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JOURNAL OF SEDIMENTARY RESEARCH, VOL. 74, NO. 2, MARCH, 2004, P. 270–284Copyright q 2004, SEPM (Society for Sedimentary Geology) 1527-1404/04/074-270/$03.00

SEDIMENTOLOGY AND FRACTAL-BASED ANALYSIS OF PERMEABILITY DATA, JOHN HENRYMEMBER, STRAIGHT CLIFFS FORMATION (UPPER CRETACEOUS), UTAH, U.S.A.

JAMES W. CASTLE, FRED J. MOLZ, SILONG LU,* AND CYNTHIA L. DINWIDDIE**Departments of Geological Sciences and Environmental Engineering & Science,

Clemson University, Clemson, South Carolina 29634-0919, U.S.A.e-mail: [email protected]

ABSTRACT: Interpretation of depositional environments combinedwith field measurement of permeability for a portion of the UpperCretaceous Straight Cliffs Formation near Escalante, Utah, providesnew results for understanding and modeling facies-dependent perme-ability variations. Offshore, transition–lower shoreface, upper shore-face, and foreshore environments are interpreted for part of the JohnHenry Member on the basis of outcrop investigation. Using a newlydesigned drillhole minipermeameter probe, permeability was measuredfor two of the facies within this unit: lower-shoreface bioturbated sand-stone and upper-shoreface cross-bedded sandstone. Approximately 500permeability measurements at a sample spacing of 15 cm were madealong four vertical profiles and three horizontal transects on a 6 m 321 m outcrop.

Permeability ranges from 41 to 1,675 millidarcies (md) in the bio-turbated sandstone facies, which is massive-bedded, moderately towell-sorted, and very fine- to fine-grained. In contrast, permeabilityranges from 336 to 5,531 md in the moderately to moderately wellsorted, fine- to medium-grained, cross-bedded sandstone facies. A highdegree of variability in permeability of the cross-bedded facies iscaused by small-scale variations in grain size and structure related todepositional processes. The geometric mean permeability in the bio-turbated sandstone is 253 md, compared with 1,395 md in the cross-bedded facies.

While the facies-dependent differences in permeability (k) are ap-parent and related to depositional and biological processes, fractal-based statistical analysis of the horizontal ln(k) increments yields near-ly identical results for the bioturbated facies and the cross-bedded fa-cies, possibly suggesting an underlying statistical commonality in theformation of both facies. Increment distributions from both facies ap-pear similar with peaking around the mean. Ln(k) increments fromthe smaller vertical data set appear similar also, but with a varianceapproximately 3.7 times larger than the horizontal value. Variancescaling analyses of horizontal and vertical data both yield a Hurst co-efficient near 0.26, which is characteristic of negative spatial correla-tion of the increments. The methodology developed herein offers a po-tential high-resolution alternative to existing methods for understand-ing and characterizing subsurface properties.

INTRODUCTION

Objectives and Significance

The objectives of this investigation are to interpret the sedimentology ofa portion of the John Henry Member of the Straight Cliffs Formation (Up-per Cretaceous) near Escalante in southern Utah (Figs. 1, 2) and to char-acterize the nature of small-scale permeability variations. An understandingof the permeability distribution in sedimentary facies and the relationshipto depositional processes are key to predicting subsurface flow patterns andthe occurrence of hydrocarbons and groundwater, as has been emphasized

* Present address: Tetra Tech, Inc., 2110 Powers Ferry Road, Suite 202, Atlanta,Georgia 30339, U.S.A.

** Present address: Southwest Research Institute, Center for Nuclear Waste Reg-ulatory Analyses, San Antonio, Texas 78238, U.S.A.

in recent studies (e.g., Weber 1982; Weber and van Geuns 1990; Hurst andRosvoll 1991; Kerans et al. 1994; White and Barton 1999). However, thesmall-scale variation (at a sample spacing of approximately 20 cm or less)of permeability is not well understood. This study examines the character-istics of small-scale permeability variation along horizontal and verticaltransects through two sandstone facies that differ both depositionally andlithologically.

Collection of field permeability data in the context of a sedimentologicalunderstanding aids in conditioning computer models to outcrop data, whichcan improve subsurface characterization and flow simulation. Several pre-vious studies have reported values of permeability measured from outcrops(e.g., Stalkup and Ebanks 1986; Goggin 1988; Tyler et al. 1991; Gogginet al. 1992; Davis et al. 1993; Fisher et al. 1993; Barton 1994; Liu et al.1996; Dutton and Willis 1998; Willis 1998; Willis and White 2000). Datafrom these outcrop investigations have confirmed the importance of un-derstanding sediment depositional processes in predicting and modeling thepermeability distribution. However, some of the previous methods used tomeasure outcrop permeability can introduce problems in data qualitycaused by a poor seal between the instrument and the outcrop surface.These problems are summarized by Dinwiddie (2001). In order to obtainpermeability values of sufficiently high quality for the current investigation,a new field permeameter, called the drillhole minipermeameter, was de-signed and built (Dinwiddie et al. 2000; Dinwiddie 2001; Molz et al. 2002;Dinwiddie et al. 2003). This instrument was used successfully to collectthe field permeability data for our study.

Geologic Setting

The study area is located approximately 10 km northwest of the townof Escalante, Utah, where the Straight Cliffs Formation crops out along thenortheastern margin of the Kaiparowits Plateau. The Straight Cliffs For-mation is underlain by the Upper Cretaceous Tropic Shale and overlain bythe Upper Cretaceous Wahweap Formation (Peterson 1969). A wide rangeof fluvial to marine depositional settings, including both wave-dominatedand tide-dominated environments, are represented within the Straight CliffsFormation (Peterson 1969; Shanley and McCabe 1991, 1993; Shanley etal. 1992; Hettinger et al. 1993; Hettinger 1995; Hettinger et al. 1996; Ste-phen and Dalrymple 2002). In general, alluvial and coastal-plain depositsin the formation grade eastward into marine deposits (Shanley et al. 1992;Hettinger et al. 1996).

