The evolution of the damage zone with fault growth in sandstone and

its multiscale characteristics

Ghislain de Joussineau1,2 and Atilla Aydin1

Received 22 August 2006; revised 4 July 2007; accepted 31 July 2007; published 6 December 2007.

[1] We document the formation and evolution of the damage zones associated with strike-slip faults in porous sandstone, through detailed field and statistical studies of faults ofincreasing slip magnitudes. The faults initiate as sheared joints with discontinuous damagezone located primarily at fault tips and fault surface irregularities. With increasing slip, thedamage zone develops by progressive fracture infilling and is organized into twocomponents with different characteristics. The first of these components is the innerdamage zone flanking the fault core with a high fracture frequency and a thickness scalingwith fault slip. It contributes to the progressive widening of the fault core withincreasing deformation. The second of these components is the outer damage zone with alarger and more variable thickness and a lower fracture frequency than the inner zone.The origin and evolution of the inner and outer damage zones are closely related to thehistory of fault development, as presented in a new conceptual model for damagezone evolution with fault growth. The statistical properties of the fault networks,determined by scan line surveys, evolve with fault growth. This is attributed to theprogressive saturation of the fault networks. Well-developed fault networks havemultifractal properties with important consequences in forecasting and characterizingfaults from limited data sets. The conceptual model and statistical data presented heremay be used as predictive tools to better estimate the geometrical and statistical propertiesof the damage zones associated with large faults with remotely resolvable slip magnitudein the subsurface.

Citation: de Joussineau, G., and A. Aydin (2007), The evolution of the damage zone with fault growth in sandstone and its multiscale

characteristics, J. Geophys. Res., 112, B12401, doi:10.1029/2006JB004711.

1. Introduction

[2] Faults may impede or enhance fluid flow in thesubsurface, and therefore affect the formation and distribu-tion of mineral deposits [Sibson, 1987], hydrocarbon mi-gration and entrapment [Aydin, 2000] and the movement ofcontaminants [National Research Council, 1996]. Faultstypically have a low-permeability core surrounded by ahigh-permeability damage zone [Caine et al., 1996; Jourdeet al., 2002]. The geometry, petrophysical properties andcontinuity of both the fault core and the damage zone havean important influence on subsurface fluid flow [Odling etal., 2004] and on the mechanical properties of the faultsystems, themselves [Lyakhovsky et al., 1997]. However,many of these faults and their components are not detectableby seismic methods which can typically resolve large faultswith a minimum throw of about 20–50 m, but only as lineelements. In other words, the best that remotely appliedgeophysical methods can do is to indicate the presence ofapproximately plane thin, geometric representations of large

faults and their slip if possible. It is consequently essentialto characterize faults and associated damage zones in fieldanalogues, to establish the geometrical, statistical and pet-rophysical properties of fault zones and to assess theirimpact on fluid flow in the subsurface.[3] The architecture, statistical properties, permeability

and development of fault damage zones have been thesubjects of many studies [McGrath and Davison, 1995;Gudmundsson et al., 2001; Harris et al., 2003; Kim et al.,2003, 2004; Odling et al., 2004; Johansen et al., 2005;Agosta and Aydin, 2006]. It has been proposed that thethickness of damage zones is proportional to the amount offault slip [Scholz, 1987; Evans, 1990; Beach et al., 1999;Fossen and Hesthammer, 2000; Shipton and Cowie, 2001].On the basis of this relationship, a conceptual model for theorigin and development of fault damage zones has beendeveloped for deformation band-type normal faults [Shiptonand Cowie, 2003]. Field and modeling studies have shownthat the largest slip typically occurs at or near the center ofthe fault segments [Walsh and Watterson, 1987, 1988;Peacock and Sanderson, 1991; Cowie and Scholz, 1992;Dawers et al., 1993; Burgmann et al., 1994; Dawers andAnders, 1995; Cartwright et al., 1995; Schlische et al.,1996; Willemse et al., 1996; Gupta and Scholz, 2000; deJoussineau et al., 2001]. If the above assumptionconcerning the relationship between slip magnitude and

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1Rock Fracture Project, Department of Geological and EnvironmentalSciences, Stanford University, Stanford, California, USA.

2Now at Beicip-Franlab, Rueil-Malmaison, France.

