13.0 0.010N10◦W 1 0.575 14.5 0.010S80◦W 2 1.950 11.5 0.005N10◦W 2 0.500 25.0 0.010

(at 5–6 m depth), and another decrease near 12 m depth at sur-face A/B, where the lithology changes to mudstone. We usedthis velocity field for 3-D prestack Kirchhoff depth migration.

3-D MIGRATION

We used a 3-D Kirchhoff prestack depth migration algorithmbased on two-point ray tracing (Epili and McMechan, 1996) tomigrate the GPR data using the velocity field in Figure 11. Themigrated 3-D image is shown in Figure 12; the spatial variabil-ity, shapes, and dimensions of individual sedimentologic fea-tures can be clearly seen in the volume. The frontal face showsthe truncated trough cross-bedding in unit 5. The continuoustop of the mudstone layer can be traced throughout at ∼12 mdepth.

The improvement in image quality obtained with the 3-Dvelocity model relative to that for a 1-D velocity model is il-lustrated in Figure 13. Figure 13a contains the vertical slice

FIG. 10. 2-D correlation functions for the velocity distributionson horizontal slices (a) above surface E and (b) between sur-faces E and A/B.

FIG. 11. The final 3-D interpolated interval GPR velocitymodel. This model is used in the 3-D prestack migration thatproduced the image in Figure 12. The subvolume cut has planesX = 16.5 m, Y = 12 m, and Z = 10 m. The magenta lines are theinterpreted bounding surfaces. The display has a 3 × 3 2-D av-eraging filter.


through the migrated volume (Figure 12) at Y = 9.5 m.Figure 13b contains the slice at the same location obtainedby migration using the 1-D velocity profile that is the averageof the velocity profiles at the four boreholes. In Figure 13a, theimproved coherence and the good tie with borehole D are aconsequence of the improved velocity model.

Interpretation

The interpretation superimposed on Figure 13a and its3-D extensions are discussed in detail elsewhere (Corbeanuet al., 2001), so only a brief summary is included here. It is of

FIG. 12. The final 3-D migrated volume. The subvolume cut hasplanes X = 16.5 m, Y = 12 m, and Z = 10 m. The magenta linesare the interpreted bounding surfaces. The display has a 3 × 32-D averaging filter. Traces are plotted with AGC scaling.

FIG. 13. Migration comparison for a vertical slice at Y = 9.5 m.(a) The final migration with the bounding layer interpretation,and (b) the migration using an average of borehole velocities.The dashed black line at the top of each image is the surfacetopography. Traces are plotted with AGC scaling.

particular interest to note that sedimentary bounding surfacesdo not necessarily correspond everywhere to large, or even tocoherent, reflections. Reflections are produced by contrasts inelectrical properties, which in this environment usually corre-late with changes in lithology (e.g., changes in sand/clay ratio),with petrophysical changes associated with either primary orsecondary processes (porosity, cementation, weathering, frac-turing, leaching), and with changes in intrapore water content.Most of the reflections at this site seem to be produced by lithol-ogy changes (Figures 5b and 13a), including mudstone drapeson repetitive channel fill and discontinuous clay clast conglom-erates that appear on the bounding surfaces (Figure 2). Thereare places where there is negligible contrast across a bound-ing surface (an absence of electrical property contrast), andothers where oblique features with similar dips lie above and

FIG.14. Cumulative distribution functions of permeability dataat the boreholes (red ◦) and pseudoholes (green �). The black←− indicates the normal score transformation to convert thecliff-face permeability distribution to the borehole permeabil-ity distribution.

FIG. 15. The final 3-D fluid permeability volume. The sub-volume cut has coordinates X = 16.5 m, Y = 12.0 m, andZ = 10.0 m. A logarithmic color scale was used in the figureso that high permeabilities can be visualized in a permeabilityvolume dominated by low values. The interpreted boundingsurfaces are displayed in magenta color. The display has a 3 × 32-D pixel smoothing.


below a bounding surface and appear to be continuous acrossit. These behaviors make location of the bounding surfaces withGPR alone a challenge. The criterion that works best is thata bounding surface separates regions of different sedimento-logical facies and geometry, whereas the corresponding GPRfacies have similar character changes at the boundary even ifthe boundary itself is not seen as a continuous reflector. Thisis not a surprise because similar concepts appear in seismicsequence stratigraphy.

3-D FLUID PERMEABILITY ESTIMATION

We applied a geostatistical approach to estimate the 3-D dis-tribution of fluid permeability by extrapolating measured verti-cal permeability logs from the boreholes and the cliff face pseu-doholes by using the 3-D correlation functions derived fromGPR reflection amplitudes. Assuming that the GPR reflectionsare produced primarily by sand/clay interfaces (as these are themain material contrasts present), the migrated reflectors definethe geometry of the clay distribution and, hence, the geometryof the permeability distribution. The migrated amplitudes areused only to provide a statistical description of the geometryof the features within the volume, not the permeability values.The permeability assigned to each position in the volume isdefined by extrapolating the measured values from the controlpoints at the boreholes and pseudoholes with the statisticalmodel. Thus, the permeability values in the model match thoseat the control points and have the same statistics laterally asthe GPR reflections. The remainder of this section details thisprocedure.