The Straight Cliffs Formation represents deposition near the westernedge of the Western Interior seaway, which covered most of modern-daycentral and midwestern North America during Middle to Late Cretaceoustime (Peterson 1969; Jordan 1995). Foreland basin subsidence in this area,which is east of the Sierra Nevada arc and the Sevier Thrust belt, wascaused by flexural loading in response to uplift associated with subductionof the Pacific plate under the North American plate and with compressioncaused by extension in eastern North America (Jordan 1981, 1995).

The Straight Cliffs Formation is divided into four members (Peterson1969): the Tibbet Canyon Member, Smoky Hollow Member, John HenryMember, and Drip Tank Member (Fig. 2). The Early Coniacian to LateSantonian John Henry Member, which includes the interval studied, con-tains coal-bearing continental strata to the west that grade eastward intonearshore-marine deposits, including shoreface sandstones (Shanley and

271SEDIMENTOLOGY AND FRACTAL ANALYSIS, UPPER CRETACEOUS, UTAH

FIG. 1.—Location map.

FIG. 2.—Stratigraphic divisions of the StraightCliffs Formation for the study area, eastern partof Kaiparowits Plateau. The ‘‘A sandstone’’through ‘‘G sandstone’’ represent informalstratigraphic units after Hettinger et al. (1996).Position of age boundaries is approximate. AfterPeterson (1969), Eaton (1991), Shanley andMcCabe (1991), Hettinger et al. (1993), andHettinger et al. (1996).

McCabe 1991; Hettinger et al. 1996). The John Henry Member is underlainby coal-bearing coastal-plain and braided-river deposits of the Smoky Hol-low Member and overlain by fluvial sandstone of the Drip Tank Member(Peterson 1969, Hettinger 1995).

On the basis of correlation with outcrops studied by Hettinger et al.(1993) several kilometers to the south, the interval of our study corresponds

to the informal stratigraphic unit called the ‘‘B sandstone’’ by Hettinger etal. (1996). The base of this unit in some of the previously studied outcropsis marked by a pebble bed interpreted as a transgressive lag on a maximumflooding surface (Shanley et al. 1992; Hettinger et al. 1993; Hettinger1995). Because of the lateral continuity and excellent quality of outcrops,the flooding surface can be traced into our study area from the outcrops to

272 J.W. CASTLE ET AL.

TABLE 1.—Depositional features in outcrops studied.

DepositionalEnvironment Thickness Lithology Physical Features Biological Features

Foreshore 9–14 m Horizontally laminated, moderatelywell sorted fine- to medium-grainedsandstone

Common horizontal lamination; minor low-angle cross-bedding and planar-tabular cross-bedding

Minor to common shell fragments; rare burrowsin lower part in interval, becoming more com-mon upward (Skolithos, Planolites, and possi-bly Psilonichnus)

Upper Shoreface 6–8 m Cross-bedded, moderately to moderate-ly well sorted fine- to medium-grained sandstone

Common trough cross-bedding and low-angle cross-bed-ding; minor horizontal lamination and planar-tabularcross-bedding; lower contact is erosional and laterallycontinuous

Common plant fragments and common shellfragments on bedding planes; rare horizontaland vertical burrows

Transition-Lower Shoreface 10–15 m Moderately to well sorted, very fine- tofine-grained sandstone; overall up-ward increase in grain size

Massive, bioturbated intervals; minor, resistant sandstoneinterbeds (15–100 cm thick) containing low-anglecross-bedding and hummocky cross-stratification

Abundant horizontal and vertical burrows includ-ing Ophiomorpha, Planolites, and Thalassino-ides; minor Ophiomorpha, Palaeophycus, andSkolithos in hummocky cross-stratified beds;minor plant fragments; minor shell fragments

Offshore 9–12 m Interlaminated to thinly interbeddedshale, siltstone, and very fine- tofine-grained sandstone

Minor ripple cross-lamination, lenticular bedding, andflaser bedding

Common, small plant fragments; minor, smallhorizontal and vertical burrows; minor shellfragments

the south studied by Hettinger et al. (1993). Above this surface, Hettingeret al. (1993) interpreted offshore marine shale coarsening upward to shore-face sandstone. These marine strata represent the lowermost part of thehighstand systems tract of the A-sequence in the John Henry Member (Het-tinger et al. 1993; Hettinger et al. 1996).

Methods

Approximately 425 m of outcrop section were described from 14 siteswithin the study area. Gamma-ray profiles were obtained from each outcropusing a hand-held scintillometer. On the basis of the sequences of grainsize and sedimentary structures, along with comparison to modern andancient analogs, depositional environments were interpreted.

One of the outcrops, with a flat, nearly vertical face measuring approx-imately 21 m across and 6 m high, was selected for study of small-scalevariation in permeability. A total of 515 permeability measurements fromtwo sandstone facies were made in triplicate at a sample spacing of 15 cmalong three horizontal transects (380 measurements) and four vertical pro-files (135 measurements). To obtain an approximation of the mineralogyand fabric in each of the two sandstone facies, thin sections were preparedand examined from 32 measurement points. Sodium cobaltinitrite was ap-plied to each thin section as a stain to aid in the petrographic identificationof potassium feldspar. Each thin section was point-counted (300 pointseach) for detrital mineral content, matrix, cements, and porosity. Secondaryporosity was identified following the criteria proposed by Schmidt andMcDonald (1979). Grain size was estimated by measuring the maximumlength of grains of approximately average size in each thin section. Sortingwas estimated following methods of Beard and Weyl (1973) and Longiaru(1987).

