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$: Stratigraphic controls on vertical fracture patterns in ...rocks, relationship between stratigraphy and hydraulic properties, land use impacts on groundwater quality, and delineation$
AAPG Bulletin, v. 87, no. 1 (January 2003), pp. 121–142 121

Stratigraphic controls onvertical fracture patterns inSilurian dolomite, northeasternWisconsinChad A. Underwood, Michele L. Cooke, J. A. Simo,and Maureen A. Muldoon

ABSTRACT

Vertical opening-mode fractures are mapped on quarry walls toassess the stratigraphic controls on fracture patterns in the relativelyundeformed Silurian dolomite of northeastern Wisconsin.Our two-stage study uses maps of vertical fractures to assess the effectivenessof various types of stratigraphic horizons (e.g., organic partings orcycle-bounding mud horizons) in terminating opening-mode frac-tures. First, the mechanical stratigraphy of the exposures is inter-preted from the observed fracture pattern. Both visual inspectionand a newly developed quantitative method are employed to iden-tify effective mechanical interfaces. The two methods show similarresults, confirming the validity of qualitative visual inspection. Thesecond stage of our study stochastically predicts mechanical stratig-raphy and subsequent fracture pattern from empirical relationshipsbetween the observed sedimentary stratigraphy and the interpretedmechanical stratigraphy. For example, 63% of cycle-bounding mudhorizons within the inner-middle and middle shelf facies associa-tions serve as mechanical interfaces. These empirical percentagesare input to a Monte Carlo analysis of 50 stochastic realizations ofmechanical stratigraphy. Comparisons of the stochastically pre-dicted and interpreted mechanical stratigraphy yield errors rangingfrom 13 to 33%. This method yields far better results than assumingthat all stratigraphic horizons act as mechanical interfaces. Themethodology presented in this article demonstrates an improvedprediction of fracture pattern within relatively undeformed stratafrom both complete characterization of sedimentary stratigraphyand understanding mechanical controls on fracturing.

Copyright �2003. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received November 16, 2000; provisional acceptance September 21, 2001; revised manu-script received June 17, 2002; final acceptance July 29, 2002.

AUTHORS

Chad A. Underwood � GeologicalEngineering Program, University of Wisconsin,Madison, Wisconsin, 53706-1692; currentaddress: Montgomery Watson Harza, OneScience Court, Madison, Wisconsin, 53711;[email protected]

Chad A. Underwood received a B.S. degree ingeology from the University of Wisconsin atEau Claire and an M.S. degree in geologicalengineering from the University of Wisconsinat Madison. He currently works as ageotechnical engineer for MontgomeryWatson Harza (MWH) in Madison, Wisconsin.

Michele L. Cooke � GeosciencesDepartment, University of Massachusetts,Amherst, Massachusetts, 01003–5820;[email protected]

Michele L Cooke received a B.S.E. degree ingeological engineering from PrincetonUniversity and an M.S. degree in civilengineering and a Ph.D. in geological andenvironmental sciences (with mechanicalengineering minor) from Stanford University.Currently an assistant professor ofgeosciences at University of Massachusetts–Amherst, her research applies structuralgeology and rock fracture mechanics toinvestigate deformation of active and ancientstructures.

J. A. Simo � Geology and GeophysicsDepartment, University of Wisconsin,Madison, Wisconsin, 53706–1692 ;[email protected]

Toni Simo received both an M.S. degree(1982) and a Ph.D. (1985) from the Universityof Barcelona. He was a Fulbright Scholarbefore joining the Department of Geology andGeophysics, University of Wisconsin–Madisonin 1989. His primary interest is in carbonatesedimentology, sequence stratigraphy ofsedimentary basins, and environmentalsedimentology. Recent work in these areasincludes Paleozoic epeiric sea deposition andshelf margins in the United States,synsedimentary facies associated withcontractional settings in Spain and Indonesia,and stratigraphic implications in rockfracturing and arsenic contamination.

122 Vertical Fracture Patterns in Silurian Dolomite

INTRODUCTION

Fracture patterns exposed on both horizontal surfaces (e.g., Dyer,1988) and vertical outcrops (e.g., Gross et al., 1995; Bahat, 1999)have been used to infer paleostress orientations and, thus, give evi-dence of the tectonic history of a region. Interpreting the geologichistory from vertical outcrop patterns of fractures requires consid-eration of both tectonics and stratigraphy, which can both producevariations in the fracture pattern (see Dholakia et al., 1988; Grosset al., 1995). Furthermore, determining the stratigraphic controlson opening-mode fracture patterns helps us better predict the sub-surface flow paths of fluids such as ground water (e.g., Muldoonand Bradbury, 1998) and hydrocarbons (e.g., Nelson, 1982). Un-derstanding the development of fracture networks within aquifersand reservoirs can improve fluid-flow prediction by constrainingsome of the uncertainty in fracture characteristics, such as fracturelength, aperture, and connectivity.

In relatively undeformed sedimentary rocks, the density andheight of opening-mode fractures (joints) are typically controlledby stratigraphy rather than faulting or folding (e.g., Becker andGross, 1996; Hanks et al., 1997). Under these conditions, fracturedensity typically depends on the material properties and bed thick-ness of stratigraphic units (e.g., Huang and Angelier, 1989), becausefractures commonly terminate at specific stratigraphic horizons(e.g., Gross et al., 1995). However, the pattern of fracturing is di-rectly controlled by mechanical stratigraphy, which does not nec-essarily correspond to the sedimentary stratigraphy (e.g., Corbettet al., 1987; Gross et al., 1995; Hanks et al., 1997). A mechanicalunit represents one or more stratigraphic units that fracture inde-pendently of other units (Figure 1). Fractures typically span thethickness of the mechanical unit and commonly abut the boundingstratigraphic horizons. Such stratigraphic horizons along whichmany fractures abut are termed “mechanical interfaces” (Figure 1)(Gross et al., 1995).

Consequently, the stratigraphic features that comprise the me-chanical stratigraphy of a sequence are those that control fractureinitiation and termination in rock strata (e.g., Gross, 1993). Verticalopening-mode fractures (joints) commonly initiate from flawssomewhere within a mechanical unit and terminate at mechanicalinterfaces (Gross, 1993). In layered formations consisting of inter-bedded brittle/ductile rocks, fractures typically initiate in the brittlelayer and terminate at the contact with ductile layers (e.g., Cookand Erdogan, 1972; Erdogan and Biricikoglu, 1973; Helgeson andAydin, 1991; Rijken and Cooke, 2001). Within relatively homo-geneous layered formations, fractures may terminate at mechanicalinterfaces because of interface slip (e.g., Teufel and Clark, 1984;Renshaw and Pollard, 1995) and/or local debonding along inter-faces that are weak in tension (Cooke and Underwood, 2001).