We measured permeability from the cores and core plugswith an automated probe permeameter (Hurst and Goggin,1995). Hassler-cell steady-state nitrogen permeability testswere also performed on a subset of the core plugs. Correlationfunctions for the permeability simulations were constructedfor each of the units 5, 4, 3, and 2 from a 3-D semivariogramvolume (Journel and Huijbregts, 1978) by combining the mi-grated GPR amplitudes with the borehole and pseudoholepermeability profiles. First, a 3-D semivariogram volume wascomputed using only the migrated 3-D GPR amplitude volumeto determine the orientations of the three semi-axes (A1, A2, A3;Table 2) of the semivariogram ellipsoid. Prior to the GPR semi-variogram computation, the rms amplitudes for each GPR linewere equalized to account for antenna coupling variations andto preserve the assumption of spatial stationarity in the data.Then a 1-D semivariogram was computed for the near-vertical(A3) axis direction from the measured permeability profiles.Prior to permeability semivariogram computation, we adjustedthe permeabilities at the cliff face to correspond to the cumu-lative distribution function of the permeabilities at the bore-holes using the normal scores back transformation (Goovaerts,1997) (Figure 14). This transformation is necessary to removebias in the cliff-face measurements due to diagenesis andweathering. The resulting permeabilities were sampled at a5 cm interval in depth (e.g., Figures 2, 5, 15, and 16c). Nestedsemivariogram computations were performed separately foreach of units 5, 4, 3, and 2. From the results (Table 2), wesee two structures are superimposed in each unit, and theseare similar in scale in all units: the first has maximum cor-relation lengths 4.75 × 3.13 × 0.5 m, and the second hasmaximum correlation lengths 11.87 × 8.87 × 1.1 m. In these

nested models, the sill values indicate the relative contribu-tion of each structure to the composite model, so the first(smaller) structure dominates the larger by a factor of ∼2.3,but both are significant. Finally, the correlation functions wereobtained for the A1 and A2 directions from the GPR ampli-tude semivariogram and for the A3 direction from the per-meability semivariogram. The correlation functions are thenused to simulate the 3-D permeability distribution (by sGs)for each of the four units separately. The final 3-D per-meability model (Figure 15) is the composite of the foursimulations.

Figure 16 displays slices of the GPR data, GPR velocity,and fluid permeability for the representative slice at Y = 9.5 m.These slices are coincident with a line containing borehole D.The GPR character is a consequence of lithologic contrasts be-tween sand, conglomerate, and clay (see lithologic log). Thevelocity field shows major velocity changes between unit 5(high velocity) and the lower units (low velocity). Permeabilitytrends in the dominant (A1) direction correspond to maximumcorrelation lengths in a nested model of ∼4.0–5.5 m and ∼10.0–12.5 m in all units, as determined from the GPR amplitude data(Table 2).

Table 2. Semivariogram parameters for stratigraphic unit 5with nested structures 1 (spherical) and 2 (exponential), andfor stratigraphic units 4, 3, 2 with nested structures 1 (Gaussian)and 2 (exponential).∗

Direction Unit Structure Sill Range (m) Nugget

A1 5 1 0.70 5.5 0.01A1 5 2 0.30 12.5 0.01A2 5 1 0.70 3.5 0.01A2 5 2 0.30 8.0 0.01A3 5 1 0.70 0.20 0.01A3 5 2 0.30 1.50 0.01A1 4 1 0.70 5.0 0.01A1 4 2 0.30 12.5 0.01A2 4 1 0.70 3.0 0.01A2 4 2 0.30 10.0 0.01A3 4 1 0.70 0.75 0.01A3 4 2 0.30 1.00 0.01A1 3 1 0.65 4.0 0.01A1 3 2 0.30 12.5 0.01A2 3 1 0.65 3.0 0.01A2 3 2 0.30 10.0 0.01A3 3 1 0.65 0.50 0.01A3 3 2 0.30 1.00 0.01A1 2 1 0.65 4.5 0.01A1 2 2 0.30 10.0 0.01A2 2 1 0.65 3.0 0.01A2 2 2 0.30 7.5 0.01A3 2 1 0.65 0.55 0.01A3 2 2 0.30 1.00 0.01∗A1, A2 and A3 are three orthogonal directions correspond-ing to the directions of the semiaxes of the 3-D correlations.Parameters in the A1 and A2 directions are based on the 3-DGPR amplitude correlations; parameters for A3 are based onthe 1-D permeability correlations. Sill values were picked tothe nearest 0.05 unit, ranges were picked to the nearest 0.5 mfor A1 and A2 and to the nearest 0.05 m for A3, and nuggetvalues were picked to the nearest 0.01 units. In unit 5, A1 dips5◦ towards N10◦W, A2 dips 0◦ towards S80◦W, and A3 dips 85◦towards S10◦E. In units 4, 3, and 2, the axis azimuths are thesame as unit 5, but A1 and A2 have dips of 0◦, and A3 has a dipof 90◦. The geostatistical convention of Deutsch and Journel(1992) is used in defining these angles.