A newly designed drillhole minipermeameter probe (Dinwiddie et al.2000; Dinwiddie 2001; Molz et al. 2002; Dinwiddie et al. 2003) was usedfor the in situ measurement of permeability. The averaging volume of theprobe is highly localized, and is thus amenable to determining small-scalepermeability variations (Molz et al. 2003). The probe was built for insertioninto cylindrical holes drilled with a standard 5/8 inch (1.59 cm) masonrydrill bit to a depth of 10.16 cm. The equipment used includes a nitrogentank, flowmeter, pressure transducer, leak-proof tubing, and the probe. Acommercially available mini-permeameter control system can be used withthe new probe to detect flow rate and pressure and to interface with aportable computer that performs various tasks such as data acquisition,transducer calibration, and permeability computation.

In preparation for testing, a cylindrical hole was drilled into the outcropsurface beyond the zone of weathering and perpendicular to the rock face.The drillhole was vacuumed to remove any dust or loose sand that remainedin the hole after drilling. The distal end of the probe was inserted into thehole, and a torque wheel was turned to expand a rubber sleeve to provide

a seal between the probe and the sides of the hole. Pressurized nitrogenwas then injected into the formation. Once steady-state conditions werereached, the in situ permeability was calculated from injection pressure,flow rate, and knowledge of the system geometry (Dinwiddie 2001; Din-widdie et al. 2003). As soon as measurements were completed, the sealwas broken by turning the torque wheel and the probe was removed. Threesteady-state measurements were performed at different gas pressures foreach drillhole.

Advantages of the approach described above include the reduction ofquestionable permeability measurements caused by weathering of the out-crop surface, a superior sealing mechanism around the air-injection zone,and the potential for making measurements at multiple depths below theoutcrop surface.

LITHOLOGY AND DEPOSITIONAL ENVIRONMENTS

Offshore

Description.—The lower 9–12 m of the interval studied consists of in-terlaminated to thinly interbedded shale, siltstone, and very fine- to fine-grained sandstone (Table 1; Figs. 3, 4). Because of the low resistance ofthis shaly interval to weathering, it tends to form vegetated slopes and ispoorly exposed in most of the study area. Common, small plant fragmentsand minor, small, horizontal and vertical burrows are present in the shaleand siltstone. The sandstone beds contain minor ripple lamination and mi-nor shell fragments. Minor lenticular bedding and flaser bedding are pre-sent.

At the base of this interval, a pebble-conglomerate lag directly overliesthe marine flooding surface at the lower contact of the ‘‘B sandstone.’’The pebble conglomerate, which ranges in thickness from 7 to 25 cm inthe study area, contains poorly sorted pebbles in a fine-grained sandstonematrix. Rare to minor shell fragments and plant fragments are present inthe sandstone matrix.

Interpretation.—On the basis of comparison with studies of modernsediments and ancient examples (Leithold 1989; Swift et al. 1991; Davisand Byers 1993; Johnson and Baldwin 1996), the lower interval of inter-laminated to thinly interbedded shale, siltstone, and very fine-grained sand-stone is interpreted as representing deposition in an offshore marine envi-ronment. The thin sandstone beds and laminae are interpreted as the basesof storm deposits, which may be analogous to laminated ‘‘storm-sand lay-ers’’ that have been described from modern shelf muds (Reineck and Singh1972). The intervening shale and siltstone beds are thought to represent themuddy top of the underlying storm-deposited sand combined with muddeposited from events too weak to transport sand out from the nearshoreenvironments.


FIG. 3.—Outcrop description at location 1. A sedimentologic profile, natural gam-ma radiation curve, and interpretation are shown. The gradual upward decrease ingamma radiation reflects the decrease in clay content relative to sand. The lowerpart of the interval studied is poorly exposed because of slope-forming shale. Themarine flooding surface, which has been interpreted as the maximum flooding sur-face of the A-sequence of the John Henry Member (Shanley et al. 1992; Hettinger1995), was traced into our study area from outcrops studied by Hettinger et al.(1993) to the south. The top of the interval studied is above the top of the outcropat this location. The rectangle on the location map corresponds to the outline of thestudy area shown on Figure 1.

FIG. 4.—Outcrop description at location 5. The upward coarsening suggests shore-line progradation. The marine flooding surface that corresponds to the base of theinterval studied (Fig. 2) is present below the exposure at this location. The rectangleon the location map corresponds to the outline of the study area shown on Figure1. See Figure 3 for legend.

Transition–Lower Shoreface

Description.—Approximately 10–15 m of moderately to well sorted,very fine- to fine-grained sandstone gradationally overlies the offshore fa-cies of the interval studied (Table 1; Figs. 3, 4, 5). Massive-bedded, bio-turbated intervals alternate with much thinner interbeds of hummockycross-stratified sandstone. Overall, grain size gradually increases upwardwithin this interval.

Abundant horizontal and vertical burrows (Fig. 6A) are present withinthe bioturbated intervals, which contain minor clay. Diameter of the bur-rows, which are identified as Ophiomorpha and Planolites, ranges fromapproximately 0.5 to 1.5 cm, with lengths up to 15 cm. Most of the burrowsare gently curving to sinuous, and some are lined with pellets. Similarlysized, branching burrows that occur in clusters near bedding contacts areidentified as Thalassinoides (Fig. 6B).