Whereas interface properties control fracture termination, me-chanical unit thickness, or spacing ofmechanical interfaces, controlsfracture density. Predicting fracture density therefore requires

Maureen A. Muldoon � GeologyDepartment, University of Wisconsin,Oshkosh, Wisconsin, 54901–8649;[email protected]

Maureen Muldoon received her M.S. degreeand Ph.D. from the University of Wisconsin–Madison. She worked at the WisconsinGeological and Natural History Survey forseven years before joining the faculty at theUniversity of Wisconsin–Oshkosh. Herresearch interests include the investigation ofgroundwater quality and flow in carbonaterocks, relationship between stratigraphy andhydraulic properties, land use impacts ongroundwater quality, and delineation ofwellhead protection zones in fractured rock.

Underwood et al. 123

FluidFlow

Mechanical Unit (may contain one or more stratigraphic horizons)

Mechanical Interface at a Stratigraphic Horizon

Fracture

Mechanical Unit

Mechanical Interface

Fracture

Exposed Vertical Fractures

(A)

(B)

Figure 1. (A) Stratigraphiccontrols on fracture patterns.Fractures develop within me-chanical units and abut me-chanical interfaces (modifiedfrom Gross et al., 1995). In-creased fracture density directlycorrelates with increased frac-ture porosity. Both effective po-rosity and effective permeabilityare highly dependent on theconnectivity of the fracture net-work; therefore, increased frac-ture density does not necessar-ily lead to increasedpermeability. (B) Termination ofvertical fractures can redirectthe vertical component of flowto horizontal features, such asdissolutionally enlarged beddingplanes. Laterally extensive hori-zontal high-permeability fea-tures are continuous up to 14km (9 mi) based on hydrogeo-logic studies of the Silurian do-lomite (Muldoon et al., 2001).

knowledge of the distribution of mechanical interfaces.Field investigations indicate that in many relativelythinly bedded rock types, the product of fracture den-sity and bed thickness is approximately 1.0 (Price,1966; Hobbs, 1967; McQuillan, 1973; Huang and An-gelier, 1989; Narr and Suppe, 1991; Gross, 1993;Gross et al., 1995; Wu and Pollard, 1995; Becker andGross, 1996; Bai and Pollard, 2000). One explanationfor this relationship relies on the concept of a stressshadow (Lachenbruch, 1961; Nur, 1982; Pollard andSegall, 1987; Gross et al., 1995) where new fracturegrowth is inhibited within a zone of decreased stressadjacent to an open fracture (Pollard and Segall, 1987).The size of the stress shadow is directly proportionalto the height of the fracture, so that thickermechanicalunits have longer and more widely spaced fracturesthan do thinner units (Pollard and Segall, 1987; Gross,1993).

This article seeks to describe the relationship be-tween sedimentary stratigraphy and mechanical stra-

tigraphy, within a relatively undeformed setting, to testpredictions of fracture pattern from stratigraphic in-formation. We interpret the mechanical stratigraphy ofa section of the shallow dipping (�2�) Silurian dolo-mite of northeastern Wisconsin (Figure 2) from carefulfracture mapping along two quarry exposures. This ar-ticle assesses the effectiveness of different types ofstratigraphic horizons as mechanical interfaces that ar-rest fractures by correlating stratigraphic horizons(characterized by Simo et al. [1998] and Harris andWaldhuetter [1996]) with interpreted mechanical in-terfaces. The resulting empirical relationships betweensedimentary stratigraphy and mechanical stratigraphyare used to predict vertical fracture pattern. We com-pare the stochastic predictions of mechanical stratig-raphy and fracture pattern with our observations andinterpretations to test the application of such empiricalrelationships toward fracture pattern prediction. Themethodology used in this article can be employed topredict subsurface opening-mode fracture networks,


Figure 2. (A) Location ofDoor County, Wisconsin (Mul-doon et al., 2001). (B) Bedrockgeology of Door County, Wis-consin (Roffers, 1996). (C)Cross section through DoorCounty, Wisconsin (Muldoon etal., 2001).

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which are poorly sampled by vertical boreholes, fromavailable observations of sedimentary stratigraphy.Such an approach enhances prediction of subsurfacefluid flow through better characterization of potentialflow paths. The key to this approach is accurate de-scription of the relations between sedimentary stratig-raphy and mechanical stratigraphy.

REGIONAL GEOLOGY, STRATIGRAPHY,AND FRACTURE PATTERN

Door County, Wisconsin occupies much of a peninsulathat lies between Lake Michigan and Green Bay innortheastern Wisconsin (Figure 2). It is underlain byapproximately 160 m (525 ft) of Lower Silurian (He-grenes, 1996) or Llandovery (Watkins and Kuglitsch,1997) dolomite. The Silurian strata were deposited inthe western margin of the Michigan basin, a relativelyundeformed cratonic structural basin (Sleep and Sloss,1978; Howell and van der Pluijm, 1990, 1999). Asidefrom early Paleozoic subsidence in the Michigan basin,the mid-continent region has been relatively free oftectonic activity since the Precambrian (Howell andvan der Pluijm, 1990). Consequently, opening-modefractures (joints) are one of the few structural featurespresent in this part of the continent. Relatively unde-formed sedimentary rocks (i.e., neither faulted norfolded), such as those at Door County, may developopening-mode fractures due to regional extension,thermoelastic contraction, and/or unloading associatedwith uplift and erosion (e.g., Price, 1966; Voight and

St. Pierre, 1974; Lajtai, 1977; Narr and Currie, 1982;Lacazette and Engelder, 1992) and/or increased porefluid pressure at depth (e.g., Secor, 1967; Ladiera andPrice, 1981; Magara, 1981; Engelder, 1985; Lorenz etal., 1991).

Stratigraphy

Chamberlain (1877) first mapped and subdivided theSilurian strata of the Door Peninsula into stratigraphicunits (Figure 2), and, later, Waldhuetter (1994),Harrisand Waldhuetter (1996), Hegrenes (1996), and Wat-kins and Kuglitsch (1997) provided a sequence strati-graphic framework. Geophysical logs from 19 wellsand core descriptions provided regional subsurface cor-relation of stratigraphic units (Gianniny et al., 1996).

Silurian lithologies of the Door Peninsula aregrouped into one of three facies associations: inner, in-ner-middle, and middle shelf facies association (Simoet al., 1998). The Mayville Dolomite, Manistique For-mation (Cordell and Schoolcraft members), and En-gadine Dolomite mostly contain middle shelf faciesassociations (Figure 2). The Byron Dolomite is char-acterized by inner shelf facies association, and theHen-dricks Dolomite corresponds to alternating inner-mid-dle and inner shelf facies associations (Figure 2).Overall, the stratigraphic succession shows a shallow-ing from the Mayville to the Byron followed by a deep-ening through the Engadine.

The inner shelf facies association is interpreted ashaving been deposited in a shallow, restricted-marine,low-energy, tidal-flat environment. Subaerial exposure


Figure 3. Fracture termination at the top of a shallowing-up-ward cycle boundary in the inner shelf facies association. Sheetcracks below the cycle boundary are indicative of a supratidalsetting. The intraclastic conglomerate above the cycle boundarywas deposited in a deeper environment. Staining along the frac-ture indicates fluid flow through this fracture network that mayhave been enhanced by blasting of the outcrop.

surfaces, some with decimeter-scale depositional relief,are common and bound thin (�0.3–0.9 m [1–3 ft])depositional cycles. Complete cycles contain a lowerpart characterized by bioturbated, fenestral mudstone-packstone with intraclasts. The upper part of a typicalcycle consists of domal stromatolites or peloidal-ostra-cod mudstone-packstone at the base and mudcracked,thin and crinkly laminites at the top of the cycle. Cycletops are affected by intense diagenesis, are very wellcemented and massive, and contain occasional micro-karst features (Figure 3). Cycle boundaries separate thevery well cemented laminite/diagenetic cap and theoverlying, less-cemented fenestral mudstone-pack-stone (Figure 3). At these contacts, thin and discontin-uous organic-rich mudstones may occur. All the li-thologies in the inner shelf facies association aredolomitized by fine-crystalline, micritic dolomite.