The permeability model in Figure 15 is based on the assump-tion that the permeability distribution is caused entirely bythe distribution of lithologic variations within the depositionalelements and their subsequent diagenetic modifications. Thus,the effects of the fracture systems, which would dominate thepermeability if the reservoir were fractured (e.g., Manzocchiet al., 1998), are not explicitly included. That is a separate issuethat we do not deal with in the present context.

The present approach to permeability model building is ahybrid, with the main bounding surfaces defined determinis-tically and the internal features between bounding surfacesdefined statistically. The interpolated predictions of permeabil-ity are constrained to match the data (in the vertical direction)at the borehole and cliff face control points, and to have thesame (horizontal) statistics as the the 3-D GPR data. A futuregoal is to eliminate the statistical modeling by relying directlyon the GPR data amplitudes for definition of the geometry ofthe permeability distribution.

FIG. 16. Two-dimensional slices at Y = 9.5 m through (a) the migrated GPR volume in Figure 12, (b) the 3-Dvelocity model in Figure 11, and (c) the fluid permeability volume in Figure 15. Traces in (a) are plotted withAGC scaling. The magenta lines are the interpreted bounding surfaces. For comparison with the borehole data,the lithology log is displayed in (a), the velocity profile is displayed in (b) (as the white line), and the permeabilityprofile is displayed in (c) (as the white line). A logarithmic color scale is used for permeabilities. The display hasa 3 × 3 2-D pixel smoothing.

CONCLUSIONS

Information on the 3-D geometry of fluvial systems con-tained in 3-D GPR data can be used effectively for 3-D charac-terization of reservoir analogs. Detailed 3-D characterizationrequires constraints on the 3-D interpretation provided by sed-imentologic mapping and core logs.

Both GPR velocities and fluvial structures vary laterally atthe scale of a few meters. Thus, accurate 3-D imaging requiresconstruction of a 3-D velocity model for input to GPR migra-tion. Here, the 3-D velocity model was obtained by 2-D krigingat each depth to interpolate velocities measured at the bore-holes by finite-difference modeling. Observed two-way travel-times and kriged interface depths provided vertical constraints.Three-dimensional prestack depth migration with the 3-D ve-locity model produced a more coherent 3-D image than thatobtained using a 1-D velocity model that is the average of theborehole velocity profiles.


Sedimentological bounding surfaces do not always corre-spond to strong contrasts in electrical properties, and hence donot always correspond to strong GPR reflections. A boundingsurface separates regions of different sedimentological faciesand geometry. The GPR data exhibit similar facies changes thatcan be interpreted to locate the bounding surfaces, even whenthey do not correspond to a strong GPR reflection. By assumingthat the GPR reflections are produced by lithology (sand/clay)variations, the geometry of the associated fluid permeabilityvariations should have the same correlation functions. Thus,we use the correlation functions computed from the migrated3-D GPR image to predict the 3-D spatial distribution of per-meability. This permeability volume will subsequently be inputinto 3-D flow simulations.

The site contains two main sedimentary regimes. The upper∼5 m contain a relatively homogeneous trough cross-beddedsandstone with GPR velocity 0.12–0.135 m/ns and fluid perme-ability that varies substantially but averages ∼40 md. Between5 and 12 m depth, there are four sequences of scour and fillfluvial deposits, with average GPR velocity decreasing from∼0.10 to ∼0.05 m/ns and average fluid permeability rangingbetween ∼30 and ∼15 md, depending on the clay content. Thegeometry of the predicted permeability in all units has A1/A2

anisotropy ranging from 1.25 to 1.67 for both main scales ofstructures.

ACKNOWLEDGMENTS

The research leading to this paper was funded primarily bythe U.S. Department of Energy under Contract DE-FG03-96ER14596, with auxiliary support from the sponsors of theUT-Dallas GPR Consortium, the Coyote Basin Consortium,and a Shell Oil fellowship. Tong Xu, Xiaoxian Xeng, and JohnThurmond assisted with the GPR field work. Constructive com-ments by Steve Arcone, Lanbo Liu, and an anonymous re-viewer are much appreciated. This paper is Contribution No.926 from the Geosciences Department at the University ofTexas at Dallas.

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