Rare mud clasts and minor fragments of plant and shell material arepresent within the bioturbated intervals. However, internal sedimentarystructures are not apparent within most of the burrowed sand, probably


FIG. 5.—Outcrop description at location 2.Locations of the horizontal transects along whichpermeability was measured are indicated (X, H,D). The marine flooding surface, which ispresent at the base of the interval studied, iscovered at this location. The rectangle on thelocation map corresponds to the outline of thestudy area shown on Figure 1. See Figure 3 forlegend.

because of destruction by burrowing. Rare ripple cross-lamination is pre-sent, particularly near the tops of beds.

As many as eight stratified sandstone beds, each 15–100 cm in thickness,are present within the transition–lower shoreface interval. These beds areclearly defined by sharp upper and lower contacts and by generally lightercolor than the bioturbated sandstone, particularly on weathered surfaces(Fig. 6C). The lower contact is erosional into the underlying sandstone.The beds contain a very low content of clay and, because of carbonatecement, tend be more resistant to weathering than the bioturbated sand-stone. Internal stratification is horizontal to hummocky, with minor ripplecross-lamination. Rare to minor vertical and horizontal burrows, includingOphiomorpha, Palaeophycus, and Skolithos are present in the hummockycross-stratified beds. Some of the hummocky beds can be traced laterallyalong the outcrop for more than 2,700 m as they pinch out and then re-appear in the same stratigraphic position.

Interpretation.—The presence of hummocky cross stratification (HCS)suggests that deposition was influenced by storm waves (Harms et al. 1975;Dott and Bourgeois 1982; Swift et al. 1983; Walker 1984; Brenchley 1985;

Duke 1985; Walker and Plint 1992). In a study of modern beach to offshoredeposits along the California coast, Howard and Reineck (1981) describedbioturbated sediments with parallel lamination, which they interpreted asprobable hummocky bedding. Ancient examples containing HCS have beeninterpreted as forming between storm wave base and fair-weather wavebase in the upper offshore to lower shoreface zone (e.g., Krassay 1994;Colquhoun 1995; Castle 2000). The upward increase in grain size in theinterval that we studied suggests possible shoreline progradation. In a pro-grading upward-coarsening shoreline succession in Upper Cretaceous strataof the Spanish Pyrenees, Ghibaudo et al. (1974) described similar shorefacedeposits of bioturbated sandstones with remnant sandstone beds havingpreserved lamination resembling HCS.

Deposition in a lower shoreface setting is consistent with occurrence ofthe trace fossils Ophiomorpha, Planolites, and Thalassinoides (Frey andPemberton 1985; Pemberton et al. 1992; Pemberton and MacEachern 1995;Pemberton et al. 2001). Ophiomorpha, Palaeophycus, and Skolithos havebeen reported in other hummocky cross-stratified Upper Cretaceous sand-stones interpreted as storm deposits (Frey 1990; Frey and Howard 1990).


FIG. 6.—Outcrop photographs. A) Burrows (predominantly Ophiomorpha) in lower-shoreface bioturbated sandstone. Much of this facies is extensively bioturbated, withindividual burrow structures commonly indistinct. From outcrop section 5, 14 m (Fig. 4). B) Thalassinoides burrows near base of sandstone bed in lower-shorefacebioturbated sandstone. Width of exposure shown is 38 cm. From outcrop section 5, 13 m (Fig. 4). C) Hummocky cross-stratified sandstone bed within the lower shorefaceinterval. Skolithos burrows (vertical) and Palaeophycus burrows (inclined) are present. Length of scale 5 6 cm. From outcrop section 5, 18 m (Fig. 4). D) Cross-beddedupper-shoreface sandstone. From 1 m above base of upper-shoreface sandstone exposed 300 m north of outcrop section 1 (Fig. 3). Length of scale near left edge ofphotograph is 5 cm.

Except for within the hummocky cross-stratified beds, most of the originalsedimentary structures, including interbedding between mud and sand, inthe transition–lower shoreface interval were probably obliterated by bio-turbation. In the lower-shoreface and transition zone, the extent of biotur-bation, and hence the preservation of storm-generated beds, depends on themagnitude and frequency of storms and the overall rate of sedimentation(Reading and Collinson 1996). The hummocky cross-stratified beds pre-served between the massive bioturbated intervals in our study area mayrecord wave processes that were more intense than during deposition ofthe bioturbated beds.

Upper Shoreface

Description.—Cross-bedded, moderately well sorted, fine- to medium-grained sandstone sharply overlies the lower shoreface interval (Table 1;Figs. 3, 4, 5). Intervals of trough cross-bedded sandstone 1–1.5 m thick(Fig. 6D) alternate with beds of low-angle cross-bedded sandstone 0.1–0.3m thick. Minor horizontal lamination, minor planar-tabular cross-bedding,and rare ripple cross-lamination are also present. Common shell debris andplant fragments occur on bedding planes, and rare horizontal to verticalburrows are present within the sandstone beds. In the outcrops studied, thisinterval ranges in thickness from 6 to 8 m.

The basal contact with the underlying lower-shoreface interval is sharply

defined and laterally continuous throughout the study area. The contact iserosional, showing approximately 1.5 m of relief among the outcrops stud-ied. The contact is directly overlain by trough cross-bedded, horizontallylaminated, or low-angle cross-bedded sandstone. Lag deposits were notobserved on the contact.