The inner-middle shelf facies association is inter-preted to represent slightly deeper depositional con-ditions and is a transition between inner and middleshelf deposition. This facies association predominantlyconsists of thin-bedded, fine-crystalline, peloidal-skel-etal rocks and mat- and fenestral-laminated mudstone-packstones. These two lithologies alternate and definemedium-bedded depositional cycles. Organic-richlaminae at cycle boundaries are less common than inthe inner shelf facies association.

The middle shelf facies association consists ofcoarse-crystalline, bioturbated and massive skeletal(brachiopods, corals, and stromatoporoids) wacke-

stone and bioturbated cherty mudstone-wackestones.Bedding planes are discontinuous, and organic-richlaminae are not present. Depositional cycles are thicklybedded (�5 m [16 ft]) (Waldhuetter, 1994) and de-fined by an upward decrease in mud and an increase ingrain size (Hegrenes, 1996).

Fractures

Fracture orientations in the Door Peninsula resemblethose in other parts of the Michigan basin (Holst andFoote, 1981; Holst, 1982; La Pointe and Hudson,1985; Roffers, 1996). These fracture orientations arelikely controlled by the present-day stress field (�50�)(Haimson, 1978) or past stress fields associated withthe Appalachian and Ouachita orogenies (134� and001�, respectively) (Craddock and van der Pluijm,1989). Roffers’s (1996) multiscale analysis identifiedfour major fracture sets (069�, 152�, 046�, and 135�)and four minor fracture sets (088�, 165�, 030�, and118�) in Door County. These fracture orientations areconsistent at different scales (from outcrop to linea-ment scale) and in different facies associations (Roffers,1996). Our fracture mapping at a quarry in DoorCounty indicated dominant fracture orientations of040� and 160�, which are consistent with an indepen-dent investigation of the same quarry by Rock ProductsConsultants (1999). Joint surface textures, includinghackle marks and fringe joints, observed along manyfracture surfaces demonstrate that the fractures inves-tigated in our study are joints, which form by opening-mode failure of the rock (e.g., Pollard and Aydin,1988). For consistency with the hydrogeologic litera-ture of the region, we refer to these features as frac-tures in this article.

METHODS

Mapping methods are used to describe the fracturepattern and density within stratigraphic layers of theSilurian dolomite, and in-situ testing is used to deter-mine relative dolomite stiffness. The mapped fracturepatterns are then used to infer the mechanical stratig-raphy of the Silurian sequence in Door County,whereas variations in rock stiffness are used to assesslithologic contrasts as factors in fracture termination.

Vertical fractures were mapped along quarry wallsexposing different facies associations (see Figures 4C,5C). The orientation of the quarry walls is controlledby the dominant fracture sets (040� and 160�) so that

126VerticalFracture

Patternsin

SilurianDolom

ite

Figure 4. (A) Sedimentary stratigraphy developed from core and outcrop observations of Simo et al. (1998) and Harris and Waldhuetter (1996); (B) mechanical stratigraphy;and (C) fracture map for the lower quarry exposure. Whereas the horizontal axis of the stratigraphic section (A) describes the texture of the facies association, the horizontal axisof the mechanical stratigraphic section (B) shows the fracture density of the mechanical unit. Dark-gray layers represent inner shelf facies associations, whereas lighter gray layersrepresent inner-middle/middle shelf facies associations. Abbreviations for mechanical interfaces: C � cycle boundaries; IC � intracycle boundaries; ORG � organic horizons;MUD � mud horizons; * � no stratigraphic equivalent. Dashed lines indicate a major scour surface; irregular circles are weathered stromatoporoids.

Underwoodetal.

127

Figure 5. (A) Sedimentary stratigraphy, developed from core and outcrop observations of Simo et al. (1998) and Harris and Waldhuetter (1996); (B) mechanical stratigraphy;and (C) fracture map for the upper quarry exposure. Dark-gray layers represent inner shelf facies associations, whereas lighter gray layers represent inner-middle/middle shelffacies associations. Abbreviations for mechanical interfaces: C � cycle boundaries; IC � intracycle boundaries; ORG � organic horizons; MUD � mud horizons; * � nostratigraphic equivalent.


Figure 6. Photo/fracture map overlay for lower quarry exposure, accompanied by stratigraphic section (stratigraphy from Harrisand Waldhuetter [1996] and Simo et al. [1998]). See Figure 8 for key to symbols. Refer to Figure 4 for inferred mechanical stratigraphy.

walls along one fracture set expose the other set offractures. For our study, we mapped in detail the frac-ture set trending 040�; enlarged photographs of theoutcrop (at a scale of 1 cm � 0.3 m) were used to aidthe fracture-mapping process (see Figures 6, 7, 8).Comparison of fractures on differently oriented quarrywalls, which expose the same strata, reveal little dif-ference in fracture density and termination character-istics between the two dominant fracture sets (Under-wood, 1999). Along both of these quarry walls, verticalfractures abut the same stratigraphic horizons (Under-wood, 1999). The close correlation of fracture patternbetween these two sets suggests that each fracture setdeveloped similarly within each stratigraphic level ofthe Silurian dolomite.

Fracture density is a function of mechanical unitthickness (e.g., Huang and Angelier, 1989) and rockstiffness (e.g., Gross et al., 1995). The in-situ stiffnessof stratigraphic units was measured using a SchmidtHammer, a portable device that measures the reboundof a hammer impacting the rock (e.g., Poole and

Farmer, 1980). The error in the stiffness values ob-tained from the Schmidt Hammer can be evaluatedfrom the range in multiple readings at the same locality(Poole and Farmer, 1980). For the purpose of this ar-ticle, the Schmidt Hammer results are not intended toindicate absolute stiffness values; instead, we use theresults to determine the relative stiffness of each faciesassociation within the Silurian dolomite. These resultsare then used to assess the influence of rock stiffnesson observed fracture pattern.

Identification of Mechanical Interfaces

We use two methods to infer the location of mechan-ical interfaces. The first method employs visual iden-tification of mechanical interfaces in the field wherenumerous vertical fractures abut distinct stratigraphichorizons (Figures 4C, 5C). Figure 3 shows an exampleof the fracture terminations used to visually identifymechanical interface locations in the field. Thismethod, however, may involve visual bias, because the


Figure 7. Photo/fracture map overlay for upper quarry exposure, accompanied by stratigraphic section (stratigraphy from Harrisand Waldhuetter [1996] and Simo et al. [1998]). See Figure 8 for key to symbols. Refer to Figure 5 for inferred mechanical stratigraphy.

mapper’s eye may be drawn to visually distinct hori-zons such as those with color contrasts or highlyweath-ered horizons. Such visual bias may overemphasize vi-sually distinctive horizons or neglect indistinct butsignificant horizons.