Copyright 2007 by the American Geophysical Union.0148-0227/07/2006JB004711$09.00

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damage zone thickness is correct, then it follows that themaximum damage zone thickness should be found in themiddle part of the faults. In apparent contradiction,however, other studies have proposed that the distributionof the damage is controlled by the stress state around faults,with the damage zone being widest in the extensional fieldsnear the fault tips and narrowest in the contractional fieldsnear the center of the faults [Knott et al., 1996; Davatzesand Aydin, 2003]. Clearly, because of the limited under-standing of the wide variety of faulting mechanisms in thecrust, existing conceptual models for damage zones andtheir geometrical and statistical properties, even if adequateto explain particular sets of conditions, are still incomplete.[4] The strike-slip fault networks in the Aztec Sandstone

exposed in the Valley of Fire State Park in SE Nevada(inset, Figure 1) present an excellent opportunity to con-tribute to the understanding of how fault damage zones formand evolve with fault growth. The sequential developmentof the faults by a repeated sheared joint mechanism has beenpreviously described [Myers and Aydin, 2004; Flodin andAydin, 2004a] and a nearly full rock exposure allows thestudy of faults at different stages of their evolution, fromincipient to large faults with several kilometers of offset.[5] In this paper, we present an integrated study combin-

ing field observations and statistical analysis based on scanline surveys, describing the evolution of damage zonesassociated with fault growth. First, we characterize thearchitecture and statistical properties of individual damagezones around faults of increasing slip magnitudes to unravelthe mechanisms involved in the progressive development offault damage zones. We propose a new classification of faultdamage zones into components whose origin is closelyrelated to the fault growth mechanisms. Second, we deter-mine the length and spacing properties of fault networksalong long scan lines that cut across many consecutive faultzones of different slip magnitudes. All of the statistical dataobtained, combined with mechanical concepts developed inthis paper and in earlier studies [Myers and Aydin, 2004;Flodin and Aydin, 2004a], form the basis for a newconceptual model for damage zone evolution associatedwith fault growth. This model illustrates the crucial roleof fault segmentation in the restructuring and evolution ofdamage zones, and it can be used as a predictive tool tobetter estimate the properties of fault networks associatedwith large faults that have resolvable slip magnitude in thesubsurface.

2. Geologic Setting

[6] This study is based on analyses of strike-slip faults inthe Aztec Sandstone exposed in the Valley of Fire StatePark, located approximately 60 miles NE of Las Vegas inSE Nevada (Figure 1, inset). The Aztec Sandstone is aneolian sandstone ‘‘laterally correlated to the Navajo Sand-stone’’ [Blakey, 1989] that was deposited in a back-arc basinduring the Early Jurassic [Marzolf, 1983] and is part of thelarge system of Colorado Plateau Mesozoic sandstonedeposits. Its thickness ranges from 800 m to nearly1400 m in the study area. It is divided into three subunitsbased on rock color which varies due to the diagenetichistory of the deposit: the lower (red) unit, the middle (buff)unit and the upper (orange) unit [Carpenter and Carpenter,

1994; Taylor et al., 1999; Eichhubl et al., 2004]. The AztecSandstone is a fine- to medium-grained quartz arenite, withfrequent dune boundaries and large-scale tabular planar andwedge planar cross strata [Marzolf, 1983, 1990]. Unde-formed samples of the Aztec Sandstone typically haveporosities of around 25% and permeabilities of up to severalDarcys [Flodin et al., 2003].[7] Deformation bands developed during the earliest

stage of deformation in the Valley of Fire [Hill, 1989;Taylor et al., 1999], in relation to the Cretaceous Sevierorogeny [Bohannon, 1983]. This stage of deformationbanding was followed by a stage of jointing and, finally,by a stage of strike-slip faulting associated with the Mio-cene Basin and Range extension [Myers, 1999]. During thestrike-slip faulting, sets of left- and right-lateral faultsdeveloped sequentially by a repeated sheared joint mecha-nism (Figure 1) [Myers and Aydin, 2004; Flodin and Aydin,2004a, 2004b], forming interconnected fault networks withstructures that range from centimeters to several kilometersin length. The youngest formations affected by the strike-slip faulting are at the base of the Muddy Creek Formation,the age of which is between 8.5 and 5.8 Ma [Damon et al.,1978]. The burial of the Aztec Sandstone at the beginningof the strike-slip faulting is estimated between 1000 and2000 m [Flodin and Aydin, 2004a].

3. Methods

3.1. Fault Slip

[8] Although kinematic indicators are not present in all ofthe faults in the study area, the faults documented in thispaper and in earlier studies in the same area [Flodin andAydin, 2004a] have rakes oriented at a low angle to thestrike of the fault surface, indicating a dominant strike-slipcomponent of displacement. As a consequence, slip alongthese faults is considered to be the maximum apparenthorizontal separation, as determined by the displacementof markers such as deformation bands, dune boundaries orcolor bands produced by diagenetic processes prior tostrike-slip faulting. When possible, slip was measured atmultiple places along a fault, with the greatest slip valueconsidered to be the maximum slip along the fault.