Interpretation.—This interval is interpreted as upper shoreface, with theabundant trough cross-beds representing subaqueous migration of dunes.Grain size and sedimentary structures are similar to those of modern, cross-stratified shoreface deposits (Howard and Reineck 1981; Heron et al. 1984;Shipp 1984; Greenwood and Mittler 1985; Swift et al. 1991) and to ancientupper-shoreface deposits (Swift et al. 1987; Walker and Plint 1992; Col-quhoun 1995; Johnson and Baldwin 1996). The previous studies demon-strated that sand deposition in this setting is controlled by a combinationof storm and fair-weather processes. The sharp basal contact of the upper-shoreface facies is interpreted as a surf diastem, which is defined by Swiftet al. (2003) as a surface cut by repeated storm scour in the surf zone andidentified in outcrop as the erosional base of the lowest high-angle cross-bed set in a shoreface succession.

Foreshore

Description.—An interval of predominantly horizontally laminated,moderately well sorted fine- to medium-grained sandstone, approximately


FIG. 7.—Locations of vertical profiles and horizontal transects along which permeability was measured by drilling into the outcrop face, section 2 (Figure 5). The strikeof the outcrop face is approximately parallel to strike of the paleoshoreline, which has been interpreted previously as northwest–southeast (Peterson 1969). Each dot onthe diagram corresponds to a permeability measurement. Approximate positions of rock overhang and soil cover are shown.

9–14 m thick, overlies the upper shoreface interval (Table 1; Figs. 3, 5).Minor low-angle cross-bedding and planar-tabular cross-bedding are pre-sent. Typically, beds of horizontally laminated and low-angle cross-beddedsandstone 0.3–3.0 m thick alternate with beds of planar tabular cross-bed-ded sandstone 0.15–0.3 m thick. A few beds within this interval contain aconcentration of common to abundant shell fragments, and minor shellfragments are present on cross-bed foresets in other beds. In most outcropsstudied, grain size shows a slight upward decrease; minor shale interbedsare present in the upper part of the interval in some outcrops.

Although burrows are rare in the horizontally laminated medium-grainedsandstone of this interval, minor to common vertical and horizontal burrowsare present in the upper, finer-grained part of the interval. The burrows,which are identified as Skolithos, Planolites, and possibly Psilonichnus, areapproximately 0.5–1.0 cm in diameter and up to 4 cm long.

The basal contact of this interval varies from sharp to gradational. Theupper contact, which marks the top of the interval studied, is sharp andoverlain by medium-grained sandstone containing abundant oyster shellsand fragments and abundant mud clasts. This bed ranges from about 0.75to 1.5 m in thickness.

Interpretation.—Horizontally laminated and low-angle cross-beddedsandstone of this interval is interpreted as representing beach-face deposi-tion in a foreshore setting. The occurrence of horizontal lamination, low-angle cross-bedding, shell fragments, upward fining, and burrows are con-sistent with descriptions of modern and ancient foreshore deposits (Cliftonet al. 1971; Hill and Hunter 1976; Hunter et al. 1979; Howard and Reineck1981; Heron et al. 1984; Short 1984; Clifton 1988; Reading and Collinson1996).

Internal structures, finer grain size, and burrowing in the upper part ofthis interval indicate lower-energy deposition than represented by the un-derlying horizontally laminated foreshore deposits. From position in theoverall succession and from comparison with other examples (e.g., Swiftet al. 1991; Walker and Plint 1992), the upper part of this interval mayrepresent backshore deposition. Bioturbated sediments, similar to those inthe upper part of the interval studied, have been described from modernbackshore environments (Hill and Hunter 1976; Frey et al. 1984; Frey andPemberton 1987). On the basis of comparison with similar contacts andassociated lithologies from other ancient successions (Bergman and Walker1987; Pattison and Walker 1992; Bergman 1994; Arnott et al. 1995), thesharp upper contact is interpreted as a wave-cut surface overlain by a lagof reworked material.

PERMEABILITY STRUCTURE

Data

Intrinsic permeability was measured in two facies at outcrop section 2(Fig. 5): lower-shoreface bioturbated sandstone and upper-shoreface cross-bedded sandstone. In the bioturbated sandstone, 353 measurements of per-meability were made along two horizontal transects and in the lower partsof four vertical profiles (Fig. 7). For the cross-bedded facies, 162 perme-ability measurements were made along one horizontal transect and in theupper parts of the four vertical profiles. The permeability values for allmeasurement points were reported by Current (2001) and are shown graph-ically in Figures 8, 9, and 10.

Permeability values range from 41 to 1,675 millidarcies (md) in thebioturbated sandstone facies. The arithmetic mean permeability value inthis facies is 276 md, and the geometric mean is 253 md. The range ofpermeability variation in this facies along both the horizontal transects andthe vertical profiles is generally less than one order of magnitude. Grainsize in the bioturbated facies also shows little variation laterally and ver-tically.

Permeability in the cross-bedded facies ranges from 336 to 5,531 md,with an arithmetic mean permeability equal to 1,746 md and a geometricmean of 1,395 md. Permeability variation exceeding 1,000 md is not un-common among nearby sample locations. At a vertical position of 5 to 7sample locations above the contact between the bioturbated facies and thecross-bedded facies, a high-permeability peak can be correlated among thevertical profiles (Fig. 8). Permeability at this position ranges from 1,924md in profile V-2 to 5,126 md in profile V-3.