To minimize visual bias, we developed a secondquantitative method to identify mechanical interfacesthat examines both the percentage of fracture termi-nations and the number of fractures that terminate atsuccessive stratigraphic horizons. With this method, astratigraphic horizon is considered to act as a mechan-ical interface only if both (1) a small percentage of frac-tures propagate through the horizon and (2) a suffi-cient number of fractures terminate at the horizon.The amount of visual bias involved in mapping inter-faces in the field can be determined by comparing thequantitatively identified interface distribution withqualitatively mapped interfaces. To our knowledge,ours is the first study to assess visual bias in character-izing mechanical stratigraphy and the first to propose

an objective methodology for evaluating mechanicalstratigraphy from mapped fracture patterns.

To quantitatively establish the locations of me-chanical interfaces within the stratigraphic sequence,fracture maps are digitized, and we count the numberof fracture tips (i.e., fracture terminations) within suc-cessive sampling intervals, as illustrated in Figure 9.Sample intervals containing a high number of fracturetips are likely to contain a mechanical interface thatlimits vertical propagation of fractures. This analysis offracture pattern is sensitive to the thickness of the sam-pling interval (Figure 9). In the presence of undulatingstratigraphic horizons, a thin sampling interval may re-sult in fracture tips along one horizon counted withintwo adjacent intervals; this yields two interfaces whereonly one exists (Figure 9). In contrast, a thick samplinginterval may group more than one horizon into a singleinterval; this yields one interface where more than oneexists (Figure 9). Within the Silurian section, the min-imum distance between two stratigraphic horizons is


Figure 8. Key to stratigraphic sections. Stratigraphic symbolsand nomenclature from Harris and Waldhuetter (1996) andSimo et al. (1998).

about 10 cm (3.9 in.), whereas typical surface undu-lations are less than 10 cm (3.9 in.). Consequently, asampling interval thickness of 10 cm (3.9 in.) generallyprevents the grouping of two adjacent interfaces andthe splitting of a single undulating interface. Highlyundulating surfaces require additional consideration inthis analysis. This evaluation is stochastic because thenumber of fracture tips that fall within each sampleinterval may vary with position of the initial interval;decreasing sample interval thickness minimizes thisvariation.

In order for a stratigraphic interval to contain amechanical interface, we require that the majority ofthe fractures that intersect the interval terminatewithin the interval rather than propagate through theinterval:

No. of Terminations

No. of Terminations � No. of Crossings� 100% � 50% (1)

The majority criterion, on its own, is not robustunless we also observe a significant number of fractureterminations. For example, if only 3 fractures intersecta horizon along 13 m (43 ft) of exposure and 2 of the3 fractures terminate at the horizon, the resulting per-cent termination is 66%. However, in the absence ofunits with anomalously low fracture density, this is nota significant horizon, because of the low number offractures that intersect the horizon. We determine thecritical number of fracture tips required for a sampleinterval to contain a mechanical interface by examiningthe frequency of fracture tips counted within each 10cm (3.9 in.) sampling interval in our study area (Figure10).

The nearly horizontal part of the data trend in Fig-ure 10 indicates relatively infrequent stratigraphic ho-rizons that contain many fracture tips, whereas the lin-early sloping data trend indicates frequent horizonsthat contain fewer fracture tips. We interpret the hor-izontal data trend (Figure 10) to represent fracture ter-mination at mechanical interfaces, whereas the slopingdata trend represents relatively random termination offractures within mechanical units (i.e., fracture termi-nation is not constrained by sedimentary stratigraphy).It follows that the cutoff between these two data trendsis the critical number of fractures within this outcroprequired for an interval to contain a mechanicalinterface.

The placement of the frequency curve in Figure10, and consequently the cutoff between stratigraphi-cally controlled and random fracture terminations, var-ies with length of the mapped interval because longerexposures have more numerous fractures than shorterexposures. Therefore, the cutoff that we estimate, 15,is relevant for the 13 m (43 ft) of available exposuremapped in our study. Because the fracture density ofmost mapped layers in our study is approximately 1.5fractures/m, an average layer exposes about 20 frac-tures, an adequate population size for assessing the per-centage of fracture termination. This also suggests thatthe termination of 15 fractures within an average in-terval (of �20 fractures) reflects the influence of stra-tigraphy on fracture termination.

If the cutoff value is too high (e.g., 20 fractures),this method may underestimate the number of me-chanical interfaces. Similarly, a cutoff value that is toolow (e.g., 10 fractures) may overestimate the numberof mechanical interfaces. To be conservative, a lowercutoff should be used, because potential interfacesmust also pass the majority termination criterion.Among all the horizons in our study area that termi-


5 cm Intervals

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BIN SIZE OUTCROP FRACTURE PATTERN STATISTICALLY DETERMINEDINTERFACES(A)

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Figure 9. The samplingmethod used to quantitativelyidentify mechanical interfaces(from digitized fracture pat-terns) counts the number offracture tips within each strati-graphic interval. (A) In the pres-ence of undulating stratigraphichorizons, a thin sampling inter-val may result in fracture tipsalong one horizon countedwithin two adjacent intervals;this yields two interfaces whereonly one exists. In contrast, athick sampling interval maygroup more than one horizoninto a single interval; this yieldsone interface where more thanone exists. (B) The optimum in-terval size correctly samples thenumber of fracture terminationsat one interface.

(B)(A)

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Figure 10. (A) The frequency of fracture tips within samplingintervals provides a method to determine which stratigraphichorizons have enough fracture tips to be considered mechanicalinterfaces. Many sample intervals contain less than 15 fracturetips, suggesting that fracture termination within these intervalsis sparse because of relatively random fracture terminationwithin mechanical units. Where fracture termination is strati-graphically controlled, the number of fracture tips within oneinterval should be greater than 15. (B) Determination of thenumber of fracture terminations at a stratigraphic horizon.

nate more than 15 fractures, only five do not pass themajority test for fracture intersection (Figure 11). A 10cm (3.9 in.)–thick sample interval could mislocate in-terfaces by up to 5 cm (2.0 in.); however, this relativelysmall error does not greatly influence the distributionof mechanical interfaces.

FRACTURE PATTERN AND MECHANICALSTRATIGRAPHY

In the outcrops studied, all fractures are vertical andperpendicular to bedding so that fracture length de-scribes the vertical trace length observed on quarrywalls. Several generalizations can be drawn from frac-ture maps in quarries representative of different faciesassociations within the Silurian dolomite. Fractures inthe thinly bedded inner shelf facies association (Figure4) are generally evenly distributed, densely spaced, andconfined to distinct layers. Fractures in these unitscommonly abut shallowing-upward cycle boundaries,and, in some cases, fractures abut horizons within ashallowing-upward cycle. Organic horizons within thisfacies association appear weak and friable in outcrop,which may suggest that these layers are weak and


Figure 11. (A) Bold lines rep-resent stratigraphic horizonsthat satisfy the mechanical in-terface criterion: greater than15 fracture tips and greaterthan 50% termination within 10cm (3.9 in.) interval spanning13 m (43 ft) horizontal dis-tance. (B) Comparison of visu-ally mapped interfaces (left)with interfaces that meet ourquantitative criterion (right) forthe quarry exposure. (C) Differ-ences between the two meth-ods are highlighted by mis-matches between mapped andstatistically determinedinterfaces.

