Detailed internal architecture of a fluvial channel sandstone

Detailed internal architecture
of a fluvial channel sandstone
determined from outcrop, cores,
and 3-D ground-penetrating
radar: Example from the
middle Cretaceous Ferron
Sandstone, east-central Utah
Rucsandra M. Corbeanu, Kristian Soegaard,
Robert B. Szerbiak, John B. Thurmond,
George A. McMechan, Deming Wang, Steven Snelgrove,
Craig B. Forster, and Ari Menitove
ABSTRACT
Ideally, characterization of hydrocarbon reservoirs requires information about heterogeneity at a submeter scale in three dimensions.
Detailed geologic information and permeability data from surface
and cliff face outcrops and boreholes in the alluvial part of the Ferron Sandstone are integrated here with three-dimensional (3-D)
ground-penetrating radar (GPR) data for analysis of a near-surface
sandstone reservoir analog in fluvial channel deposits. The GPR survey covers a volume with a surface area of 40 ⳯ 16.5 m and a depth
of 12 m. Five architectural elements are identified and described in
outcrop and well cores, using a sixfold hierarchy of bounding surfaces. Internally, the lower four units consist of fine-grained,
parallel-laminated sandstone, and the upper unit consists of
medium-grained, trough cross-bedded sandstone. The same sedimentary architectural elements and associated bounding surfaces
are distinguished in the GPR data by making use of principles developed in seismic stratigraphic analysis.
To facilitate comparison of geologic features in the depth domain and radar reflectors in the time domain, the radar data are
depth migrated. The GPR interpretation is carried out mainly on
migrated 100 MHz data with a vertical resolution of about 0.5 m.
Measures of the spatial continuity and variation of the first- and
second-order bounding surfaces are obtained by computing 3-D experimental variograms for each architectural element (each radar
Copyright 䉷2001. The American Association of Petroleum Geologists. All rights reserved.
Manuscript received October 27, 1999; revised manuscript received September 14, 2000; final acceptance
November 9, 2000.
AAPG Bulletin, v. 85, no. 9 (September 2001), pp. 1583–1608
1583
AUTHORS
Rucsandra M. Corbeanu ⬃ University of
Texas at Dallas, 2601 N. Floyd Road, Richardson, Texas,
75080; rcorbeanu@hotmail.com
Rucsandra M. Corbeanu received her B.Sc. degree in
geoscience from the University of Bucharest, Faculty of
Geology and Geophysics, Romania, in 1991 and is
currently working toward her Ph.D. in geology at the
University of Texas at Dallas. Rucsandra’s interests include
all aspects of reservoir characterization, geostatistics, and
ground-penetrating radar applications.
Kristian Soegaard ⬃ E&P Research Centre,
Norsk Hydro ASA, N-5020 Bergen, Norway;
kristian.soegaard@hydro.com
Kristian Soegaard received his high school degree in
Denmark in 1974, his B.Sc. honors degree in geology
from the University of the Witwatersrand in
Johannesburg, South Africa, in 1980, and his Ph.D. from
Virginia Polytechnic Institute in Blacksburg, Virginia, in
1984. Kris’s interests are in description and interpretation
of sedimentary systems at all scales and of all ages.
Robert B. Szerbiak ⬃ University of Texas at
Dallas, 2601 N. Floyd Road, Richardson, Texas, 75080
Robert Szerbiak received his B.S. degree (1971) in
geoscience at Michigan State University and an M.S.
degree (1980) in geophysics from Texas A&M University
and is currently working toward his Ph.D. in geophysics at
the University of Texas at Dallas. His interests include
reservoir characterization and shallow geophysics, fluidflow modeling, geostatistics, ground-penetrating radar,
and effective medium theory.
John B. Thurmond ⬃ Massachusetts Institute of
Technology, 77 Massachusetts Avenue, 54-913,
Cambridge, Massachusetts, 02139
John Thurmond is currently working on his Ph.D, in
carbonate sedimentology at the Massachusetts Institute of
Technology. He received his B.S. degree in geology with
highest honors from the University of Texas at Dallas in
1997. His work currently involves 3-D mapping of
carbonate stratigraphy to understand evolving
morphologies and the processes that control them.
George A. McMechan ⬃ University of Texas at
Dallas, 2601 N. Floyd Road, Richardson, Texas, 75080;
mcmec@utdallas.edu
George McMechan received a B.A.Sc. degree in
geophysical engineering from the University of British
Columbia in 1970 and an M.Sc. degree in geophysics
from the University of Toronto in 1971. His main research
interests are wavefield imaging, 3-D seismology, reservoir
characterization, and ground-penetrating radar.
Deming Wang ⬃ University of Texas at Dallas,
2601 N. Floyd Road, Richardson, Texas, 75080
Deming Wang received a B.S. degree with honors (1986)
in exploration geophysics from Hefei Polytechnic
University, China, an M.S. degree (1993) in geophysics
from Peking University, China, and an M.S. degree (2000)
in geosciences from the University of Texas at Dallas. He
has done research on prestack imaging and crosshole
imaging.
Steven Snelgrove ⬃ University of Utah, 423
Wakara Way, Salt Lake City, Utah, 84108
Stephen H. Snelgrove received a B.S. degree in geophysics
and an M.S. degree in geological engineering from the
University of Utah. He is currently completing his Ph.D. in
civil engineering at the University of Utah. His research
interests include characterization of aquifers and
petroleum reservoirs using geophysics and geostatistics,
and numerical modeling of subsurface flow.
Craig B. Forster ⬃ University of Utah, 423
Wakara Way, Salt Lake City, Utah, 84108;
cforster@mines.utah.edu
Craig Forster holds degrees in geology and hydrogeology
from the University of Waterloo, Canada (M.S. degree),
and the University of British Columbia (B.S. degree and
Ph.D.). His current research program employs
interdisciplinary outcrop-to-simulation studies to assess
how geologically derived permeability heterogeneity
should be incorporated in numerical models of
subsurface fluid flow, mass transport, and heat transfer.
Ari Menitove ⬃ University of Utah, 423 Wakara
Way, Salt Lake City, Utah, 84108
Ari Menitove is currently working as a geological engineer
for Kleinfelder, Inc., in Salt Lake City, Utah. He received
his B.S. degree in geophysics from Bates College in
Lewiston, Maine, in 1993 and his M.E. degree in
geological engineering from the Colorado School of Mines
in Golden, Colorado, in 2000.
ACKNOWLEDGEMENTS
The research leading to this article was funded primarily
by the U.S. Department of Energy under Contract DEFG03-96ER14596 to McMechan and Soegaard with auxiliary support from the University of Texas at Dallas
Ground-Penetrating Radar Consortium. The migrated GPR
data were interpreted using the PC-based seismic interpretation software WinPICS of Kernel Technologies Ltd.
The geostatistical analysis was done using the Geostatistical Software Library (GSLIB) programs. The outcrop
gamma-ray scintillometer was provided by ARCO, and
gamma-ray measurements on split cores and Hassler cell
permeability/porosity testing were performed by Terra
Tek Labs in Salt Lake City.
Gerard “Neil” Gaynor initiated the use of GPR on outcrop of the Ferron Sandstone for reservoir analog studies.
We thank John S. Bridge for his insight into the fluvial
barform in the upper 5 m of the channel complex and
Coco van den Bergh and Jim Garrison from The Ferron
Group Consultants for discussions in the field and for
providing insight into the position of the Coyote basin site
in the greater depositional framework of the Ferron Sandstone. We acknowledge Marie D. Schneider for help in integrating geologic outcrop and geophysical data. We also
thank Janok Bhattacharya for his review of an earlier version of the manuscript. AAPG reviewers Bruce S. Hart,
Peter J. McCabe, and Keith W. Shanley provided many
comments that improved the final version of the article.
This article is contribution No. 927 from the Geosciences
Department of the University of Texas at Dallas.
1584
Ferron Sandstone Internal Architecture
facies). The maximum correlation length of the dominant internal
features ranges between 4 and 6 m, and the anisotropy factor ranges
between 0.6 and 0.95.
INTRODUCTION
Over the past 15 years an acute realization of the limitations of onedimensional (1-D) facies models (i.e., from measured sections, core
descriptions, and well logs) in reconstruction of depositional systems architecture has led to studies of continuous two-dimensional
(2-D) outcrop facies maps (Miall and Tyler, 1991). Facies mapping
of outcrop analogs yields reliable sedimentologic and stratigraphic
detail that, in conjunction with outcrop permeability and porosity
information, may be used for characterizing subsurface reservoirs
in three dimensions (e.g., Flint and Bryant, 1993). As is the case for
1-D stratigraphic sections, however, 2-D outcrop facies maps also
fall short of providing continuous empirical information regarding
sedimentary deposits in the third dimension.