3.2. Scan Lines and Sampling Biases

[9] To establish the statistical properties of the faultnetworks, scan lines were measured across the damagezones of individual faults of increasing apparent maximumslip magnitudes, and also across several consecutive faultzones. The first group of scan lines was measured perpen-dicular to the average trends of the individual fault zonesand covered the complete extent of the damage zone onboth sides of the faults. The second group of scan lines wasoriented perpendicular to the dominant fault strike definedby the main left-lateral faults shown in Figure 1.[10] Along the scan lines, the nature (opening mode or

sheared discontinuities), orientation, length and spacing ofeach of the fractures were determined. Fracture spacing wasconsidered to be the distance between two consecutivefractures along a scan line, regardless of their nature. Dipmeasurements were taken along the scan lines and thespacing data were projected on a horizontal plane. Thelengths of the very long fractures (large faults) that were

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crosscut by the scan lines were determined by measure-ments from aerial photographs.[11] The cumulative frequency distribution technique was

used to analyze the statistical properties of the fault net-works studied. This technique is both simple and appropri-

ate for analysis of one-dimensional scan line data [Gillespieet al., 1993]. In the fracture length distributions, joints andsheared joints were analyzed separately, with the lattergroup including all sheared discontinuities, regardless ofthe amount of offset. In the fracture spacing distributions,

Figure 1. Geographic location (inset) and fault map of the Valley of Fire State Park, SE Nevada(modified from Flodin and Aydin [2004a]). The location of the faults studied is marked on the map, andthe long scan lines measured in the park are shown as thick lines.

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however, joints and sheared joints were not treated sepa-rately, due to our definition of fracture spacing as thedistance between two consecutive fractures, regardless oftheir nature. Furthermore, since all of the fractures formedoriginally as opening mode fractures and some of them weresheared later, there is no reason to expect that differentiatingbetween opening mode and sheared fractures would affectthe fracture spacing.[12] Several sampling biases are inherent to scan line

surveys and were taken into account when interpreting thestatistical distributions based on scan line data. First, small-scale fracture lengths or fracture spacings are usually under-estimated. This effect is called the truncation of the data[Einstein and Baecher, 1983; Barton and Zoback, 1992;Pickering et al., 1995]. In the case of scan lines measuredon maps, this truncation is due to the limit of resolution ofthe maps. Every structure with dimensions smaller than orwithin the limits of resolution of the maps cannot besampled. In the case of scan lines measured in the presentstudy, many short fractures may be missed depending on theposition of the scan lines, resulting in the undersampling ofshort fracture lengths. The very short fractures may beclosely spaced, implying that small fracture spacings mayalso be undersampled.[13] Second, large-scale fracture lengths or large fracture

spacings are significantly underestimated or overestimated.This effect is called the censoring of the data [Einstein andBaecher, 1983; Yielding et al., 1992] and may have severalcauses. First, censoring is related to the size of the survey.Fracture lengths and fracture spacings larger than thisparticular size are not sampled, and fracture lengths canbe underestimated if one tip of the long fractures liesbeyond the boundary of the survey. Second, censoring isrelated to the level at which measurements are made. If this

level is different from the nucleation level of the fractures,fracture lengths can be underestimated.[14] Because of the sampling biases inherent to scan line

surveys, the parts of the statistical distributions cor-responding to extreme values (smallest and largest features)were never taken into account when interpreting the cumu-lative frequency distributions in this study. Ranges overwhich data were interpreted are given in Table 1.[15] For each analysis, the data were fit with several types

of distributions and the interpretations presented here arethose that best fit the data, even if they may not be the onlypossible solutions. In general, curve fitting also has inherentambiguities and this deficiency can be partially remedied byancillary information relevant to the structural and mechan-ical evolution of the system under consideration.[16] For complex data sets that could not be fit by a single

distribution over the whole range of data, analysis was doneseparately for different parts of the data, and several best fitswere defined to describe different ranges of the data sets. Inparticular, some distributions were broken down into sev-eral fractal (power law) segments, some of which coveringless than one order of magnitude of the data. This multi-fractal analysis with the definition of several fractal seg-ments over short ranges to fit complex statisticaldistributions is not uncommon in the literature [Berkowitzand Hadad, 1997; Wojtal, 1996; Fossen and Rørnes, 1996].

3.3. Mapping

[17] Maps and sketches, based on ground and aerialphotographs, were used in this study. The scales of thesephotographs were determined by distance measurementsmade in the field and the structural interpretations of themaps were validated by field observations.[18] Data from these methods is crucial not only for the

conceptual model that we present in this paper but also for

Table 1. Summary of the Characteristics of Fracture Length and Fracture Spacing Distributions Based on the Scan Line Surveys