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(B) (C)Map Stat.


should arrest vertically propagating fractures (Cookeand Underwood, 2001). Although mud horizons donot appear as weak and friable as organic horizons,fractures also commonly abut these types of shallow-ing-upward cycle boundaries.

The fracture pattern differs in the transitional in-ner-middle shelf facies association (Figure 4). Verticalfractures in the inner-middle shelf facies associationterminate both at mud cycle boundaries and at hori-zons within shallowing-upward cycles. The faunal-bearing bases of shallowing-upward cycles in this fa-cies association commonly fracture independentlyfrom the thinner, laminated mudstone top of the shal-lowing-upward cycle; this results in abundant fracturetips within individual shallowing-upward cycles (e.g.,19.5 m in Figure 4). Fracture density within an indi-vidual shallowing-upward cycle is typically higher inthe thinner, mudstone top than in the thicker faunal-bearing base. Although the inner-middle shelf faciesassociation exhibits continuous and distinct bedding,in some cases, fractures span several shallowing-up-ward cycles.

The middle shelf facies association exposed withinthe quarry studied does not exhibit the massive bed-ding (�5 m [16 ft] thickness) documented elsewherein Door County (Waldhuetter, 1994). Whereas thoseexposures display long (up to 8 m [26 ft]) and morewidely spaced (5 to 7 m [16 to 23 ft]) fractures thatmay not be confined to distinct stratigraphic horizons(Underwood, 1999), fractures within the limited ex-posures of the middle facies association of this studyarea are similar to those observed in the inner-middleshelf facies association.

Stiffness Variations among Facies Associations

Our fracture maps of vertical outcrops suggest thatsedimentary stratigraphy controls fracture patterns;fractures are largely contained within distinct strati-graphic units and abut stratigraphic horizons acting asmechanical interfaces (Figures 4, 5). Because eithercontrasts between layer stiffness or stratigraphic hori-zons can control fracture pattern (e.g., Cook and Er-dogan, 1972; Huang and Angelier, 1989), we assessthe variation of stiffness between facies associations ofthe Silurian dolomite by taking in-situ stiffness mea-surements at several locations within each faciesassociation.

The in-situ stiffness tests yield average stiffness of57.2 � 5, 52.8 � 5, and 60.9 � 5 GPa for inner, inner-middle, and middle shelf facies associations, respec-

tively. The stiffness variation between facies associa-tions throughout the Silurian does not exceed the errorof this testing method. We suspect that dolomitizationmay have contributed to present-day uniform strengthproperties and that fracturing likely occurred after do-lomitization. Because stiffness changes are minimalthroughout the Silurian dolomite, fracture terminationis unlikely the result of material property differencesbetween mechanical units, such as grain-size differ-ences or cementation variations. Consequently, thetermination of vertical fractures is likely controlled bythe nature and distribution of stratigraphic horizonsthat act as weak mechanical interfaces.

Identification of Mechanical Interfaces

Interfaces inferred in the field are compared to quan-titatively identified interface locations to assess visualbias. In general, interface locations determined fromour quantitative method correspond well to thosequalitatively assessed from fracture maps (Figure 11),suggesting that little visual bias occurred during themapping process. Only one subtle interface that passedthe quantitative criterion was missed in the visual iden-tification (at 9.3 m in Figures 4, 11). Additionally, onlyone visually distinct mechanical interface delineatedduring fracture mapping in the field does not pass thequantitative definition of a mechanical interface (at12.65 m in Figure 11). Interestingly, the visual iden-tification approach was better suited for areas withhighly undulating stratigraphic horizons or areas wherethe photographs used to aid in fracture mapping de-veloped vertical distortion. The quantitative methodfailed to identify several horizons with greater than 10cm (3.9 in.) undulations, such as the prominent ex-posure surface at 4.35 m (Figures 4, 11) and an inter-face at 7.8 m (Figures 4, 11). Because the photographsof regions high along the quarry walls (�20 m [66 ft])developed vertical distortion, some apparent interfaceundulations are greater than the 10 cm (3.9 in.) sam-pling interval in the upper part of the mapped intervalin Figure 5. Results from the two methods are mergedby modifying the distribution of mechanical interfacesmapped in the field so that each interface conforms tothe new quantitative definition with special consider-ation for undulating surfaces.

The close correlation between the visually andquantitatively identified nonundulating mechanical in-terfaces (Figure 11) suggests that the 15 fracture ter-mination cutoff used to delineate the presence of a me-chanical interface within a sample interval (Figure 10)


does not greatly over- or underestimate mechanical in-terfaces. Although the two methods of identifying me-chanical interfaces produced similar results, the appli-cation of quantitative criteria adds rigor to the analysisbecause we require that all interfaces pass the sameobjective definition of a mechanical interface.

Mechanical Interface Classification

Mapping mechanical interface distribution allows us todevelop a mechanical stratigraphic section for mappedintervals (e.g., Figures 4B, 5B). We identify two groupsof horizons that act as mechanical interfaces in the Si-lurian dolomite of Door County (cycle and intracycleinterfaces). Cycle interfaces occur at the top of shal-lowing-upward cycles, whereas intracycle interfacesoccur within an individual shallowing-upward cycle.Each group of interfaces includes distinct subcategoriesbased on characteristics of stratigraphic horizons.

Cycle interfaces are most abundant in sections ofthe Silurian dolomite consisting of thinly bedded innerand inner-middle shelf facies associations. The shallow-ing-upward cycles may be separated by thin, weak de-posits such as organic partings and mud layers thatterminate fractures to differing degrees. Two subcate-gories of cycle-bounding interfaces were observed: or-ganic partings and thin mud layers.

Organic cycle interfaces are generally character-ized by the presence of brown, thinly laminated or-ganic material; thickness generally ranges from 0 to 1cm (0 to 0.4 in.) along any one interface. In outcrop,the organic interface is very friable, poorly cemented,and commonly iron stained. Organic cycle interfacesare less abundant than other interface types and areobserved only within the inner shelf facies association(Figure 4).

Mud cycle interfaces range in thickness from lessthan 0.5 to 4 cm (0.2 to 1.6 in.); thickness is relativelyuniform along individual horizons, but larger variationsoccur between horizons. These interfaces are generallyplaty and commonly mudcracked or are associatedwith storm deposits. Mud interfaces associated withstorm deposits commonly undulate with amplitudesranging from 1 to 10 cm (0.4 to 3.9 in.) and are com-monly visually distinct and easily identifiable in thefield.

Intracycle interfaces separate parts of individualshallowing-upward cycles that fracture independentlyof one another. As with cycle interfaces, different typesof intracycle interfaces terminate fractures to differingdegrees. Two subcategories of intracycle interfaces

were observed: thin mud layers and contacts betweenlayers of contrasting lithology.