A new technology for characterizing sedimentary rocks in three
dimensions is now emerging through the use of ground-penetrating
radar (GPR) (Baker and Monash, 1991; Gawthorpe et al., 1993).
A high-resolution geophysical technique, GPR can provide indirect
information on lithologic and petrophysical properties of shallow
subsurface rock units. The vertical resolution of GPR is on the order
of a few decimeters, and the depth of penetration is in the range of
meters to tens of meters (Davis and Annan, 1989). The GPR antennas send electromagnetic pulses into the ground to image the
subsurface through the energy reflected and diffracted by spatial
changes in electromagnetic properties. Depending on the desired
resolution and depth of penetration, frequencies from 25 MHz to
1 GHz can be used. The maximum penetration depth depends on
the attenuation of the GPR signal, which is inversely proportional
to the effective electrical resistivity. The propagation velocity and
amount of reflected energy depend mainly on the complex dielectric permittivities of the materials encountered (Davis and Annan,
1989).
The data from GPR have the same potential for describing
stratigraphic geometries in specific depositional environments as
seismic data have had in providing understanding of larger-scale
stratigraphic sequences (Vail, 1977; Posamentier and Vail, 1988;
Van Wagoner et al., 1990; Weimer and Posamentier, 1993). Unlike
conventional seismic data used in oil exploration, which generally
have vertical and horizontal resolutions no better than upward of
5 and 25 m, respectively, GPR is capable of resolving sedimentary
features at the decimeter scale necessary for describing and interpreting depositional paleoenvironments. To date, most GPR surveys have been performed on unconsolidated, recent sediments
rather than on consolidated sedimentary sequences in which hydrocarbon accumulations occur (e.g., Bridge et al., 1995). In nearsurface settings, a shallow water table is significant because the GPR
signal will be strongly attenuated in the saturated zone
and under the water table. In arid environments, such
as the site studied for this article, the water table is not
encountered at depths of GPR penetration. Diagenesis,
subsequent fracturing, and preferential weathering of
exposed outcrops are factors that influence the electrical properties of consolidated rock. These factors
overprint the response of primary sedimentary features
and complicate the GPR signature. Data preprocessing, velocity analysis, and depth migration can focus
the GPR image and reduce artifacts that are unrelated
to primary lithology (Szerbiak et al., in press).
The GPR data commonly consist of 2-D profiles
(Alexander et al., 1994) or pseudo-3-D grids of widely
spaced intersecting 2-D lines (Bristow, 1995). Notable
exceptions are 3-D GPR surveys of recent-delta gravels
in Switzerland (Beres et al., 1995), and Cretaceous
shoreface sandstone bodies in Utah (McMechan et al.,
1997). If the signal attenuation and dispersion are sufficiently low, the kinematic properties of GPR data are
similar (except for scale) to seismic reflection data
(Fisher et al., 1992a, b). This implies that many of the
processing techniques developed in contemporary seismic studies, and the techniques and facilities developed for interpreting 3-D seismic stratigraphic data
(Brown, 1996) may also be used in 3-D GPR investigations. Acquisition of GPR data on 3-D grids, and 3-D
GPR migration enhance the horizontal and vertical accuracy of the GPR image (Szerbiak et al., in press).
To facilitate the integration of geologic and geophysical data, geostatistical prediction and simulation
algorithms are applied to interpolate the sparse geologic control data. Geostatistical analysis of radar reflections has previously been used to quantify the correlation structures found in 2-D GPR profiles and to
provide a means for interpretation based on the assumption that correlation structures in GPR data are
directly related to lithologic variation and the internal
structure of different depositional environments (Rea
and Knight, 1998). In this article, quantitative comparative evaluation of the spatial variability of heterogeneities encountered in fluvial deposits is based on
computation of 3-D experimental variograms of the
GPR amplitude data corresponding to each architectural element.
The objective of this article is to evaluate the potential of 3-D GPR surveys for investigating ancient
sedimentary systems and constructing accurate 3-D
reservoir analog models suitable for subsequent hydrocarbon flow simulation. This evaluation is made
through a case study of a fluvial channel sandstone at
Coyote basin, in the Cretaceous upper Ferron Sandstone Member of the Mancos Shale in east-central
Utah. The procedure for, and utility of, applying 3-D
GPR data to ancient siliciclastic rocks is demonstrated.
GEOLOGIC SETTING
The Coyote basin field site is located in east-central
Utah, in the upper part of the Cretaceous Ferron Sandstone known as the “Last Chance Delta” (Garrison et
al., 1997) (Figure 1). The Ferron Sandstone crops out
along the southwestern flank of the San Rafael swell
and is the product of a series of fluvial-deltaic complexes that prograded toward the northeast. Excellent
exposures are present along vertical cliffs parallel with
the progradational direction. Exposures perpendicular
to the progradation direction are afforded by eastwest–oriented canyons. The outcrop at Coyote basin
includes a cliff face oriented northwest-southeast and
extends approximately 45 m laterally and approximately 12 m vertically. The surface above the cliff face
is a relatively flat and barren mesa top favorable to GPR
surveys. Seismic surveys near cliff faces typically contain strong reflections from features at the cliff face;
however, GPR acquisition design, with dipole antennas
oriented perpendicular to the acquisition lines that are
parallel with the cliff face, produces and records energy
that is polarized near the plane below the survey line
and discriminates against energy coming from the sides
of the line. Thus cliff face reflections are less of a problem in GPR data than in seismic data.
Stratigraphic Setting
The Cretaceous Ferron Sandstone Member is one of
several northeastward-thinning clastic wedges that
prograded into the Mancos Sea along the western margin of the Cretaceous Interior Seaway during the middle to late Turonian (Ryer, 1981; Gardner, 1992). The
upper part of the Ferron Sandstone is a thick fluvialdeltaic complex deposited during a third-order sea
level rise combined with a progressively decreasing rate
of sedimentation (Gardner, 1992, 1995).
The Ferron Sandstone is subdivided into seven discrete delta lobes (genetic sequences GS1 to GS7)
(Ryer, 1981) or major stratigraphic cycles (SC1 to
SC7) (Gardner, 1992, 1995). The lower three sequences (SC1 to SC3) are interpreted as progradational with sea level constant or slowly falling, and
exceeded by sediment input. The following two
Corbeanu et al.
1585
Figure 1. Location of the
Coyote basin site in the Ferron
Sandstone outcrop (the shaded
areas) along the southwestern
flank of the San Rafael Swell in
east-central Utah.
sequences (SC4, SC5) are considered aggradational,
with sea level slowly rising and balanced by sediment
input. The final two sequences (SC6, SC7) are retrogradational with relative sea level rising at an increasing
rate (Gardner, 1995).
Each sequence or stratigraphic cycle is capped by
a major coal bed or coal zone. Recent work of Garrison
et al. (1997) identified at least 12 parasequence sets
that appear to form four high-frequency, fourth-order
depositional sequences (FS1 to FS4) within the upper
part of the Ferron Sandstone clastic wedge (Figure 2).
The fluvial channel complex at Coyote basin is located
at the top of stratigraphic cycle SC3 of Gardner (1995)
or parasequence set 3, in the FS2 sequence of Garrison
et al. (1997) (Figure 2). SC3 is capped by coal zone C
and is represented at Coyote basin by nonmarine facies
associations composed of large distributary channel
belts (Garrison et al., 1997). The paleoshoreline during
1586
Ferron Sandstone Internal Architecture
deposition of parasequence set 3 is more north-south
oriented (approximately 345⬚ azimuth) than that of
the underlying and overlying parasequence sets (Garrison et al., 1997). The channels at Coyote basin are
generally straight or of low sinuosity (Garrison et al.,
1997).
FIELD DATA
The Coyote basin site contains a surface area of 40 ⳯
16.5 m on the mesa top (Figure 3) and 45 ⳯ 12 m
vertical exposure at the adjacent cliff face. The data
consist of detailed sedimentologic, stratigraphic, and
petrophysical data and 3-D GPR data. A leveling survey provided accurate topographic corrections and a
reference datum for all data sets. For reference, the
volume extent of the survey is roughly equal to the size
Corbeanu et al.