Data Type Range, m Power law Exponent R2 Coefficient

Fracture length 80 cm Fault exponential 0.1 � 0.8 0.982Fracture spacing 80 cm Fault exponential 0.015 � 0.18 0.983Fracture length 8 m Fault lognormal 0.1 � 5.4 0.989Fracture length 8 m Fault power law 5.4 � 20 1.74 0.986Fracture length 14 m Fault lognormal 0.1 � 3.95 0.983Fracture length 14 m Fault power law 3.95 � 23 1.41 0.981Fracture spacing 8 m Fault power law 0.02 � 0.39 0.53 0.997Fracture spacing 8 m Fault power law 0.39 � 2.13 1.43 0.991Fracture spacing 14 m Fault power law 0.02 � 0.51 0.45 0.994Fracture spacing 14 m Fault power law 0.51 � 3.2 1.94 0.980Fracture length 80 m Lonewolf Fault power law 0.29 � 3.04 0.62 0.993Fracture length 80 m Lonewolf Fault power law 3.04 � 30 1.3 0.995Fracture spacing 80 m Lonewolf Fault power law 0.014 � 1.1 0.76 0.997Fracture spacing 80 m Lonewolf Fault power law 1.1 � 4.98 1.13 0.984Fracture length scan line 1 power law 0.14 � 0.64 0.29 0.989Fracture length scan line 1 power law 0.64 � 3.43 0.67 0.998Fracture length scan line 1 power law 3.43 � 50.6 1.05 0.988Fracture length scan line 2 power law 0.21 � 2.25 0.56 0.988Fracture length scan line 2 power law 2.25 � 20.8 0.87 0.989Fracture length scan line 2 power law 20.8 � 48.8 2.61 0.991Fracture spacing scan line 1 power law 0.02 � 0.52 0.6 0.997Fracture spacing scan line 1 power law 0.52 � 5.5 1.22 0.989Fracture spacing scan line 2 lognormal 0.01 � 1 0.991Fracture spacing scan line 2 power law 1 � 3.54 1.5 0.965Fracture spacing scan line 3 power law 0.05 � 0.38 0.62 0.986Fracture spacing scan line 3 power law 0.38 � 1.38 0.88 0.993Fracture spacing scan line 3 power law 1.38 � 7.28 1.47 0.984

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providing temporal and spatial information to complementthe statistical data.

4. Characteristics of Damage Zones AroundFaults of Increasing Slip Magnitudes

[19] We present field data on the damage zone of faults ofincreasing slip magnitudes. Each fault type described insections 4.1–4.4 represents a separate class, as defined byslip magnitude.

4.1. Incipient Faults (Approximately Millimeters toCentimeters of Slip)

[20] At the incipient stage of development, the faultsare slightly sheared joints or en echelon joint zones[Myers and Aydin, 2004] displaying millimeters to centi-meters of slip. The damage zones of these initial faultsconsist of splays located only at the tips of the faults andat fault surface irregularities (asperities, zones with anangular change, etc; Figure 2). The middle parts of theindividual sheared joints do not have splays. Two differ-ent splay geometries are observed in the tip zones: asingle splay (Figure 2a) or a cluster of splays resemblinga horse’s tail (Figure 2b).

4.2. Small Faults (Approximately Tens ofCentimeters of Slip)

[21] Faults with several tens of centimeters of slip areconsidered to be at an early stage of fault development and

have discontinuous fault cores and damage zones. Anexample of this class is the right-lateral fault shown inFigure 3, which displays 80 cm of slip, hereafter referred toas ‘‘the 80 cm Fault.’’ Figure 3a is a sketch of this fault,which is composed of several segments, with detailed mapsof compressive (Figure 3a, top inset) and extensional(Figure 3a, bottom inset) relays along the fault. The damagezone of the 80 cm Fault is composed of splays located at thetips of the segments (splay zones 1, 2, and 5 in Figure 3a)and at fault surface irregularities (splay zones 3, 4, and 6),as well as dense splays located primarily in the extensionalrelays. Discontinuous pockets of fault rock, formed byfrictional gouge (i.e., embryos of fault core), exist in someof the relay zones. Figures 3b and 3c show cumulativefracture length and fracture spacing distributions based onmeasurements of several scan lines overlaid across thedamage zone of the 80 cm Fault. In Figure 3b, the term‘‘whole fracture population’’ refers to both joints andsheared joints that were considered together for the pur-poses of measurement. This term is used consistently infigures showing fracture length frequency distributionsthroughout the paper. The distributions in Figures 3b and3c are negative exponential. More information about thesestatistical distributions and about other distributions to bepresented is provided in Table 1.

4.3. Intermediate Faults (Approximately 10 m Slip)

[22] Faults with �10 m of slip are considered to be at anintermediate stage of fault development. Their structures are

Figure 2. (a) Photograph and corresponding map of a fault with 1 mm slip, showing splays located atthe fault tip and at a fault surface irregularity. (b) Photograph and corresponding map of the tip region of afault with 2 cm slip, displaying a series of splays.

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Figure 3. (a) Geometry and damage zone distribution along the 80 cm Fault. Photograph-based maps of(top inset) compressive and (bottom inset) extensional relays are shown and the number of splaysobserved in splay zones 1 to 6 is indicated. (b and c) Plots showing the cumulative fracture lengthdistribution (Figure 3b) and the cumulative fracture spacing distribution (Figure 3c) for the damage zoneof the fault. Distributions are negative exponential.