Mud intracycle interfaces resemble muds of thecycle interface group but are generally thinner andmore planar than cycle muds. Like cycle muds, intra-cycle muds may also exhibit mudcracks or may be as-sociated with storm deposits (e.g., at 6.4 m in Figure4). This interface type is observed in both the innerand inner-middle shelf facies associations.

Lithologic intracycle interfaces typically separatecoarse-grained, faunal-bearing lithologies, which aredeposited in a more open-marine environment, fromfine-grained, thinly laminated lithologies deposited ina more restricted-marine environment. This interfacetype is observed only in the inner-middle shelf faciesassociation (e.g., at 19.8 m in Figure 5).

In places, we identified a mechanical interfacewithin a shallowing-upward cycle that did not correlateto any specific stratigraphic horizon noted in previousstratigraphic studies; we denoted such interfaces by thesymbol IC* on Figures 4 and 5 (e.g., at 5.6 m in Figure4). More detailed stratigraphic description is requiredto classify these interfaces.

Note that although mechanical interfaces correlatewell with sedimentary stratigraphy, not all strati-graphic horizons contribute to fracture pattern. For ex-ample, some fractures propagate across mud horizonsthat, in the field, appear no different from nearby ho-rizons along which the fractures terminate. This sug-gests that visually similar stratigraphic horizons maynot have the same mechanical properties. Laboratorytesting of interface mechanical properties may providefurther insight into stratigraphic controls on fracturetermination; however, such laboratory analysis is be-yond the scope of our study.

Observed Fracture Density

Fracture density within our study area is measured asthe number of vertical fractures per meter along bed-parallel transects across the vertical quarry exposures(approximately 13 m [43 ft] in length). Fracture den-sity is measured in each interpreted mechanical unitwithin the study outcrops. To determine the influenceof mechanical interface distribution on fracture den-sity, we only report the number of fractures that, at aminimum, span the entire thickness of each mechani-cal unit. Fracture terminations within interpreted me-chanical units do not meet our criterion for expressionof a mechanical interface and seem to have a randomdistribution (Figure 10). Furthermore, fractures that


Oversaturated

Under-saturated

Saturated

O+

++ O

O

O OO

+

O

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O

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+

+O

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O

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+ +++

++

+

+

+

+ +

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ctu

re D

en

sity

(#

of fr

act

ure

s/m

ete

r)

Mechanical Unit Thickness (m)

D = 0.8 + 0.29T

+ Inner Shelf Facies

(DT = 1.00)(DT = 1.25)

(DT = 0.83)(best-fit)

O Inner-Middle andMiddle Shelf Facies

-1

Figure 12. Fracture density vs. mechanical unit thickness forunits in the quarry exposures. Fracture density is calculated fromfracture maps (Figures 4, 5). The bold line represents the best-fit line though all of the data. Dashed curves represent densitytimes mechanical unit thickness (DT) of 0.83, 1.00, and 1.25.Bai and Pollard (2000) suggest cutoff values for undersaturation(DT � 0.83) and oversaturation (DT � 1.25) based on layer-parallel stresses between adjacent fractures.

span entire mechanical units may more effectively con-duct fluids than fractures that terminate within units,because they enhance the overall connectivity of thefracture network.

Fracture density in the inner, inner-middle, andmiddle shelf facies associations in the quarry expo-sures decreases with increasing bed thickness but doesnot follow the expected density (D) times thickness(T) equals 1.0 curve based on numerous field obser-vations (e.g., Price, 1966; Hobbs, 1967; McQuillan,1973; Huang and Angelier, 1989; Narr and Suppe,1991; Gross, 1993; Gross et al., 1995; Wu and Pol-lard, 1995; Becker and Gross, 1996; Bai and Pollard,2000) (see Figure 12). If fracture density conforms tothe relationship, DT � 1, then the beds are consid-ered to be fracture-saturated (Bai and Pollard, 2000).However, over- or undersaturation may be the resultof either sequential infilling of fractures in highlystrained beds (e.g., Wu and Pollard, 1995; Becker andGross, 1996) or low levels of tectonic strain, respec-tively. Ladeira and Price (1981) note that thicker bedshave lower than expected fracture density and thatfracture density becomes nearly constant with bedsthicker than 1.5 m (4.9 ft) (Ladeira and Price, 1981)(e.g., Figure 12). As a result, the DT � 1 relationshipmay not be an appropriate method to predict fracture

density in thick (�1.5 to 2.0 m [4.9 to 6.6 ft]) me-chanical units.

Fracture density data (Figure 12) indicate that me-chanical units are generally undersaturated with re-spect to fracturing; this is expected because of the low-strain tectonic environment. As mechanical unitthickness increases, fracturing tends toward oversatur-ation; however, very few data points define this part ofFigure 12. Fractures observed in core were not used inthe density analysis, but these observations also suggestincreased density with thinner beds (Underwood,1999).

Fracture density also has been shown to correlatewith the stiffness of mechanical units (e.g., Huang andAngelier, 1989; Gross, 1993). Although in-situ mea-surements did not detect systematic stiffness differ-ences between facies associations, some variation wasdetected within each facies association. The observedscatter of data in Figure 12 may be due to stiffnessvariation within each facies association, which was notrigorously assessed by our study. Furthermore, littledistinction could be made between the trend of frac-ture density for the inner and inner-middle/middleshelf facies associations.

PREDICT ING MECHANICALSTRATIGRAPHY AND FRACTURE DENSITY

Fracture mapping and analysis indicates that the length(vertically) and density of fractures in the Silurian do-lomite are primarily controlled by the distribution ofmechanically weak interfaces. Therefore, determiningthe distribution of these interfaces is a requirement forpredicting fracture patterns at depth. If the distributionof subsurface mechanical interfaces can be determined(i.e., using sedimentary stratigraphy from rock core),fracture patterns at depth may be inferred by relation-ships developed from outcrop observations. To testthis methodology, we develop empirical relationshipsbetween sedimentary stratigraphy and mechanicalstratigraphy, which we use to predict the distributionof mechanical interfaces and subsequent fracturepatterns. In this section, we establish empirical rela-tionships between sedimentary and mechanical stratig-raphy based on field observations. In the next section,we use these empirical relations to stochastically pre-dict mechanical stratigraphy and compare one sto-chastic realization to the mechanical stratigraphy in-ferred from outcrop fracture pattern to assess theerrors in this methodology. Then we use quantitative


Mismatch

7 21

% ERROR =# Mismatch

Total # of Interfaces= 70%

Mech. Stratig.

MECHANICALINTERFACES

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rry

Hei

ght (

m)

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(A) (B)

0

5

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25

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Mech. Stratig.

Figure 13. (A) Comparison of interpreted mechanical inter-face distribution (left) with all noted sedimentary stratigraphichorizons (right) within the quarry exposures. Mechanical inter-faces are identified from both visual inspection and from ourquantitative criterion. (B) Not all stratigraphic horizons act asmechanical interfaces. Some mechanical interfaces occur whereno sedimentary stratigraphic horizons had been noted. Abbre-viations for mechanical interfaces: C � cycle boundaries; IC �intracycle boundaries; ORG � organic horizons; MUD � mudhorizons; LTH � lithologic contact.