Figure 2. Generalized cross section of upper part of the Ferron Sandstone clastic wedge (modified from Garrison et al., 1997). Stratigraphic location of survey site at Coyote
basin is illustrated. See Figure 1 for location of cross section. Letters A to M identify marker coal horizons; SB1 to SB5 are sequence boundaries; FS1 to FS4 are fourth-order
sequences; 1a to 8b are parasequence sets.
1587
Figure 3. Surface geology of the GPR survey site at Coyote basin. Heavy black lines represent conjugate fracture set oriented
northwest-southeast and northeast-southwest, and the cliff face. CB1 through CB5 are locations of measured stratigraphic sections at
the cliff face. A through D are locations of boreholes from which cores were extracted. The map shows the location of the cliff face
(Figure 4), trough cross-bed outcrop (Figure 12), the 3-D grid, and a 200 MHz GPR crossline at x ⳱ 31.5 m (Figure 13). The origin
(x,y) ⳱ (0,0) is at the southeast corner of the GPR grid; the total grid size is (x,y) ⳱ (40.0,16.5) m.
1588
Ferron Sandstone Internal Architecture
of a single voxel in contemporary reservoir flow
simulators.
Geologic Data
A wide spectrum of geologic and petrophysical data
were collected at Coyote basin. The surface geology
was mapped on the top of the outcrop where the GPR
survey was conducted, and the map includes crossbedding, fractures, and soil cover (Figure 3). A facies
map with architectural elements and bounding surfaces of sedimentary deposits was made along the eastfacing cliff face (Figure 4). Paleocurrent orientations
from 81 trough cross-beds inside the GPR grid and
from an additional 130 trough cross-beds adjacent to
the survey yielded information about depositional
trends (Figure 5). Five stratigraphic sections, evenly
spaced along the 45 m long outcrop, provided detailed
sedimentologic information (Figure 4). Four 15 m
long, 2.5 in. (⬃6.3 cm) diameter cores were obtained
from wells drilled behind the outcrop (Figure 3). Permeability measurements were performed on 485 core
plugs extracted from the outcrop along the stratigraphic sections at a sample spacing of 10 cm and on
the well cores at a sample spacing of 5 cm; permeability
measurements on the outcrop core plugs were obtained using a probe permeameter to test one end of
each core plug, and along the well cores using a
computer-controlled, stage-mounted, electronic probe
permeameter (Snelgrove et al., 1998). Total gammaray measurements at a sample spacing of 25 cm along
the stratigraphic sections were obtained using a handheld scintillometer. Full spectral gamma-ray measurements were made along the well cores at a sample spacing of about 3 cm. Measurements of electrical
properties (dielectric permittivity and electrical conductivity) were performed on a set of 33 cylindrical
plugs, 1 in. (2.5 cm) in diameter, drilled orthogonally
to the well-core axes, providing GPR velocity and attenuation information as a function of water saturation. Hassler cell permeability/porosity tests were performed on the same 33-sample set. Petrographic
analysis of thin sections (Snelgrove et al., 1998) provided quantitative mineralogy information for dielectric constant modeling, and parameters such as clay
content and porosity for GPR modeling.
Ground-Penetrating Radar Data
Three 3-D common-offset digital GPR data sets were
recorded using antenna frequencies of 50, 100, and
200 MHz. Interpretation was performed mainly on the
100 MHz data to obtain a good compromise of vertical
resolution (⬃0.5 m) and depth of penetration (⬃15
m). The 200 MHz GPR data set, which has higher resolution (⬃0.3 m) but shallower penetration (⬍10 m),
was used only for detailed interpretation of the upper
5 m of the fluvial sandstone. The 50 MHz data (1 m
vertical resolution and ⬎20 m depth of penetration)
were too coarse to be of use at the scale of interest.
The 3-D GPR survey at Coyote basin was performed on a rectangular grid of 34 approximately
north-south–oriented lines (azimuth 350⬚) at a spacing
of 0.5 m between adjacent lines (Figure 3). Each GPR
line contains 81 traces, equally spaced at 0.5 m. The
GPR equipment used in the survey was a PulseEKKO
IV system with a transmitter voltage of 1000 V. Dipole
antennas were oriented parallel with each other and
perpendicular to the in-line direction. A common midpoint (CMP) gather, covering an offset range of 26 m,
was recorded for each data set. The CMPs provided
initial velocity control and helped optimize the sourcereceiver offset for the 3-D data acquisition. The offsets
used were 3 m at 50 and 100 MHz and 2 m at 200
MHz. Vertical and crosshole GPR surveys were also
recorded at 100 MHz using boreholes A, C, and D
(Figure 3); the results of analysis of these data, the
petrophysical data, and the flow modeling will be reported elsewhere.
GEOSTATISTICAL METHODOLOGY
Geostatistics is used to estimate the spatial variability
of different geologic and GPR parameters, based on the
assumption that properties in the earth are not random, but have spatial continuity and are correlated
over some distance. Variogram modeling has been successfully used by Rea and Knight (1998) to quantify
the correlation length of radar reflections to characterize heterogeneities of the subsurface in two dimensions. The main assumption is that there exists a link
between the lithology of layers and their electrical
properties, and thus a relationship between the correlation structure of radar reflections and lithology. This
spatial relationship is expressed through standard
variograms (Rea and Knight, 1998).
An essential assumption in the calculation of the
variograms is that the data are stationary in space,
which means that any subset of the data has the same
statistics as any other subset. For GPR data, the stationarity requirement is not satisfied because of the
Corbeanu et al.
1589
1590
300
200
100
600
800
600
800
400
300
200
100
CB1
400
300
200
100
CB3
800
600
CB2
400
600
800
300
200
100
CB4
400
600
F
800
300
200
100
NORTH
CB5
400
UNIT 5
UNIT 4
E
D
UNIT 3
C
UNIT 2
B
A
400
0
GAMMA RAY
(Total Count)
800
600
Massive & Parallel-Laminated Fine-Grained Sandstone
PERMEABILITY
(md)
300
Trough Cross-Bedded Medium-Grained Sandstone
150
Ferron Sandstone Internal Architecture
SOUTH
10 meters
UNIT 1
1 meter
Mudstone-Intraclast Conglomerate
Mudstone
Ripple Cross-Laminated Siltstone
Figure 4. Sedimentary facies map of the cliff face at Coyote basin. Higher-order bounding surfaces (A through E, in red) outline major architectural elements (units 1 through
5). Surface F is the topographic surface. Less-significant, lower-order bounding surfaces are in black. Exposed surfaces are shown as solid lines; dashed lines are inferred where
outcrop is covered. Also shown are five measured stratigraphic sections (CB1 through CB5) in which primary sedimentary structures, textural information, permeability, and
gamma-ray data were recorded. The position of the outcrop relative to the 3-D GPR grid is shown in Figure 3.
Figure 5. Paleocurrent measurements for the upper surface
of the fluvial sandstone. The
paleocurrent rose diagrams are
exclusively for the uppermost
unit, unit 5, of the channel
complex and represent flow direction inferred from mediumscaled trough cross-beds. The
general progradation direction
of the parasequence set 3, in
the upper part of FS2 sequence
of the upper Ferron Sandstone
delta complex (Garrison et al.,
1997) is illustrated using the
heavy arrow. The orientation of
the 211 cross-beds in relation
to parasequence set 3 paleogeography is explained as a local phenomenon of the radial
sediment dispersal pattern in
delta systems. The trough crossbedded sandstone in unit 5 is
interpreted as a channel bar.
The GPR survey site is located
in an upstream position on the
bar. A possible areal extent of
the barform (the stippled region) and the corresponding
cross sectional geometry and
internal reflectors (cross-bed
cosets), illustrated below, are
schematically extended from
outcrop facies maps.
strong decay of the amplitude down a radar trace due
to radar signal attenuation, and also by changes in radar
facies both vertically and laterally (Rea and Knight,
1998). To compensate for radar signal attenuation an
automatic gain control (AGC) with a window length
of 2.5 m was applied to each GPR trace after migration. Between profiles, the GPR amplitudes were normalized relative to the maximum amplitude value in
the survey. To account for changes in radar facies, the
migrated GPR volume was subdivided into four units
(referred to as units 2 to 5) defined by specific radar
facies, prior to the variogram computations.
The experimental variograms were computed for
the 3-D GPR relative amplitude data within each GPR
facies using the equation (Deutsch and Journel, 1998)
c(h) ⳱
兺(xi ⳮ yi)2
2N(h)
(1)
where h is the separation distance between two data
points (the lag), N(h) is the number of pairs of data
points separated by h, xi is the data value at one of the
points of the ith pair, and yi is the corresponding data
value at the second point. Equation 1 can be applied
to 1-D, 2-D, or 3-D data sets. For 3-D data, the separation vector h is specified together with its direction
defined by three angles, azimuth, dip, and plunge
(Deutsch and Journel, 1998).