Geologic Controls

Compared to the bioturbated facies, permeability values are greater inthe cross-bedded facies because of coarser grain size, greater primary po-rosity, and smaller percentages of clay matrix and cement (Table 2). Onthe basis of petrographic observation, primary pores are larger and betterconnected in the cross-bedded facies than in the bioturbated sandstone,which is related to coarser grain size in the cross-bedded facies. Smallamounts of grain-moldic secondary porosity have formed by dissolution offeldspar grains in both sandstone facies. Although the percentage of moldicporosity is greater in the bioturbated facies than in the cross-bedded facies,its contribution to permeability is small because of low connectivity amonggrain-moldic pores. The growth of minor, pore-lining chlorite cement has


FIG. 8.—Vertical permeability profiles. Most permeability values in the cross-bedded sandstone are greater than values in the bioturbated sandstone. Intersections ofhorizontal transects D, H, and X are shown.

FIG. 9.—Horizontal permeability transects.Permeability values vary over a greater range inthe cross-bedded sandstone (transect X) than inthe bioturbated sandstone (transects H and D).Intersections of vertical profiles V1, V2, V3, andV4 are shown.


FIG. 10.—Horizontal permeability transects Hand D (bioturbated sandstone) plotted at anexpanded scale. Intersections of vertical profilesV1, V2, V3, and V4 are shown.

TABLE 2.—Texture, composition, and fabric of facies tested for permeability in the John Henry Member. Data are averaged from petrographic counting of 300 pointsper sample.

FaciesNumber of

SamplesMean GrainSize (mm)

*MeanSorting

**Proportion of DetritalFramework Grains (%)

Quartz FeldsparLithic

Fragments

Proportion of Fabric Components (%)

FrameworkGrains

ClayMatrix

CalciteCement

ChloriteCement

PrimaryPorosity

SecondaryPorosity

Upper Shoreface 12 0.23 3.4 65. 2.4 32. 67. 1.0 3.0 2.3 25. 1.8(Cross-bedded Sandstone)

Lower Shoreface 20 0.11 4.8 80. 3.5 16. 65. 2.9 5.2 2.5 21. 3.3(Bioturbated Sandstone)

* Mean sorting estimated using the methods of Beard and Weyl (1973) and Longiaru (1987): 1 5 very poor; 2 5 poor; 3 5 moderate; 4 5 moderately well; 5 5 well; 6 5 very well.** Feldspar mineralogy is orthoclase. Lithic grains are predominantly chert, with minor sedimentary and volcanic rock fragments. The higher proportion of detrital quartz to lithic grains in the bioturbated sandstone than

in the cross-bedded sandstone is probably related to grain size difference between the two facies.

reduced permeability in both sandstone facies. From qualitative petrograph-ic observations from both facies, the individual samples with the highestpermeability values contain the largest amount of porosity and the leastamount of matrix and cement.

Field permeability measurements from lower-shoreface bioturbated sand-stone and upper-shoreface cross-bedded sandstone demonstrate facies-de-pendent variations in permeability. Because of lithologic homogenizationby extensive burrowing, the bioturbated sandstone exhibits a small rangeof permeability variation over a scale of several meters. In contrast, per-meability in the cross-bedded facies varies by more than an order of mag-nitude over distances as small as 30 cm, which is caused predominantlyby variations in grain size and sorting related to the depositional processes(Current 2001). The primary textural properties are preserved better in thecross-bedded facies than in the bioturbated facies, where they have beenmodified by burrowing.

STATISTICAL ANALYSES OF PERMEABILITY STRUCTURE

Like virtually all small-scale permeability (k) data collected during thepast decade (Painter 2001; Lu et al. 2002), the k or ln(k) data from ourstudy appear irregular and spatially nonstationary in a statistical sense. Ir-regular means that the slope of k versus distance changes abruptly in avariable ‘‘saw-tooth’’ fashion (a discontinuous first derivative; Fig. 10),and nonstationary means that statistical parameters computed from the data,such as mean and variance, depend on position. For example, if each ofthe four plots shown in Figure 8 is divided into a top half and a bottomhalf, then one can calculate a mean (m) and variance (s2) for each half.Proceeding from V-1 to V-4 across the top half and averaging the results,one computes a m of 1,237 md and a s2 of 901,356 md2. Similar analysisof the bottom half of the data yields m 5 336 md and s2 5 52,544 md2.As apparent from visual inspection of the data, these values differ signif-

icantly, so the statistical parameters are not unique, but rather are a functionof vertical position. The same observation applies to the horizontally dis-tributed data shown in Figure 10. Dividing these data sets into a left halfand right half yields m 5 330 md and s2 5 17,628 md2 for the left half,but m 5 222 md and s2 5 7,393 md2 for the right half, again indicatingdependence of statistical parameters on position. Strictly speaking, it is notappropriate to perform a statistical analysis of spatial data that are notstationary in space or temporal data that are not stationary in time. Eventhough means, variances, and (possibly) other parameters come out of suchanalyses, what they represent is not clear, because the results depend onthe spatial or temporal variable in an unknown way. So how should oneproceed?

A traditional approach is to attempt to detrend the data (e.g., Gelhar1993). Using this procedure, one attempts to identify the large-scale trendsin the data and remove them, so that what is left is stationary. Then sta-tistical analyses are performed on the detrended data. This approach is oftennot satisfactory, however, because the detrending process is highly subjec-tive. A more rigorous approach, increasingly supported by measurements,is to accept the fact that most data from natural sedimentary systems arenonstationary, and to make use of the theory of nonstationary stochasticprocesses with stationary increments (Lu et al. 2002). The mathematicalbasis for this theory was developed during the first half of the past century(Feller 1971, and earlier editions) and first applied to petroleum geologyduring the late 1980s (Hewitt 1986) and to hydrogeology during the early1990s (Neuman 1990; Molz and Boman 1993).