C-ORG C-MUD IC-MUD IC-LTH0.0

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Inner-Middle/Middle Shelf

Pro

babi

lity

No

t P

rese

nt

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t P

rese

nt

No

t P

rese

nt

Figure 14. Probability of a stratigraphic horizon acting as amechanical interface. Probability for each horizon is calculatedas the number of stratigraphic horizons in the study outcropsthat act as mechanical interfaces divided by the total numberof that stratigraphic horizon type. Abbreviations for mechanicalinterfaces: C � cycle boundaries; IC � intracycle boundaries;ORG � organic horizons; MUD � mud horizons; LTH � lith-ologic contact.

relationships between mechanical stratigraphy andfracture density to predict fracture pattern.

The quantitative relationships between sedimen-tary and mechanical stratigraphy are derived by com-paring characterizations of sedimentary stratigraphy

and mechanical stratigraphy determined from outcropobservation (Figure 13). This comparison reveals thatnot all stratigraphic horizons effectively terminate frac-tures (Figure 13). If we assume that each stratigraphichorizon acts as a mechanical interface (i.e., each rec-ognized horizon is abutted by many fractures), wewould predict many more closely spaced mechanicalinterfaces (Figure 13). This would yield shorter andmore densely spaced fractures than those observed andmapped (Figures 4, 5). Because this method greatlyoverpredicts the distribution of mechanical interfaces,sedimentary stratigraphy should not be directly usedto determine fracture patterns. Instead, statistically de-veloped empirical relations can guide prediction ofme-chanical stratigraphy from sedimentary stratigraphy.

We evaluate the probability that each type ofstratigraphic horizon acts as a mechanical interface(Figure 14). In addition to investigating the types ofstratigraphic horizons, we assess whether facies asso-ciation influences the degree of fracture termination atthe stratigraphic horizon. Within the inner shelf andinner-middle/middle shelf facies associations, shallow-ing-upward cycle boundaries, both mud and organic,commonly act as mechanical interfaces, whereas intra-cycle mud horizons are less effective (Figure 14). Be-


Fre

quen

cy

% Error

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lity

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30.0%25.0%20.0%15.0%0.00

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Figure 15. The average percent error for 50 realizations is 23� 4%. The probability of encountering a given error value iscomputed by dividing the error frequency (left vertical axis) bythe total number of realizations used in the analysis (50). Theprobability of extreme minimum and maximum error of 13 and33%, respectively, is only 0.02. We are 96% certain that thepercent error in any model run will fall within the range of 13–33%; this certainty is based on integrating the area under theprobability curve.

cause the middle shelf facies association is not abun-dantly exposed within the quarry exposures used forour study, our statistical analyses group middle shelfand inner-middle shelf facies associations to createlarger sample populations. Intracycle horizons be-tween contrasting lithologies occur mostly within theinner-middle/middle shelf facies associations and ar-rest fractures as effectively as cycle-bounding muds inboth facies associations (Figure 14).

We use the probabilities developed for each typeof mechanical interface in each facies association tostochastically predict the distribution of mechanical in-terfaces from only descriptions of sedimentary stratig-raphy. To illustrate our predictive method, a cycle-bounding mud horizon within the inner-middle/middle shelf facies associations has a 63% chance ofacting as a mechanical interface that effectively ter-minates fractures. Among all of the observed strati-graphic horizons that are cycle-bounding mud layers,only 63% are randomly chosen to act as mechanicalinterfaces (Figure 14). This process is repeated for eachtype of mechanical interface.

Some intracycle interfaces do not correlate to spe-cific stratigraphic features. Because there is no corre-lation with sedimentary stratigraphy, the location ofthese interfaces can not be predicted using the ap-proach outlined in the preceding paragraph. For thepurpose of testing our model predictions against inter-preted mechanical interfaces, those interfaces that donot correlate to distinct stratigraphic horizons are notconsidered. Because these horizons are relatively infre-quent (Figures 4, 5), the mislocation of these mechan-ical interfaces does not greatly influence the overallpredicted fracture pattern.

Testing Mechanical Stratigraphy Predictions

We test ourmethod for predictingmechanical interfacedistribution by comparing the predictions, based onsedimentary stratigraphy mapped in the field (Wald-huetter, 1994; Simo et al., 1998), to the mechanicalstratigraphy inferred from the mapped fracture patternof the same stratigraphic interval. By testing our pre-dictive tool on the same stratigraphic section that wasused to develop the empirical relationships, we can as-sess the error in predicted fracture pattern. This predic-tive model is stochastic because each realization, basedon random assignment of mechanical interfaces, canproduce different interface distributions.

To assess the error of our model predictions, werun a Monte Carlo simulation using 50 realizations

(e.g., Harbaugh et al., 1977). This predictive methodhas a 0.32 probability of having the average errorwithin the 50 model realizations (23 � 4% in Figure15). Although significant error (13–33%) occurs in pre-dicting the exact location of mechanical interfaces, anexample realization demonstrates important similari-ties between predicted and fracture-inferred me-chanical stratigraphy (Figure 16). Correlation betweeninterpreted and predicted mechanical interface distri-bution is best for the lower part of the quarry exposurewhere the dominant interface types are mud andorganic, which have higher probabilities of acting asmechanical interfaces (Figures 14, 16). The degree ofcorrelation decreases higher in the quarry exposurewhere intracycle interfaces, which have lower proba-bilities of acting as mechanical interfaces, are moreprevalent (Figures 14, 16). Overall, the empiricallypredicted mechanical interface distribution equally ov-erpredicts and underpredicts the location of mechani-cal interfaces (Figure 16). The error of our stochasticmethod for predicting mechanical stratigraphy fromsedimentary stratigraphy is less than the error incurredif we assume that every stratigraphic horizon acts as amechanical interface (25% � 70%) (see Figures 13,16).


Qua

rry

Hei

ght (

m)

Mismatch

Total # ofMismatch

10 10

% ERROR =# Predicted Mismatch

Total # of Interfaces

= 25%

Interpreted Predicted

Total # ofInterfaces = 40

(A)(B)

MECHANICALINTERFACES

C-ORGC-MUDIC-MUDIC-LTH

0

5

10

15

20

25

30

IC* = no stratigraphicequivalent

}

}

}

Interpreted Predicted

Figure 16. (A) One realization of predicted mechanical stra-tigraphy (right) vs. interpreted mechanical interface distribution(left) for the quarry exposures. (B) The percent error of 25% isevaluated from mismatches between predicted and interpretedmechanical interface distribution. Abbreviations for mechanicalinterfaces: C � cycle boundaries; IC � intracycle boundaries;ORG � organic horizons; MUD � mud horizons; LTH � lith-ologic contact. Interfaces with no stratigraphic correlation arenot included in this analysis.