In most geologic data sets, the data values along
certain directions are more coherent than along others.
The direction with best continuity represents the maximum correlation direction of the data set. The
minimum correlation direction is perpendicular to the
maximum correlation direction. The ratio between
minimum and maximum correlation lengths is the
anisotropy factor (Isaaks and Srivastava, 1989). Commonly, variograms are presented as 1-D curves along
a particular direction. A more global view of the
Corbeanu et al.
1591
variogram values in all directions is achieved by computing variogram volumes. A variogram volume is a
3-D plot of the sample variogram c(h) computed in all
directions for all available separation vectors h ⳱
(hx,hy,hz). The lowest values of c(h) generally form an
ellipsoid centered at the value c(o) ⳱ 0, which is also
the symmetry center (Deutsch and Journel, 1998).
Variogram volumes are used to determine the orientation and dip of vector h for which data sets show best
spatial continuity. Directions and amount of anisotropy are given by the orientation of the major and
minor axes of the ellipsoid. The major axis is coincident with the maximum correlation direction.
DATA PROCESSING AND ANALYSIS
Context: Hierarchy of Bounding Surfaces
Miall (1985, 1988) emphasized the importance of
identifying and correlating bounding surfaces at various
scales rather than simply documenting vertical facies
transitions to clearly understand the complexities of
fluvial depositional systems. He developed a sixfold
hierarchy of bounding surfaces. First-order surfaces
separate similar sedimentary features such as cross-bed
set bounding surfaces (Allen, 1983; Miall, 1985).
Second-order bounding surfaces outline cosets of genetically related facies without significant evidence of
erosion, but with dissimilar lithofacies above and below the surface (Miall, 1985). Third- and fourth-order
bounding surfaces envelop larger-scale architectural
elements constituting facies associations (Miall, 1985;
Soegaard, 1991). A third-order bounding surface envelops any architectural element with uniform composition of facies or facies sequences such as a bar or
channel element (Soegaard, 1991). Fourth-order surfaces envelop a complex of stacked architectural elements composed internally of similar facies sequences
such as composite bars (Soegaard, 1991). Fifth-order
bounding surfaces outline larger depositional systems
composed of diverse but related architectural elements. They are marked by erosion and local cut-andfill relief and basal gravel lags (Miall, 1985). Sixthorder surfaces separate depositional sequences whose
distribution is generally dictated by allogenic effects.
Fifth- and sixth-order surfaces can be mapped using
high-resolution 3-D seismic data (Miall, 1988; Thomas
and Anderson, 1994). Lower-order surfaces, generally
observed only at the outcrop, can be imaged using GPR
technology.
1592
Ferron Sandstone Internal Architecture
GPR Facies
Interfaces that generate GPR reflections can include
bedding planes, fracture planes, or any other boundary
separating rock types with different electrical properties. Electrical properties of a rock correlate mainly
with lithologic composition (sand/clay ratio, grain size,
sorting, etc.) and water saturation (Knight and Nur,
1987; Annan et al., 1991). Generally, saturation is a
measure of permeability and porosity of rocks, which
in turn, are generally consistent with lithology (Rea and
Knight, 1998).
Identification of bounding surfaces using GPR reflections is based not only on the contrast in electrical
properties above and below surfaces that produce significant reflection amplitudes, but also on the hierarchy
of reflection terminations, reflection continuity, and
geometrical configurations above and below the surface (see the “radar facies” of Gawthorpe et al. [1993]).
First-order surfaces separate similar lithofacies below
and above the surface and present a contrast in electrical properties only if there is a change in petrophysical properties (e.g., permeability, porosity) across the
surface (e.g., due to a change in grain size). In this case
a first-order surface correlates with a single continuous
GPR reflection that truncates against higher-order
bounding surfaces. If no contrast is present, the position of the bounding surface does not correspond to a
reflector and must be inferred from the attributes previously listed. Second-order surfaces separate different
lithofacies above and below and are thus more likely
to have disparate electrical properties. Therefore, a
second-order bounding surface is almost everywhere
represented by a continuous GPR reflection (see Gawthorpe et al., 1993). First- and second-order surfaces
are generally several decimeters to several meters in
length (Miall, 1985, 1988). Third- and fourth-order
surfaces should give rise to continuous GPR reflections
where different electrical properties are encountered
above and below the surface but commonly are defined
by characteristic reflection terminations (truncation,
onlap or downlap) against a surface, and also by the
existence of different radar facies (specific patterns of
reflection continuity, configuration, amplitude, and
frequency) above and below the surface (see Gawthorpe et al., 1993; Alexander et al., 1994; Bridge et
al., 1998). Third- and fourth-order surfaces are generally several tens of meters in length (Miall, 1985,
1988). Fifth-order surfaces are represented by continuous, through-going reflections where they are characterized by sharp contacts but may be more complex
or completely obscured where gradational contacts occur. Fifth-order surfaces clearly separate different “radar sequences” (see Gawthorpe et al., 1993). No sixthorder surfaces are present in the study volume.
GPR Data Preprocessing
Several processing steps were applied to the 3-D GPR
data before depth migration. Preparation and preprocessing of the GPR data consisted of trace editing,
time-zero corrections, air-wave removal (to reduce
near-surface interference), bandpass filter analysis (to
discriminate high-frequency events associated with
small sedimentary structures from the high-amplitude
energy near the median signal frequency), gain analysis, and predictive deconvolution. Detailed information on this processing was given by Szerbiak et al. (in
press).
The most important step in processing GPR data
is 3-D depth migration, which allows direct and accurate comparison (in 3-D space) between geologic
data and radar data, especially where velocity varies
significantly in three dimensions (Szerbiak et al., in
press). An initial migration, using a single average interval velocity function, produced a poorly migrated
GPR image and also poor ties with the borehole depth
control points. These poor results are explained by significant lateral variation in velocity that is produced,
not only by the spatial variation of lithologic facies, but
also by the fracture systems at the site. The fracture
systems are oriented northwest-southeast and northeast-southwest (Figure 3) and influence the amount
and pattern of weathering in each block bounded by
the fractures. Depending on the amount and type of
weathering, different parts of the same lithologic unit
can have different electrical properties, which in turn,
may substantially change the GPR propagation velocity. Also, the permeability values at the outcrop are
determined to be significantly higher than permeability
values in well cores because of increased weathering at
the cliff face (Snelgrove et al., 1998). Because surface
waters have been moving along the fractures in recent
times, the rock adjacent to the fractures has likely been
exposed to weathering in a way similar to the rock at
the present cliff face.
Velocity Model Building and Migration
The 3-D velocity model was obtained in two steps:
(1) obtaining vertical velocity profiles at control points,
and (2) spatially interpolating between these velocities
by kriging (Deutsch and Journel, 1998).
In the first step, synthetic GPR traces are simulated to estimate vertical velocity functions at the four
wells and the five stratigraphic sections. Bounding surface depths and two-way reflection traveltimes were
available at the wells, but only depths were available
at the cliff face stratigraphic sections. Reflection travel
times were estimated at the cliff face by extrapolation
of the two-way traveltime surface observed in the 3-D
grid to the cliff face. Each 1-D model was parameterized by electrical properties based on correlation of
lithology and permeability, and lab measurements of
dielectric permittivity (which is the main determinant
of the velocity of the GPR wave) and electrical resistivity (which is the main determinant of GPR signal
attenuation). The finite-difference modeling algorithm used was described in detail by Xu and McMechan (1997). Figure 6 shows the simulated GPR
response at well A; the synthetic radargrams have
matched the reflection amplitude, polarity, and frequency content of the main events in the 3-D data.
This modeling procedure yields a robust velocity estimate in depth at the control sections in the survey
and also provides a direct correlation of major bounding surfaces identified at the cliff face and in boreholes, with reflections in GPR profiles in the time domain (Figure 6).
The second step in building the 3-D velocity
model consisted of spatially interpolating and extrapolating the vertical velocity profiles obtained by modeling. The interpolation procedure was based on
building 3-D experimental variograms from two main
average velocity facies (one facies above surface E and
the other one between surfaces E and A/B in Figure
6), and then simulating 2-D velocity surfaces at regular depth intervals from the vertical velocity control
profiles. The complete procedure of building a smooth
3-D velocity model based on geologic control and geostatistical techniques was discussed by Szerbiak et al.