In the following analysis of the data collected in our study, the basicproperty will be ln(k), which was measured at a number of points a knowndistance apart. Then each pair of points defines an increment of ln(k) [Dhln(k) 5 ln(k(x 1 h))—ln(k(x)) that is associated with the constant mea-surement separation, h. Thus n points along a transect where ln(k) is mea-


FIG. 11.—Empirical frequency distribution for the horizontal ln(k) increments (‘‘Sample Frequency’’) along with that of the best fitting Gaussian distribution (‘‘NormalDistribution’’). The data are from horizontal transects D and H in the bioturbated sandstone facies. The empirical distribution was obtained by first computing a cumulativedistribution function and then differentiating this curve numerically. A Chi-Square test made on the empirical data directly suggested that the Gaussian fit was significantat only the 51% confidence level, with apparently non-Gaussian peaking observed around the mean.

sured define n-1 ln(k) increments. All statistical analyses are then performedon the increment distributions, the set of values of Dhln(k), and not on theln(k) distributions directly. According to theory, such distributions shouldhave a mean of zero that is independent of h and a variance that increaseswith h as a power function (Molz et al. 1997). Traditionally, this power-law dependence is written as s2(h) 5 s2(1)h2H, with H being called theHurst coefficient. Furthermore, property distributions that are constructedfrom sets of stationary increments, with and without correlation of theincrements, display scaling properties characteristic of a group of self-affinestochastic processes (to distinguish from self-similar when H 5 ½) knownas stochastic fractals (Molz et al. 1997). The basic analysis procedure thenis to:

(1) compute Dhln(k) frequency distributions for a variety of h values;(2) assuming that such distributions are Gaussian, compute the mean

(should be zero) and variance for the various Dhln(k) sets;(3) plot s2 versus h on double logarithmic paper; and(4) if the plot is a straight line, determine the slope of the line, which

enables one to calculate H.

In practice, the variance calculation is highly sensitive to the relativelysmall number of data points for the larger lags, so a lot of noise is produced.This has led to the development of less data-sensitive techniques such asrescaled range analysis and dispersional analysis (Lu et al. 2002). Theselatter two techniques are simply mathematical surrogates for the use ofdirect variance scaling plots to determine H, which is discussed later.

When such analyses were applied previously, most scaling requirementswere met (Painter 2001), but the resulting frequency distributions forDhln(k) usually appeared non-Gaussian, with a distinct resemblance to theLevy distribution, which has undesirable statistical properties (Painter1995; Liu and Molz 1997). However, later studies showed that such dis-tributions, while appearing Levy-like, did not exhibit true Levy behaviorin the tails of the distributions (Lu and Molz 2001; Painter 2001). This isfundamental, because it is the tail behavior that gives Levy distributionstheir famous property of infinite variance.

In order to explain the appearance of Levy distributions as possible ar-tifacts of the data analysis-procedure, Lu et al. (2002) presented what they

called the ‘‘fractal/facies model,’’ which is a hypothesis that Dhln(k) fre-quency distributions within a single facies will be Gaussian. The oftenobserved Levy-like distributions would then result because of mixing datafrom several different facies, which would be equivalent to superimposingseveral Gaussian distributions, in general of different variance. Thus, theapproach advocated by Lu et al. (2002) would require that data gatheredfrom each facies of a multi-facies structure be analyzed separately. To theextent practical, this approach was followed in the analysis of the presentdual-facies data set.

As shown in Figure 11, the ln(k) increment frequency distribution fromthe horizontal transects of the bioturbated sandstone displays some aspectsof a Gaussian distribution of mean 0.0013 and variance 0.122; however, achi-square test suggests that the hypothesis of a Gaussian fit is significantat only the 51% confidence level. This result is likely due to the poor fitin the vicinity of the mean, where one would expect the comparison to berelatively good for a true Gaussian fit. The frequency distribution of thesmaller horizontal data set from the cross-bedded facies, shown in Figure12, displays more noise, but behavior in the vicinity of the mean is similar.In addition, the best-fit Gaussian has a mean of 0.0014 and a variance of0.127, nearly indistinguishable from the bioturbated facies. This varianceresult was unexpected, and it indicates that in a statistical ln(k) incrementsense the two facies are not distinguishable in terms of mean and variance,at least in the horizontal direction. The combined increment data are shownin Figure 13, which is a plot of all the horizontal Dhln(k) with h 5 15 cm.Having a mean of 0.0013 and a variance of 0.123, this combined plot is agood example of the appearance of a spatially stationary stochastic process,as required by theory.

Analysis of all the vertical Dhln(k) data resulted in the frequency distri-bution and best-fit Gaussian shown in Figure 14, with the qualitative resultnot unlike that shown in Figure 12. Here the mean is 0.033 and the sig-nificantly larger variance is 0.454. The individual means to two decimalplaces are 0.03 for both facies, with a variance of 0.33 for the cross-beddedsandstone and 0.46 for the bioturbated sandstone. Thus in the vertical di-rection there is a significant difference in variance between facies. In sed-imentary deposits it is common for variability perpendicular to bedding todiffer from that along bedding, so the factor of 3.7 increase in the variance


FIG. 12.—Empirical frequency distribution for the horizontal ln(k) increments from transect X in the cross-bedded sandstone facies. The best-fit Gaussian is essentiallythe same as that for transects D and H (Fig. 11), indicating that ln(k) increments from both facies display similar statistical structure.

FIG. 13.—Ln(k) increments for all of the horizontal data as a function of position. This plot provides a good example of the ‘‘appearance’’ of a portion of a spatiallystationary stochastic process. These numbers represent the statistically meaningful data extracted from the irregular, nonstationary, property distribution. That one shouldbe able to do this is the basis of the stochastic fractal theory.

of the vertical increments compared to the horizontal increments is notsurprising, and can be viewed as a type of statistical anisotropy, as dis-cussed in Lu et al. (2003).