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more complex than those of the smaller faults comprisingthe previously described classes, and they have longer andwider fault cores and damage zones. Examples of suchfaults are the two left-lateral faults with 8 and 14 m slip,shown in Figure 1 and hereafter referred to as ‘‘the 8 mFault’’ and ‘‘the 14 m Fault.’’ The 8 m Fault and the 14 mFault have comparable damage zones with complex archi-tectures. Figure 4 shows the damage zone of a section of the14 m Fault, which can be separated into two components.The first component of the damage zone is a relativelynarrow zone of very dense joints and sheared joints,bounded by the fault wall on one side and on the otherside by what remains of initial en echelon joints that weresheared and linked together to form the present-day fault.We call this component of the damage zone the innerdamage zone, the details of which are shown in Figure 4b.It contains many generations of splays, demonstrating thatthe fracture infilling in the zone occurred progressively inseveral stages due to repeated shearing. In this process, thepre-existing joints were sheared, producing secondary jointsthat were subsequently sheared and produced their ownsplays, etc. In these zones, the host rock is generallyfragmented, with the most intense deformation seen in thetriangular zones at the intersections between the fault walland the remains of the initial sheared and unsheared enechelon joints.[23] The second component of the damage zones of the

8 m Fault and the 14 m Fault is defined by long splays withen echelon geometry. These long splays have a typicallength of several tens of meters and a spacing of 5 to10 m (Figure 4a). We call this component of the damagezone the outer damage zone. It flanks the inner damage

zone and its outer limit is marked by the tips of the longsplays associated with the corresponding fault segments(Figure 4a).[24] Figure 5 shows the variations in thickness and

fracture frequency in the inner and outer damage zones ofthe 8 m Fault and the 14 m Fault. The inner damage zonehas a thickness (measured perpendicular to the faults) on theorder of several tens of centimeters, which shows littlevariation along the faults (blue in Figures 5a and 5c). Thefracture frequency in this inner zone is very high withseveral tens of fractures per meter, and it varies signif-icantly, reflecting the selective localization of fractureinfilling within the damage zone (blue squares inFigures 5b and 5d). The thickness of the outer damagezone varies significantly along the faults and is on the orderof several meters for the 8 m Fault and 1–20 m for the 14 mFault (red in Figures 5a and 5c). The fracture frequency inthe outer zone is very low, with only a few fractures permeter, showing little variation along the measured section ofthe faults (red circles in Figures 5b and 5d).[25] Eight parallel scan lines were measured across the

damage zone of the 8 m Fault and the 14 m Fault. Thecorresponding cumulative fracture length and fracture spac-ing distributions are plotted in Figure 6. The fracture lengthdistributions (Figures 6a and 6b) are similar for the twofaults with lognormal distributions for the smaller fracturelengths and fractal (power law) distributions for the largerfracture lengths. The shift in the fracture length distributionsis particularly easy to observe for fracture lengthscorresponding to the longest joints (5.4 and 3.95 m forFigures 6a and 6b, respectively). The lognormal part of thedistributions corresponds to joints and sheared joints whilethe steep fractal part of the distributions is composed of

Figure 4. (a) Photograph showing the two components of the damage zone of a section of the 14 mFault: the inner damage zone with high fracture frequency flanking the fault core and the outer damagezone, defined by long splays propagating away from the fault. (b) Detailed photograph and map showingthe architecture of the inner damage zone of the 14 m Fault and its sequential evolution (color coded).

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sheared joints or small faults only. All of the relatively longfractures are sheared, indicating either that shearing resultsin increased fracture length and/or that long fractures areprone to slip more than shorter fractures. The fracturespacing distributions are also similar for the two faults(Figure 6c) and are multifractal with two straight segments(bifractal).

4.4. Large Faults (Approximately 100 m Slip)

[26] Faults with slip in the order of 100 m are consideredto be at a relatively mature stage of fault development withthick fault cores and damage zones. A left-lateral fault withabout 80 m slip, informally named "the 80 m LonewolfFault," provides a good example for this class of faults. Thelocation of the fault is shown in Figure 1. Figure 7 displaysground and aerial photographs of a portion of this fault andits damage zone. Figure 7a shows that the fault is flanked bya zone with high fracture frequency (the inner damage zone)from which long splays emanate, propagating away fromthe fault, forming the outer damage zone. Figure 7b showsthat some much longer splays exist along the fault thanthose documented along the short section of the fault shownin Figure 7a, defining the outermost periphery of the outerdamage zone. This indicates that the outer damage zone of

the 80 m Lonewolf Fault is defined by various long splayswith very different lengths. Figure 8 shows the variations inthickness and fracture frequency in the inner and outerdamage zones along a section of the 80 m Lonewolf Fault.Measurements of the inner damage zone were taken wher-ever possible along this section because of occasional cover.The inner damage zone of the 80 m Lonewolf Fault has athickness on the order of 1 m to several meters, showinggreater variation than was seen in the 8 and 14 m faults(blue in Figure 8a). The fracture frequency in this inner zoneis very high with several tens of fractures per meter and itfluctuates noticeably, as is also the case in the 8 and 14 mfaults (blue rectangles in Figure 8b). The outer damage zoneof the 80 m Lonewolf Fault also has characteristics similarto those of the outer damage zones of the 8 and 14 m faults.Its thickness varies significantly along the fault and rangesfrom several meters to 20 m in the area studied (red inFigures 8a). The fracture frequency in this outer zone is verylow (a few fractures per meter) and shows little variationalong the measured section of the fault (red circles inFigures 8b).[27] One long scan line was measured across the damage

zone of the 80 m Lonewolf Fault and the correspondingcumulative fracture length and fracture spacing distributions

Figure 5. (a) Distribution of the thicknesses of the inner and outer damage zones along a section of the8 m Fault. (b) Fracture frequency distribution along the same fault. (c) Distribution of the thicknesses ofthe inner and outer damage zones along a section of the 14 m Fault. (d) Fracture frequency distributionalong the same fault.