(in press).
A 3-D Kirchhoff algorithm (Epili and McMechan,
1996) was used to migrate the GPR data into a depth
image. Depth migration provided high-resolution images of the sedimentary features and also relative amplitude data for the geostatistical correlation analysis.
Because 3-D GPR data volumes have a format similar
to that of 3-D seismic data, 3-D seismic interpretation
software provides a flexible and efficient means for
display, attribute computation, and analysis of the
3-D GPR data. Figure 7 shows representative slices
through the 3-D GPR data volume, without and with
interpretive labels.
Corbeanu et al.
1593
1594
Ferron Sandstone Internal Architecture
Geostatistical Analysis
Figure 8A shows three orthogonal slices from the variogram volume of the GPR relative amplitudes from the
uppermost interpreted unit (unit 5 in Figure 7) of the
migrated GPR volume. The azimuth, dip, and plunge
of the maximum correlation direction (the longest axes
of the ellipsoid) can be computed from the projections
onto the three orthogonal planes of the variogram volume (the red arrows in Figure 8A). The dip angles extracted from the variogram volumes for each unit were
also compared with the dip of GPR reflections from
the migrated GPR volume. The resulting parameters
for each unit are presented in Table 1.
The experimental variograms were computed
along the maximum and minimum correlation directions for each radar facies identified in the GPR volume
(units 2 to 5). Satisfactory fitting of the experimental
variograms commonly requires use of “nested structures” containing a linear combination of two basic
models, rather than a single model (Isaaks and Srivastava, 1989). Each model in the nested structure provides different contributions to the final composite
model. The fitting was done by iterative manual trials
until the best nested structure fitting was obtained. Figure 8B shows an example of an experimental variogram and the nested model fitted to it, from the uppermost unit of the GPR volume. The results from
modeling the experimental variograms in each unit are
also given in Table 1 and are interpreted in the following section.
INTEGRATED INTERPRETATION OF
SEDIMENTOLOGIC AND GPR DATA
Five architectural elements are identified in the outcrop at Coyote basin and referred to as units 1 to 5 in
ascending stratigraphic order. Five bounding surfaces
separate these units and are referred to as surfaces A
to E, also in ascending order (Figure 4). The same units
and bounding surfaces are mapped in the GPR
migrated-data volume, except for units 1 and 2, which
are grouped together and referred to as unit 2. Surfaces
A and B at the outcrop are also mapped together in
the GPR data volume and referred to as surface A/B
(Figure 7). The contour maps with the depths of the
four bounding surfaces that resulted from the interpretation of the GPR volume are presented in Figure 9.
Fifth-Order Bounding Surface: A/B
The sharp erosional contact between the underlying
extensive, thick mudstone and the overlying 12 m
thick sandstone is interpreted as a fifth-order bounding
surface that separates the fluvial flood-plain mudstone
from the channel sandstone and is referred to as A/B
in outcrop and in the GPR interpretation (Figures 4,
7). The sandstone above this surface and the mudstone
below it have very different electrical properties so that
the GPR reflection at the boundary should be strong
and continuous. Surface A/B is defined locally by mudstone intraclast conglomerate and small-scale scourand-fill relief. The mudstone intraclast conglomerate
and associated siltstone deposits have average electrical
properties between the sandstone and mudstone end
members, causing the A/B surface to be less sharply
defined by the radar signal. Depending on the thickness
and complexity of the transition zone, surface A/B
produces locally dispersed reflections with reduced
amplitudes analogous to the transition that occurs at a
water table (Annan et al., 1991).
Tracking the continuous, strong GPR reflection
(the dashed red line on the interpreted profile in
the lower panel of Figure 7, which correlates with the
A/B surface in wells A, C, and D) toward the northern
part of the survey, there is an apparent mistie around
well B. The strong GPR event correlates with the mudstone intraclast conglomerate layer (B) at about 14 m
in well B, rather than with the A surface (top of floodplain mudstone). Around well B and measured section
CB1, surfaces A and B delineate a local scour-and-fill
element, which in outcrop was originally interpreted
as unit 1 (Figure 4) and in the GPR interpretation lay
between the two red lines (A and B in Figures 7,
10A). The presence of the conglomerate obscures the
Figure 6. Input and output of the synthetic radargram modeling at well A. Panel (A) shows details 1 m from the core emphasizing
the correlation between lithology and permeability. Panel (B) shows the lithofacies model and the permeability profile on which the
synthetic radargram was built, together with the interval velocity profile resulting from the radargram modeling. Panel (C) contains
the synthetic radargram for well A (in the middle) and five traces from the 3-D GPR volume adjacent to well A (on either side). E and
A/B are two major bounding surfaces interpreted in outcrop and boreholes and identified using GPR reflections in time profiles. These
two surfaces provide ties that control the average velocity facies from which velocity correlation functions were obtained.
Corbeanu et al.
1595
N
Well C
Well D
Well B
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
Relative
amplitude
13.1
Depth (m)
Ferron Sandstone Internal Architecture
Depth (m)
Well A
6.66
0
Well A
Well C
Well D
Well B
0
0
2
2
4
4
Unit 5
E
6
8
Unit 4
10
Unit 3
12
Unit 2
6
D
8
10
C
Depth (m)
Depth (m)
1596
S
-6.66
12
A/B
B
14
A
16
14
16
-13.1
x 1000
10 meters
Figure 7. Uninterpreted (upper panel) and interpreted (lower panel) GPR profiles from the migrated 3-D 100 MHz volume, connecting wells A, C, D, and B. Lithologic columns
and permeability profiles from each well are shown for correlation with the GPR reflectors. Colored lines in the lower panel show the interpreted bounding surfaces (A/B to E);
red arrows below interpreted surfaces C to E show the truncation of the GPR reflections against the third- and fourth-order erosional surfaces. The dashed rectangle in the lower
right corner shows the location of the area analyzed using instantaneous frequency in Figure 9. The dashed red line marks the continuous, strong GPR event tracked from wells
A, C, and D, which correlates with the top of unit 1 (surface B) and obscures below the reflection corresponding to the upper bounding surface of the flood-plain mudstone
(surface A). The black arrow in the upper panel marks the reduced amplitude reflection correlated with surface A.
(A)
γ (h)
1.60
0.2
Z
N
0.0
(XZ)
-0.2
-0.4
(XY)
1.20
0.80
N
3.0
0.40
(YZ)
2.0
1.0
Y
0.00
0.0
-1.0
-2.0
-3.0
-3.0 -4.0
-2.0
0.0
-1.0
3.0
2.0
1.0
4.0
X
(B)
Nested structure = gaussian + exponential
Nested structure = spherical + exponential
1.20
1.00
γ (h)
0.80
0.60
0.40
direction of maximum correlation
hmax = 5.75 m
0.20
0.00
0.0
5.0
10.0
h (m)
15.0
20.0
direction of minimum correlation
hmin = 3.4 m
0.0
4.0
8.0
h (m)
12.0
16.0
Figure 8. Example of variogram analysis in unit 5. (A) three orthogonal slices through the center of symmetry of the variogram
volume displaying the variogram values computed along all directions and for all available separation lags. The direction of the
maximum correlation of the GPR amplitudes projects on the three slices along the longest axis of the central dark blue ellipses (red
arrows) defined by the lowest values of c as a function of the separation vector (blue colors on the color bar). These projections
indicate the azimuth, dip, and plunge of the direction of maximum correlation. Azimuth is measured in the horizontal symmetry plane
clockwise from the y axis; dip and plunge are measured in the vertical symmetry planes clockwise toward the z axis (Deutsch and
Journel, 1998). The parameters inferred from the variogram volume analysis are given in Table 1. (B) Experimental variograms along
directions of maximum and minimum correlation of the GPR amplitudes in the uppermost unit interpreted in the GPR volume. The
red squares are data points of the experimental variograms, whereas the green continuous lines are the nested model fitted to each
variogram; the results of the variogram analysis are presented in Table 1. For definitions of symbols used in the figure see equation
1 in the text.
Corbeanu et al.