When applied to individual data sets, direct variance scaling tests aregenerally quite noisy (Mandelbrot and Wallis 1969), as mentioned previ-ously. In addition, the results described in the previous paragraph indicatethat the two facies are nearly statistically indistinguishable in a Dhln(k)sense in the horizontal direction. Therefore, we applied dispersional anal-

ysis to all of the horizontal data and all of the vertical data. The resultsyielded Hurst coefficients of 0.24 and 0.28 for the horizontal and verticaldata, respectively. (It may be of interest to note that both results are near0.25, a value inferred by Neuman (1990) on the basis of an analysis oflarge-scale tracer tests and the resulting observation of scale dependenceof hydrodynamic dispersivity for a large variety of materials. Given thelimitations of our data set from the perspectives of size and rock type, thismay be a coincidence.) Straight lines of slopes 2H (half slopes of 0.24 and


FIG. 14.—Empirical frequency distribution for the vertical ln(k) increments (profiles shown in Fig. 8). Here the best-fit Gaussian has a variance that is 3.7 times largerthan the horizontal value (Fig. 13). This is a type of statistical anisotropy that was discussed by Lu et al. (2003).

FIG. 15.—Double natural logarithm plot of the variance of the increments (var) as a function of lag (h) for all horizontal data. The straight line was computed independentlyof the variance using dispersional analysis (Lu et al. 2003). The Hurst coefficient (H) of 0.24 is one-half the slope of the line, and indicates that the increments arenegatively correlated.

0.28, respectively) were superimposed on the direct variance plots deter-mined independently as shown in Figures 15 and 16 for the horizontal andvertical data, respectively, with the result confirming that the H valuesresulting from the dispersional analysis are reasonable. Magnitudes of Hin the vertical and horizontal directions are similar, although the ln(k) in-crement variances are quite different. Very few data sets contain both hor-izontally distributed and vertically distributed data, so additional measure-ments are needed to see whether similar results hold for different sedi-mentary formations. In particular, one would like to better understand the

peaking around the mean that seems to appear in all the computed ln(k)increment frequency distributions and causes the plots to display an ap-parent non-Gaussian shape.

CONCLUSIONS

From sedimentological study of strata within the ‘‘B sandstone’’ of theJohn Henry Member, the following depositional environments are inter-preted: offshore, transition–lower shoreface, upper shoreface, and fore-


FIG. 16.—Double natural logarithm plot of the variance of the increments (var) as a function of lag (h) for all vertical data. The straight line was computed independentlyof the variance using dispersional analysis (Lu et al. 2003). The Hurst coefficient (H) of 0.28 is one-half the slope of the line, and indicates negative increment correlation.

shore. Shoreline progradation is indicated by upward coarsening in grainsize and by the sequence of sedimentary structures, which indicate an up-ward increase in wave energy. Closely spaced field permeability measure-ments made in the lower-shoreface bioturbated sandstone and upper-shore-face cross-bedded sandstone demonstrate facies-dependent variations andsimilarities that are caused by lithologic differences related to depositionalprocesses.

As illustrated by our study of the John Henry Member, sedimentarydeposits are typically characterized by distinct facies that may changeabruptly in both the vertical and horizontal directions, with facies structurerelating to the depositional processes. Lu et al. (2002) proposed the fractal/facies model as a new approach for quantifying the underlying structure ofgeological heterogeneity on the basis of an understanding of facies. Ratherthan using Levy probability density functions (PDFs) to describe ln(k) in-crement distributions, the fractal/facies hypothesis proposes GaussianPDFs, with a (potentially) different PDF for each facies (Lu et al. 2002).However, statistical analysis of data from the bioturbated and cross-beddedsandstone facies of the John Henry Member, while providing evidence fornon-Levy behavior of ln(k) increments, particularly the tail behavior, yield-ed similar Dhln(k) frequency distributions in both facies in the horizontaldirection. Variance scaling of Dhln(k), as determined by the value of theHurst coefficient, also appeared consistent across facies. These results maysuggest some type of underlying commonality in the formation of thesetwo facies that is not obvious from visual inspection. Additional data andstatistical analysis are needed to fully determine the applicability of thestochastic fractal model (nonstationary stochastic functions with stationaryincrements) as well as the fractal/facies hypothesis, because non-Gaussianpeaking in the vicinity of the mean appeared in all empirical frequencydistributions and Chi-square tests for a normal fit were not definitive.

ACKNOWLEDGMENTS

This study would not have been possible without the unselfish contributions ofBob Hettinger, who introduced us to the area, guided us in the field, and providedvaluable discussion. We thank Nicole McMahan and Joey Koon for their untiringefforts in describing outcrops and tracing beds. Caitlin Current and Robert Bridgesassisted with collecting the outcrop permeability data. We gratefully acknowledgethe contribution of Chris Hepler, who diligently point counted the thin sections, and

Jinjun Wang, who performed the statistical calculations underlying Figures 11through 16. We express our sincere appreciation to David Dominic, Donald Swift,and Gary Weissmann, who reviewed the manuscript and provided many valuablesuggestions that significantly improved the paper.

This research was supported by the U.S. Department of Energy, Fossil EnergyOil Technology Program, through the National Petroleum Technology Office undercontract number DE-AC26-98BC15119.

The work conducted by C.L. Dinwiddie as described in this article was initiatedand completed at Clemson University when she was a Ph.D. candidate, before thebeginning of her current employment with the CNWRA.

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Received 24 February 2003; accepted 28 August 2003.

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