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are plotted in Figure 9. The two distributions are multi-fractal with two straight segments (bifractal). As was thecase for the 8 m Fault and the 14 m Fault, the shift in thefracture length distribution occurs for a fracture length

approximately corresponding to the longest joints (3.04 m,Figure 9a). The fractal segment with the smaller slopecorresponds to small fracture lengths, defined by jointsand slightly sheared joints, while the steep fractal segmentcorresponds to large fracture lengths, defined solely by longsheared joints or small faults.

5. Long Scan Lines

[28] We have described the characteristics of the damagezones of selected faults of increasing slip magnitudes andhave distinguished between the prominent components ofthe fault zones. We now consider long scan lines crosscut-ting many different fault zones of different slip magnitudes,to determine the statistical properties of the fault networks ata larger scale of several hundred meters, larger than thespacing of the left-lateral faults with slip magnitudes greaterthan about 40 m. We measured two long scan lines in thenorthern part of the study area (scan lines 1 and 2, Figure 1).We also reprocessed data from one other long scan line thatwas previously measured by Myers [1999] in the southernpart of the study area as part of his thesis, which wasproduced under the supervision of the second author of thispaper (scan line 3, Figure 1).[29] Figure 10a shows a map of the main faults crosscut

by scan lines 1 and 2. Figure 10b details the position andlength of the fractures along scan line 1, and Figure 10cshows the corresponding fracture frequency. Figures 10dand 10e present similar data for scan line 2. In Figures 10b–10e, joints (in black, Figures 10b–10e, top) and shearedjoints, including large faults (in blue, Figures 10b–10e,bottom) are shown separately. The locations of coveredareas (gray shading) along the scan line are shown and faultrock presence and thicknesses (red) are provided whereobserved. Figures 10d and 10e indicate that the fracturelength distributions are irregular along the scan lines and arenot related directly to the distance from the main faults. Thisis partly because splays initiate at different locations alongthe fault zones and propagate at an acute angle to the faults.The highest fracture frequencies are found at and around themain fault zones, defined by the fault cores and slipsurfaces, and correspond to fault damage zones. However,the frequency and length distributions are not quite sym-metrical about the fault cores.[30] Figures 11a and 11b present cumulative fracture

length distributions for scan line 1 and scan line 2, respec-tively. These two distributions are more complex than thedistribution for the 80 m Lonewolf Fault presented earlier.They are multifractal but with at least three straight seg-ments (trifractal). As in all the previous fracture lengthdistributions, a shift occurs in the distributions for fracturelengths corresponding to the longest joints (respectively3.43 and 2.25 m for scan lines 1 and 2). It should be notedthat the fracture lengths in Figure 11 are constrained by thespacing between the 80 m Lonewolf Fault and the 175 mClassic fault (the next large subparallel fault to the east, seeFigure 1) because the longest fractures along scan lines 1and 2 are the right-lateral faults bounded by the 80 mLonewolf Fault and the 175 m Classic fault (Figure 10a).Figures 12a and 12b present cumulative fracture spacingdistributions for scan line 1 and scan line 2, respectively.The distributions are bifractal for scan line 1, but for scan

Figure 6. (a and b) Plots showing cumulative fracturelength frequency distributions for the damage zone of the8 m Fault (Figure 6a) and 14 m Fault (Figure 6b), based oneight parallel scan line surveys for each fault. Distributionsare lognormal for short fractures and fractal for longerfractures. Slopes of the fractal segments are provided.(c) Plots showing cumulative fracture spacing frequencydistributions for the damage zone of the 8 m Fault and the14 m Fault based on the same surveys as Figures 6a and 6b.Distributions are bifractal. Slopes of the fractal segments areprovided.

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line 2 appear to be lognormal for small fracture spacingsand fractal for larger fracture spacings.[31] Figure 13a shows a map of the main faults crosscut

by scan line 3. No data concerning fracture lengths areavailable for this scan line but, due to its substantial length(�800 m, much longer than scan lines 1 and 2), we thinkthat it provides very useful information that complementsour contemporary data. Figure 13b presents the cumulativefracture spacing distribution for this scan line. It is a multi-fractal distribution with at least three straight segments

(trifractal) and the slope values increase as the spacingbetween fractures increases.