1597
Table 1. Semivariogram Analysis: Parameters and Results
Unit
Unit 5
Unit 4
Unit 3
Unit 2
Facies
Correlation Direction*
Model
Range
Nugget
Sill
Trough cross-bed
Maximum Azimuth ⳱ 90
Dip ⳱ 7
Minimum Azimuth ⳱ 0
Dip ⳱ 0
Maximum Azimuth ⳱ 90
Dip ⳱ 0
Minimum Azimuth ⳱ 0
Dip ⳱ 0
Maximum Azimuth ⳱ 90
Dip ⳱ 0
Minimum Azimuth ⳱ 0
Dip ⳱ 0
Maximum Azimuth ⳱ 90
Dip ⳱ 0
Minimum Azimuth ⳱ 0
Dip ⳱ 0
Spherical exponential
5.75
15.00
3.40
8.00
5.00
12.50
3.00
10.00
4.00
15.00
3.00
8.00
4.20
15.00
4.00
10.00
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.70
0.35
0.80
0.30
0.70
0.30
0.65
0.45
0.70
0.35
0.65
0.32
0.65
0.35
0.80
0.40
Scour and fill
Scour and fill
Scour and fill
Gaussian exponential
Gaussian exponential
Gaussian exponential
Gaussian exponential
Gaussian exponential
Gaussian exponential
Gaussian exponential
Anisotropy Factor
0.59
0.53
0.6
0.8
0.75
0.53
0.95
0.67
*By convention the azimuth is measured clockwise from the y axis, whereas dip is measured clockwise toward the z axis (Deutsch and Journel, 1998).
GPR reflection from surface A, and where unit 1
pinches out against surface A and becomes thinner
than one-quarter of the wavelength, differentiating between the two surfaces A and B becomes more difficult
because of tuning effects. Displaying radar data with
other attributes, such as instantaneous frequency, clarifies the position of the A/B surface at well B and
throughout the northern part of the survey. The instantaneous frequency attribute is the time derivative
of the instantaneous phase and represents a measure of
the frequency of the waveform at every sample. Lateral
heterogeneity, including pinch-outs or abrupt changes
in lithofacies, tends to change the instantaneous frequency more rapidly. If this is the case, then the GPR
reflection of surface A/B around well B is not a mistie
but the product of a composite reflection due to abrupt
lateral changes in facies not resolved by the 100 MHz
GPR. Figure 10 shows a comparison of the instantaneous frequency attribute for the GPR data in two profiles, one running through well B (see also Figure 7)
and the other located farther eastward, nearer the cliff
face. The dashed line in Figure 10A delineates the
strong continuous GPR event B (interpreted on the
relative amplitude display in Figure 7 as corresponding
to the mudstone intraclast conglomerate at 14 m depth
in well B), and the attenuated reflection from the top
bounding surface of flood-plain mudstone is shown by
solid line A. In Figure 10B, the two GPR events corresponding to surfaces A and B become coincident, as
1598
Ferron Sandstone Internal Architecture
unit 1 pinches out or is thinner than the vertical resolution and is no longer resolved by the 100 MHz GPR
data.
The contour map with the depths of surface A/B
(Figure 9) shows a general dip of the surface toward
the northwest and an erosional depression in the northern part of the survey, more accentuated around well
B where the scour-and-fill element 1 has its maximum
thickness.
Fine-Grained, Parallel-Laminated Sandstone Facies
Association: Units 1 to 4
Sedimentologic Description
Units 1 to 4 cover approximately the lower 7 m of
the channel complex and consist of fine-grained lenticular sandstone bodies that pinch out over distances
of several tens of meters parallel to the cliff face (Figure 4). Internally, these architectural elements consist
of low-angle, parallel-laminated, fine-grained sandstone that scour into underlying, similar parallellaminated sandstone. The base of each of unit (1 to
4) is erosional and commonly has mudstone intraclast
conglomerate along the basal scour. Locally, the erosional scours can have a steep cut relief of almost 1
m filled with mudstone intraclast conglomerate (see
Figure 4 near section CB1 at depths of ⬃9 and 12 m)
resulting in abrupt lateral changes in thickness of
conglomerate layers. The upper part of units 1 to 4
Corbeanu et al.
Figure 9. Depth contour maps of the four surfaces (A/B to E) that bound the major architectural elements in the fluvial sandstone at Coyote basin; depths are in meters, and
the depth contour increment is 0.25 m. These contours maps are generated from the 100 MHz migrated GPR data and are relative to the GPR horizontal datum. A to D are
locations of the wells inside the GPR grid. Notice the abrupt erosional depression around well B on surface A/B, the relatively flat character of surfaces C and D, and the erosional
scour oriented parallel with the paleoflow on surface E.
1599
N
B
7.5
7.5
10.0
10.0
12.5
12.5
150.00
B
15.0
A
17.5
20.0
(B)
111.00
15.0
17.5
25.0
30.0
X (m)
35.0
40.0
S
72.00
N
7.5
7.5
10.0
10.0
12.5
12.5
A/B
5.88
15.0
15.0
17.5
17.5
20.0
Depth (m)
Depth (m)
33.10
Instantaneous Frequency (MHz)
S
Depth (m)
Depth (m)
(A)
25.0
30.0
X (m)
35.0
40.0
Figure 10. Instantaneous frequency displays of the northern half and lower 10 m of two GPR profiles. (A) The GPR profile through
well B at y ⳱ 12.0 m; (B) the profile at y ⳱ 7.0 m. The continuous line in (A) is the interpretation of the A/B surface revealed as
a composite reflection due to the gradational character of the contact; the dashed line marks the continuous GPR reflector, which is
interpreted as the top of unit 1 (see also Figure 6). In panel (B) the two continuous lines show complete coincidence as apparently
unit 1 is pinched out or thins beyond the vertical resolution of the GPR data.
are capped by mudstone layers, generally 5–10 cm
thick, which are also laterally discontinuous because
of truncation by the overlying unit (Figure 4). Permeabilities measured in units 1 to 4 are on the order
of tens of millidarcys with very low values (a few
millidarcys) in the mudstone and mudstone intraclast
conglomerate intervals. The lowest average permeability is measured in unit 4, but the highest disper1600
Ferron Sandstone Internal Architecture
sion about the mean value is observed in units 2 and
3 (see Figures 4, 7; Table 2).
Units 1 to 4 are interpreted as scour-and-fill elements deposited during flood events within a fluvial
channel. Because units 1 to 4 are covered beyond the
extent of the 45 m survey area, the larger-scale sedimentologic architecture is not revealed in outcrop for
the lower part of the channel complex.
Table 2. Characterization of Major Units of Fluvial Channel by Means of Lithofacies, Permeability Values, and Range, and the
Corresponding Radar Facies
Units
Sedimentologic Description
Permeability Statistics
Radar Facies
~ 1 to 270 md
Medium- to large-scale, trough crossUnit 5
bedded, medium-grained sandstone
Mean ~50 md
Std ~40 md
~ 1 to 80 md
Unit 4
Unit 3
Low-angle, parallel-laminated,
Mean ~20 md
Std ~10 md
fine-grained lenticular sandstone
~ 1 to 90 md
capped by mudstone layers and
with mudstone intraclast
conglomerates on the basal scours
Mean ~30 md
Std ~13 md
~ 1 to 80 md
Unit 2
Mean ~30 md
Std ~15 md
GPR Interpretation
GPR reflections in approximately the lower 7 m of
the data volume correlate well with second-order
bounding surfaces between sandstone layers and
mudstone or mudstone intraclast conglomerate layers because these correspond to a significant change
in electrical properties between the three lithologies.
The irregularity in thickness and shape of these
mudstone and conglomerate layers is evident in the
GPR images as discontinuous, irregular reflections
(Figures 7, 11). Many layers that are significantly
thinner than 0.5 m are not resolved using the 100
MHz GPR data (see Figure 7 at ⬃10.5 m depth
around wells C and D).
Third-order bounding surfaces C and D, interpreted in the GPR profiles, are continuous surfaces
defined by downlap or truncation of second-order
reflections above and below the third-order surfaces,
respectively (Figures 7, 11). Both surfaces C and D
dip gently toward the north, following the regional
structural dip, and have limited erosional relief (Figure 9).
A cube view of the 3-D GPR data shows, on a
horizontal amplitude slice cut at constant depth
through unit 3 (Figure 11), high-amplitude zones
correlated with mudstone and mudstone intraclast
conglomerate layers striking approximately northsouth and dipping slightly toward the east.
The mudstone and conglomerate layers inside
units 2 to 4 could affect fluid flow if these layers
are continuous. Commonly, the mudstone and conglomerate layers are laterally discontinuous in outcrop, and GPR reflectors display the same pattern.
The GPR radar facies identified in units 2 to 4 contain subparallel, discontinuous GPR reflections (Figures 7, 11; Table 1). Units 2 to 4 are characterized
by generally similar radar facies in terms of continuity and configuration of reflections, with more discontinuous GPR reflections in units 2 and 3 related
to higher variability in permeability values (Table 2).