Testing Fracture Density Predictions

Once the distribution of mechanical interfaces is pre-dicted, fracture density can be estimated from me-chanical unit thickness, defined as the distance be-tween mechanical interfaces. We use a best-fitlinear-inverse function through the density-thicknessdata collected at the study site (bold curve in Figure

12; D � 0.8 � 0.29/T) to predict fracture density.This function is similar in form to the DT � 1 rela-tionship described by Bai and Pollard (2000) and com-monly observed in outcrop (e.g., Huang and Angelier,1989).

A comparison between the predicted and inter-preted fracture density is provided in Figure 17. Gen-erally, the predicted fracture density exceeds observeddensity within beds thinner than about 0.3 m (12 in.)(Figure 17). This is a consequence of the overestima-tion of fracture density in thin beds by the best-fit lin-ear-inverse function (Figure 12). Within the lowerquarry section, clusters of high- and moderate-densitybeds were observed, whereas the stochastic realizationpredicts less clustering of high-density beds and somealternating high- and moderate-density beds. Withinthe upper section, both interpreted and predicted se-quences have clusters of high-fracture-density beds.Furthermore, both sections have repeated sequences ofdecreasing fracture density upsection (�22 and �26 min Figure 17).

This predictive realization does not accurately re-produce the distribution of fracture density every-where in the sequence; however, the correlation is bet-ter than a prediction of fracture density based solelyon stratigraphic unit thickness that does not considermechanical units. Because a mechanical unit may con-sist of one or more stratigraphic units, the thinner unitspredicted by stratigraphic inference of mechanical stra-tigraphy (e.g., Figure 13) would yield much greaterfracture density throughout the sequence.

The method used in our study of identifying andusing empirical relationships between fracture patternand stratigraphy to predict fracture pattern capturessome of the overall trends in observed fracture pattern.For example, variations in predicted fracture densitywithin the upper section on Figure 17 closely matchinterpreted variations. Because our method reasonablypredicts the mechanical stratigraphy and first-orderfracture density for the mapped intervals, this predic-tive method provides valuable inferences regardingfracture pattern at depth using detailed stratigraphicdescriptions of available core. This method may alsoprovide a useful tool in predicting fracture pattern insimilar stratigraphic environments and a wide range oftectonic environments.

IMPLICATIONS FOR FLUID FLOW

Because many carbonate reservoirs are fractured, pre-diction of flow characteristics requires an understand-


0

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PREDICTED FRACTUREDENSITY

Fracture Density(# of fractures/meter)

Fracture Density(# fractures/meter)

>1.5

1.0 - 1.5

<1.0

Figure 17. Interpreted andpredicted fracture density forthe quarry exposure. Mechani-cal interfaces in the predictedsequence represent the samerealization shown in Figure 16.Fracture density predictions useempirical relationships with me-chanical unit thickness (Figure12). Gray shading indicatesrelative fracture density of units.

ing of the surface and subsurface fracture pattern. De-veloping a method for predicting vertical fracturepatterns at depth is an important step toward charac-terizing flow processes. In our case study, the predic-tive model could allow us to compare expected frac-ture patterns with hydrogeologic data for thecorresponding depth interval. Additionally, predicted

fracture density could provide storage estimates for theaquifer or reservoir.

The positions of horizontal high-flow features inDoor County generally correlate with changes in sed-imentary stratigraphy, such as cycle boundaries orother lithologic changes (Sherrill, 1978; Bradbury andMuldoon, 1992; Gianniny et al., 1996; Muldoon et al.,


2001). Variations in vertical fracture patternsmay con-tribute to the development of these hydrogeologic fea-tures. For example, horizontal high-flow features maydevelop at mechanical interfaces where abundant ver-tical fractures terminate. The termination of many ver-tical fractures at a stratigraphic horizon could redirectvertical flow horizontally along the bedding interface(Figure 1). In addition, a decrease in fracture densitybelow an interface reduces the number of vertical flowpaths and can increase the tortuosity of vertical flowpaths; both effects impede vertical flow and may pro-mote horizontal flow. Within carbonate strata, such asthe Silurian dolomite, increased groundwater flow en-hances dissolution and enlarges flow features such asbedding planes. Continued dissolution may promotethe development of regionally extensive high-perme-ability features that are observed throughout DoorCounty (Muldoon et al., 2001).

Using mechanical stratigraphy to better under-stand fracture patterns is important not only in aquifercharacterization but also in petroleum reservoir stud-ies. Recent work on the Austin Chalk in Texas (Cor-bett et al., 1987; Rijken and Cooke, 2001) and theLisburne carbonate group in Alaska (Hanks et al.,1997) has emphasized the importance of mechanicalstratigraphy in understanding and predicting fracturepatterns in petroleum reservoirs.

CONCLUSIONS

Our study introduces an innovative technique to quan-titatively identify mechanical interfaces from fracturepatterns. The identification of mechanical interfacesthrough such quantitative means can minimize the vi-sual bias involved in conventional identification. Strati-graphic horizons that both have a majority of abuttingfractures and exceed a cutoff number of abutting frac-tures are considered to act as mechanical interfaces.However, this method is sensitive to undulation of sur-faces and underidentifies mechanical interfaces wherestratigraphic horizons undulate excessively. Visual es-timates of mechanical stratigraphy performed in thefield compare well with the quantitatively determinedmechanical stratigraphy, indicating that our estima-tions incurred little visual bias.

Through correlation of mapped vertical opening-mode fractures with sedimentary stratigraphy, we haveidentified several stratigraphic controls on fracture pat-terns within two exposed intervals of the Silurian do-lomite in Door County, Wisconsin. First, mechanical

interfaces correspond to many, but not all, distinctstratigraphic horizons (Figures 4, 5). Consequently,predictions of mechanical stratigraphy should not useeach observed stratigraphic horizon. Second, the typeof stratigraphic horizon is a greater factor in the ter-mination of fractures than the facies association (Figure14). Cycle-bounding organic partings and mud hori-zons are more effective at terminating fractures thanintracycle mud horizons or horizons between contrast-ing lithologies.

The probability of a stratigraphic horizon acting asa mechanical interface can be used to stochasticallypredict mechanical stratigraphy from sedimentary stra-tigraphy. Because all stratigraphic horizons do not actas mechanical interfaces, interface locations are chosenstochastically, based on the empirically developed re-lationships for each interface type. A Monte Carloanalysis indicates that this predictive method yieldsmuch lower error than that incurred by using everydistinct stratigraphic horizon as a mechanical interface(Figure 13 vs. Figure 16). Once the distribution of me-chanical interfaces is developed, we can predict frac-ture density from mechanical unit thickness. The bestlinear-inverse fit between the fracture density and me-chanical unit thickness of the outcrops studied pro-duces fracture pattern similar to the interpreted distri-bution (Figure 17).

The methods presented in this article allow theprediction of opening-mode fracture patterns usingonly sedimentary stratigraphic data. This is of partic-ular interest where dealing with unexposed parts of astratigraphic sequence. This study provides the foun-dation for groundwater and hydrocarbon flow studiesthat use fracture data, such as fracture density andlength, as input parameters into flow models. Flowmodels that incorporate vertical fracture data based onthe stratigraphic controls on fracturing within an aqui-fer/reservoir are likely to better represent flowconditions.

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stratigraphic controls on vertical fracture patterns in ...rocks, relationship between stratigraphy...

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