6. Interpretations

[32] In this study we collected data focusing specificallyon (1) the fracture types in terms of their mechanical mode,(2) the spatial relationship between the fault core and thedamage zone structures, (3) the temporal relationshipamong damage zone structures and the progressive infillingof fractures, (4) the mechanism of faulting, and (5) the

Figure 7. (a) Photograph of the 80 m Lonewolf Fault showing the inner damage zone flanking the faultcore and long splays defining a part of the outer damage zone. (b) Interpretation of an aerial photographshowing large splays along different strands and segments of the 80 m Lonewolf Fault: these splaysdefine the outermost periphery of the outer damage zone.

Figure 8. (a) Distribution of the thicknesses of the inner and outer damage zones along a section of the80 m Lonewolf Fault. (b) Fracture frequency distribution along the same fault.

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geological and geomechanical framework for particularsettings. Our statistical data, together with the field mapsand theoretical information about the splay angles [deJoussineau et al., 2007], can help to visualize the physicalfault patterns and fault components. Thus we are able torelate the statistical data and the physical attributes of thefault zones including their spatial characteristics. Thisallows a better understanding of the physics and geologybehind the statistical data.

6.1. Conceptual Model for Damage Zone EvolutionWith Fault Growth

[33] Here we present a conceptual model for the evolutionof the damage zones as faults expanded in the Valley ofFire, based on a combination of field observations, includ-ing those described by Myers and Aydin [2004] and Flodinand Aydin [2004a], and on the statistical characteristics ofthe fault damage zones presented in sections 4 and 5.[34] Figure 14a depicts the geometry of an arbitrary,

initial, en echelon joint zone. As this joint zone is sheared,splays form at and around the tips of the sheared joints, inextensional relays between the sheared joints and occasion-ally at fault surface irregularities (Figure 14b). Measure-ments made in the study area suggest that the length of thelongest splays produced by the faults is correlated to thefault length by a power law [de Joussineau et al., 2007]. Inother words, the dimension of the splays at the fault tipscorrelates with the length of the fault segment, which is a

consistent characteristic at all other stages of fault evolutionstudied. For a slip of �1 m (Figure 14c), more splays form(when compared to Figure 14b) and discontinuous pocketsof fault rock localize in the fragmented relays. The damagezone bordering this fault has negative exponential statisticalproperties.[35] For a slip of about 5 m, two large fault segments

develop by the linkage of earlier segments, labeled 1, 2, 3,4, and 5, respectively (Figure 14d). The two new faultsproduce new, longer splays at their tips because of theirincreased size and slip after linkage [de Joussineau et al.,2007]. They have irregular fault cores, incorporating theearlier relay zones, and have many surface irregularities,which allow the formation of splays in locations along thecentral part of the faults. The preexisting generations ofsplays along the faults are sheared, thereby producing theirown splays. This process is likely to be responsible for theprogressive fracture infilling observed in the field.[36] For a slip of about 10 m, the two previous faults

become linked, forming a new longer fault (Figure 14e).The new fault has a well-developed fault core that includessuccessive episodes of linkage of the fault segments andassociated rock fragmentation. The fault damage zone haslognormal fractal and multifractal statistical properties andis organized into well-defined inner and outer damage zoneswith different characteristics. The inner damage zone is arelatively thin belt flanking the fault core. It is denselyfractured by progressive infilling from many generations ofsplays. As the slip increases, the inner damage zone, scalingwith the slip, progressively widens through the propagationof new generations of splays into the host rock. However,there is also a competing process by which parts of the innerzone are incorporated into the fault core as the fracturefrequency in the inner zone becomes so high in certain areasthat the rock cannot maintain its physical integrity. Thiscontributes to the progressive widening of the fault core atthe expense of the inner damage zone. The outer damagezone has a low fracture frequency and varying thickness. Itis dominated by long splays at the fault tips and by thesplays associated with the tips of earlier, shorter faults. Withincreasing slip, the outer damage zone progressivelyexpands through the propagation of new, longer splaysfrom the tips of new, longer fault structures.[37] It is notable that in the initial or intermediate stages

of fault evolution (Figures 14b to 14e), the thickness of theinner and outer damage zones can be affected by twoparameters. First, the angle between the throughgoing faultand the previously isolated fault segments is expected toinfluence the geometry of the fault damage zones. For agiven level of strain, it is easier and requires less work tobreak the step overs and link segments when the segmentsmake a small angle with respect to the orientation of thefinal throughgoing fault, as opposed to wider angles. The80 cm Fault is an example where the angle between thegeneral fault and the previously isolated segments is verysmall, less than 10�. The 14 m Fault is an example wherethe angle between the initial segments and the fault is larger(>15�). In this case, a higher degree of strain is required tobreak the step overs between the segments and to achievesegment linkage, resulting in a rather thick damage zone.The second parameter that affects the extent of the damagezone for small and intermediate faults is the arrangement of

Figure 9. (a and b) Plots showing the cumulative fracturelength frequency distribution (Figure 9a) and the cumulativefracture spacing frequency distribution (Figure 9b) for thedamage zone of the 80 m Lonewolf Fault. Distributions arebifractal and slopes of the segments increase for largescales, as marked.