Corbeanu et al.
1601
1602
S
Depth (m)
Ferron Sandstone Internal Architecture
E
5.0
Relative
amplitude
1.0
D
N
10.0
Uni
0.5
t5
C
A/B
0.0
Un
it 4
15.0
0.0
-0.5
10.0
Uni
t3
-1.0
X (m)
20.0
15.0
Unit
2
10.0
30.0
5.0
Y (m)
40.0
Figure 11. Cube display of the 3-D GPR data, made of two lines at y ⳱ 1.5 m and y ⳱ 10.5 m, two crosslines at x ⳱ 18 m and x ⳱ 40 m, and two horizontal slices at z
⳱ 4 m and z ⳱ 9.5 m. The x and y axes coincide with the long and short axes of the GPR grid (Figure 3). Red, blue, orange, and green labels on the left side of the cube mark
the interpreted A/B, C, D, and E bounding surfaces, respectively. Inside the vertical GPR profiles, the purple arrows mark downlap, onlap, and truncation of the GPR reflections
against the major bounding surfaces. The relation between high-GPR-amplitude zones on the horizontal slice and the inclined reflections on the vertical profiles in unit 5 is
illustrated using thin black lines portraying the climbing cross-beds in the vertical plane and their shape on the surface. In unit 5, the black arrows show paleoflow direction, and
in unit 3 they show the dip direction of the mudstone and mudstone intraclast conglomerate layers.
Geostatistical Interpretation
To quantify the lateral extent of mudstone and conglomerate layers, from the continuity of the corresponding GPR reflections, experimental variograms are
computed for each unit from the GPR relative amplitude data, along both maximum and minimum correlation directions. The maximum correlation directions
of the GPR amplitude data coincide with the long side
of the GPR grid in all units (Table 1). The data in the
experimental variogram are fitted with a nested structure composed of two basic models: Gaussian and
exponential.
The correlation lengths (or ranges) of the Gaussian
contribution range from 4 to 5 m in the maximum
correlation direction and from 3 to 4 m in the minimum correlation direction (Table 1). These correlation
lengths are interpreted as characterizing the lateral
continuity of the mudstone or mudstone intraclast conglomerate layers with thicknesses comparable to vertical resolution of the GPR (⬃0.5 m), and enveloped
by second-order bounding surfaces, inside each unit.
The anisotropy factors of these short-wavelength structures are 0.95, 0.75, and 0.6, respectively, for units 2,
3, and 4. These anisotropies imply that mudstone and
mudstone intraclast conglomerate inside the channel
fills have more elongated shapes toward the upper part
of the channel (unit 4) and more isometric shapes at
the base of the channel (unit 2), but all have a maximum lateral extent of 5 m. These results compare fairly
well with the facies map at the cliff face, especially the
mudstone intraclast conglomerates in units 2 and 3.
Where making direct comparisons of the mudstone
and mudstone intraclast conglomerate layers with the
GPR reflections, one should consider the limitation of
the 100 MHz GPR data on resolving features significantly thinner than about 0.5 m. Sometimes mudstone
layers are interpreted in the outcrop to be laterally continuous over more than 10 m (e.g., at the base of unit
4 and the top of unit 2 in the southern part of the
outcrop in Figure 4) but are relatively thin and irregular
in thickness and may not be well resolved by the GPR
reflections. These layers are described by longer correlation lengths (the exponential model in the nested
structure), but they have a smaller contribution to the
combined model (Table 1).
Medium-Grained Trough Cross-Bedded Sandstone Facies
Association: Unit 5
Sedimentologic Description
Unit 5 (the uppermost 4.5–5.5 m of the sandstone
complex) consists exclusively of medium- to largescale, trough cross-bedded, medium-grained sandstone
(Figure 4). Permeabilities in unit 5 are in the range of
few hundreds of millidarcys with high dispersion about
the mean (Table 2).
This trough cross-bedded unit is lenticular in geometry with a relatively flat (erosional) base and a convex upper surface (Figure 5). The base of unit 5 is defined by surface E both in outcrop (Figure 4) and in
the interpreted GPR volume (Figures 7, 11). Unit 5
has been mapped outside the GPR survey area and extends about 640 m to the south in a downcurrent direction before pinching out (Figures 3, 5). The upcurrent (northward) extent of unit 5 is not determined
because of the lack of a cliff face exposure, but the unit
is present at least 30 m outside the 3-D GPR grid,
based on information from a 2-D GPR profile extending toward the north beyond the 3-D grid. Trough
cross-beds in the upcurrent position are clearly climbing, with first-order coset bounding surfaces truncating
against the fourth-order E surface in an upcurrent direction (Figures 4, 5). In the downcurrent part of unit
5, south of the survey area, trough cross-bed coset surfaces truncate against the lower E surface in the downcurrent direction (Figure 5). The thickness of the
trough cross-beds in the lower half of unit 5 is 10–30
cm, with a significant proportion of the cross-beds being preserved. In the upper half of unit 5, trough crossbed sets tend to be less than 10 cm thick (Figure 4).
The smaller cross-bed sets are either a result of smaller
original bedforms on the upper bar surface or due to
scouring by overlying cross-beds (Figure 4).
On the upper surface of the survey site, trough
cross-beds are up to 1.5 m wide and extend in a downcurrent direction for a distance of up to 7 m (Figure
3). Along the cliff face, similar lateral extents of several
meters are seen for individual cross-bed sets (Figures
4, 12). The paleocurrent measurements from the upper surface of unit 5 (Figure 5) show a more eastsoutheastern (115 to 150⬚ azimuth) paleoflow for the
distributary channels at Coyote basin than the general
east-northeastern (075⬚ azimuth) progradational direction of delta lobes forming parasequence set 3 (Garrison et al., 1997). This change in flow may be due to
active bifurcation as the main distributary channels approach the coastline.
Unit 5 is interpreted as a channel barform. Coset
boundaries outline the geometry of the upper surface
of the barform. The survey site at Coyote basin is in
the upcurrent part of the barform on the northwestern
side of the channel bar based on dip orientations of
Corbeanu et al.
1603
Figure 12. Detailed outcrop map of trough cross-beds on two orthogonal outcrop faces in unit 5 immediately southeast of the GPR
survey area (Figure 3). The north-south panel shows the geometry of trough cross-beds parallel with flow direction, whereas the eastwest panel is perpendicular to flow. Heavy lines mark the coset bounding surfaces that are most likely resolved by GPR data; these
are compared in the text with the maximum correlation lengths from the geostatistical analysis.
cross-bed cosets seen both at the outcrop and in the
GPR data (Figure 5). The upward climb of cross-bed
cosets in the upcurrent part of the barform implies that
sedimentation rates were high and that bar accretion
occurred both in an upcurrent and a downcurrent direction. More commonly, barforms tend to experience
erosion in an upcurrent direction and bar growth in a
downcurrent direction (Bridge, 1986; Miall and
Turner-Peterson, 1989). In these last instances, firstorder cosets truncate against the upper surface of barforms (i.e., fourth-order bounding surfaces) in an upcurrent direction.
GPR Interpretation
The base of unit 5 is a fourth-order bounding surface
(E) separating a medium-grained trough cross-bedded
sandstone with high permeabilities (hundreds of millidarcys) from underlying fine-grained, parallel- to
slightly obliquely laminated sandstone with low permeabilities. Locally, discontinuous mudstone intraclast
conglomerate lies immediately above surface E (Figure
4). On GPR profiles, surface E is defined by a change
of geometry from baselapping reflections above to
truncated reflections below the surface, rather than a
single continuous reflection (Figures 7, 11). This pattern in the GPR data is consistent with the truncation
relationships between bounding surfaces seen at the
outcrop. Based on interpretation of the GPR data, the
geometry of surface E has an erosional scour oriented
approximately north-south, with a northward dip (Fig1604
Ferron Sandstone Internal Architecture
ure 9). The orientation of this scour is also parallel with
the paleoflow indicators at the site (Figure 5).
The internal configuration of radar facies inside
unit 5 along profiles is generally parallel with the
paleoflow (see the GPR section between wells D and
B in Figure 7 and the north-south faces of the data
cube in Figure 11) and show continuous, slightly
oblique reflections (Table 2). These reflections are interpreted as first-order bounding surfaces inside unit
5. A horizontal amplitude slice cut at a constant depth
of 4 m through unit 5 (the uppermost face of the GPR
cube in Figure 11) shows high-amplitude zones correlating with first-order cross-bed cosets striking
northeast-southwest, perpendicular to the flow direction as measured from the trough cross-beds at the
surface. These high-amplitude zones are a result of the
intersection between the horizontal slice and the upward climb of trough cross-bed cosets to the southeast
(Figure 11).
Migrated 200 MHz GPR data are useful for interpreting detailed sedimentologic structures of about 0.3
m thickness inside unit 5. The GPR profile transverse
to the paleoflow direction at the position x ⳱ 31.5 m
(Figure 3) from the 200 MHz migrated GPR data
shows cross-bed cosets of medium scale interpreted in
the lower part of unit 5 (Figure 13). Upwardly concave
discontinuous reflectors truncate against adjacent or
overlying reflectors, thus mimicking the geometries
seen in the nested trough cross-beds in the facies map.
The GPR reflections in areas with thin trough cross-
beds outline cosets of several such cross-beds rather
than individual trough bed sets. These reflections are
the GPR expression of the first-order bounding
surfaces.
Geostatistical Interpretation
To quantify the lateral extent of cosets of trough crossbeds bounded by first-order surfaces, experimental
variograms were computed along both the maximum
and minimum correlation direction on GPR relative
amplitude data. The maximum correlation direction of
the GPR amplitudes corresponds to the long side of
the GPR grid. The data in the experimental variograms
were fitted with a nested structure composed of two
basic models (spherical/Gaussian and exponential)
(Table 1).
In the maximum correlation direction, the shorter
range (corresponding to the spherical model from the
nested structure fitted to the experimental variogram)
is 5.75 m and represents the main contribution to the
combined model (Table 1). This correlation length is
in good agreement with the length of trough cross-bed
sets measured at the outcrop of up to 7 m. In the minimum correlation direction, the range of 3.4 m (Table
1) is almost twice the maximum width of the trough
cross-bed sets measured in outcrop (up to 1.5 m). The
100 MHz GPR data have a horizontal spacing between
traces of about 0.5 m, so laterally and vertically stacked
cross-bed cosets with dimensions less than a meter or
so are not resolved, and a direct comparison with individual sets is no longer possible (Figure 12).
The longer correlation lengths resulting from the
nested structure fitted to the experimental variograms
are 15 and 8 m, respectively, for the spherical and
Gaussian models (Table 1); these correlation lengths
have a smaller contribution to the combined nested
model and are interpreted as probably the net result of
the lateral and vertical stacking of some of the crossbed sets.
DISCUSSION AND CONCLUSION
The 3-D GPR data are used together with detailed sedimentologic and stratigraphic information to analyze
the detailed 3-D architecture of a fluvial channel reservoir analog in the Ferron Sandstone beneath a surface
area of 40 ⳯ 16.5 m, at Coyote basin in east-central
Utah. The fluvial channel at Coyote basin belongs to
the seaward-stepping parasequence sets and is straight
or slightly sinuous.
The 100 MHz data are a good compromise between vertical resolution (⬃0.5 m) and depth of penetration (⬃15 m) for the scale and detail studied at the
outcrop. The 200 MHz GPR data have a better vertical
resolution (⬃0.3 m) but are not useful at depths
greater than 9–10 m where the signal is strongly attenuated. The bulk of our interpretation was carried out
on migrated 100 MHz GPR data, and only our interpretation of the upper 5 m of the stratigraphic succession used information from the migrated 200 MHz
GPR 3-D images.
To effectively integrate geologic and GPR data,
3-D migration of the GPR data from the time domain into the depth domain was essential. A good
depth migration was obtained only after constructing
a detailed velocity model containing both vertical
and lateral changes in electrical properties of the
rock volume surveyed. Synthetic radargrams were
generated to estimate vertical velocity profiles and
to correlate key GPR reflections in the time domain
to geologic boundaries in the depth domain. Kriging
was used to interpolate the lateral distribution of the
velocity.
To identify and separate architectural elements
and bounding surfaces in outcrop and well cores, the
sixfold hierarchy of bounding surfaces developed by
Miall (1985) was used together with techniques for
interpreting stratigraphic sequences from seismic data.
Five architectural elements, referred to as units 1
through 5 in ascending stratigraphic order, and their
bounding surfaces, referred to as surfaces A through
E, were correlated in outcrop and well cores. Units 1
through 4 are scour-and-fill elements deposited during
flood events within a fluvial channel, and unit 5 is a
channel barform accreting in both upcurrent and
downcurrent directions. The same architectural elements and bounding surfaces were interpreted in the
migrated GPR data.
Radar facies characteristic to each element were
interpreted based on the internal configuration and
continuity of reflections as well as reflection termination patterns against higher-order bounding surfaces. First- and second-order surfaces generally correlate directly with the GPR reflections. Where the
contact between two elements is gradational rather
than sharp, the GPR expression is a composite reflection that can be resolved using information from additional attributes such as instantaneous frequency.
Abrupt lateral changes in lithofacies (e.g., unit 1
around well B in Figure 10) are effectively addressed
through instantaneous frequency attribute analysis.
Corbeanu et al.
1605
1606
Y (m)
E
W
0.0
16.5
Y (m)
E
0.0
0
1.6
W
Depth (m)
E
3.2
4.8
E
6.4
1 meter
Ferron Sandstone Internal Architecture
W
16.5
1 meter
8.0
(A)
(B)
(C)
Figure 13. Upper 7 m of the uninterpreted (A) and interpreted (B) versions of the migrated 200 MHz GPR profile, at x ⳱ 31.5 m (Figure 3). Cross-bed sets and cosets can be
interpreted as upward-concave reflections in the GPR data and are marked with continuous orange lines in (B). For comparison, (C) shows the cliff face map of trough crossbeds from unit 5, perpendicular to flow as illustrated in Figure 12, for comparison. The sketch of trough cross-beds appears distorted because of a two-time vertical exaggeration
for direct comparison with the GPR profiles. The dashed lines at the top of (A) and (B) represent the topographic surface.
Because of their high variability in thickness and
lateral extent, flow barriers inside fluvial reservoirs
cannot be confidently mapped in 100 MHz data sets
over large areas away from geologic control points.
A quantitative description of the distribution of flow
barriers inside each unit is achieved by modeling
3-D experimental variograms of GPR amplitude.
The assumption is that GPR amplitude is an indirect
function of changes in permeability and, ultimately,
of existence of flow barriers. Correlation lengths of
the nested model fitted to variograms in unit 5 are
similar to dimensions of trough cross-bed sets and
cosets measured in outcrop. The nested models in
units 2 to 4 suggest that the channel at Coyote basin
contains discontinuous and randomly distributed
mudstone barriers and baffles, as is expected for
straight distributary channels in a progradational
parasequence set such as SC3 in the Ferron Sandstone (Barton, 1994).
Detailed mapping of first- and second-order
bounding surfaces needs additional information from
higher-frequency (e.g., 200 MHz) GPR surveys. The
tradeoff is that higher frequencies provide higher resolution (though higher bandwidth) at the expense of
a reduction in depth of penetration. First-order bounding surfaces from unit 5 in the upper 5 m of the channel
complex are successfully imaged in the migrated 200
MHz data and compare well with first-order bounding
surfaces mapped in outcrop.
The area studied at Coyote basin represents a small
fraction (40 ⳯ 16.5 ⳯ 15 m) of a fluvial reservoir analog in which we show that depth-migrated GPR data
from closely spaced 3-D grids can be successfully used
to image individual architectural elements and heterogeneity at the scale of a single voxel cell in a reservoir
flow simulator. Szerbiak et al. (in press) have used permeability measurements from cores and outcrop to
transform the GPR data into the permeability domain
throughout the survey volume discussed herein. Although correlation lengths for the permeability structure within the survey volume are far too short to be
built into a full-field petrophysical model of fluvial reservoirs, flow simulations performed by Snelgrove et al.
(1998) do provide effective permeability in X, Y, and
Z. These permeability tensors may be used directly in
larger flow simulation models with a coarser grid.
Moreover, the flow simulations performed on the data
volume at Coyote basin indicate that 5% less oil is recovered from the fluvial reservoir if the detailed heterogeneity described in this article is considered compared with a homogeneous model (Snelgrove et al.,
1998). This type of information will assist in better
volumetric calculations and history matching for the
larger, more-crude flow simulation models needed for
entire fields. In light of the efficiency of GPR surveys
(modest costs and acquisition time), larger grids can be
employed in the future to extend the detailed interpretation presented herein to larger volumes approaching the scale of the interwell spacing in actual hydrocarbon reservoirs (Corbeanu et al., 2000).
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