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Figure 10

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the en echelon joints in the initial joint zones, as proposed inmodels of fault evolution by Myers and Aydin [2004] andFlodin and Aydin [2004b]. However, with increasing slip,these sheared en echelon joints are rapidly obliterated andno longer influence fault evolution or the properties of thedamage zone.[38] Finally, for a slip of about 100 m, the fault in

Figure 14e is linked with neighboring faults to form anew and much longer fault (Figure 14f, bottom left). Thedamage zone of this fault has multifractal statistical prop-erties, as is the case for all the larger faults. At the scale ofFigure 14f, it is difficult to show the inner damage zonewith clarity, and the main slip surfaces and associated faultcore are idealized. The splays shown in black in Figure 14frepresent the outer damage zones of the faults in the earlierstages of fault development. The fault segments inFigure 14f are long enough to produce splays connectingto neighboring subparallel faults located several tens ofmeters away. These long splays will eventually becomesecondary faults with their own core and inner and outerdamage zones. Such secondary faults enhance fractureconnectivity and influence the statistical properties of frac-ture networks. They may also contribute to the compart-

mentalization of the medium due to low cross-faultpermeability.

6.2. Evolution in the Statistical Properties ofDamage Zones With Fault Growth

[39] The frequency distributions in this paper wereobtained from detailed scan line data which have theinherent shortcoming of truncation of small-scale features[Einstein and Baecher, 1983; Pickering et al., 1995] andcensoring of large-scale features [Yielding et al., 1992].Accordingly, we did not take into account the data fromthose extremes in our analyses. It is therefore possiblethat the number of segments identified in the plots isslightly less than the actual and that some segments arelikely unidentified.[40] The results of our analysis of faults of increasing slip

magnitudes suggest that the statistical properties of damagezones change with fault size and slip. This statisticalevolution accompanies the progressive development of thedamage zones through fracture infilling. Following theconcepts proposed for joint (mode I fracture) set evolutionby Rives et al. [1992] and Wu and Pollard [1992], weattribute the evolution in the statistical properties of damagezones to the progressive development of the fracture andfault networks. At an early stage of fault development(slip � 1 m), fracture length and fracture spacing distribu-tions are negative exponential. At an intermediate stage offault development (slip � 10 m), the distributions forfracture length are lognormal fractal while those for fracturespacing are multifractal. Finally, in relatively mature stagesof fault development (slip � 100 m), both the fracturelength and fracture spacing distributions are multifractal.[41] This statistical evolution, associated with the pro-

gressive saturation of the fracture and fault networks, mayexplain the differences observed between the long scan linesdescribed in section 5. In that data, the fracture spacingdistributions are multifractal for scan line 1 and lognormalfractal for scan line 2 (Figure 12). That difference mightreflect the fact that scan line 1 samples a more saturatedfault network than scan line 2 because multifractal proper-ties are observed for well-developed fault networks [Cowieet al., 1995]. This possibility is supported by the fact thatmore large faults with fault cores and associated damagezones are found along scan line 1 than along scan line 2,even though the two scan lines are of comparable lengths.Furthermore, the mean fracture spacing is 25 cm along scanline 1, compared to 34 cm along scan line 2.

6.3. Multiscale Properties of Fault Damage Zones

[42] The fault damage zones in the Valley of Fire oftenexhibit multiscale or multifractal statistical properties. In theliterature, multifractal properties of fault networks areattributed to the existence of distinct fracture sets [Jiandonget al., 1999] or to several fracture mechanisms [Berkowitzand Hadad, 1997]. Cowie et al. [1995] also proposed thatthe multifractal properties of fault networks reflect a maturestage of fault development where fault coalescence domi-

Figure 10. (a) Map showing the location of scan lines 1 and 2 and the main fault zones in the area. (b) Position and lengthof joints/sheared joints along scan line 1. Faults with a core are also identified. (c) Joints/sheared joints frequencydistribution along scan line 1. (d) Position and length of joints/sheared joints along scan line 2. (e) Joints/sheared jointsfrequency distribution along scan line 2.

Figure 11. (a and b) Plots showing cumulative fracturelength frequency distributions for scan line 1 (Figure 11a)and scan line 2 (Figure 11b). Distributions are trifractal withthe slopes of the fractal segments as indicated.

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nates over nucleation. Here, we propose a specific processresponsible for the multiscale properties of fault networks,based on analyses of fracture length distributions. In themultiscale distributions shown in Figures 6, 9a, and 11, theparts of the distributions corresponding to short fractures aredefined by joints and slightly sheared joints while the partscorresponding to the longer fractures are defined by shearedjoints or small faults only. This suggests that the contrastinglength properties of joints, sheared joints and small faultsare the basis for the multiscale distributions observed. Wepropose that the different parts of the fracture lengthdistributions reflect different stages of the evolution of thefault networks. Shorter fractures form during all stages ofnetwork evolution while longer fractures (or faults) form inan increasing number in the later stages of the networkevolution, by linkage of individual segments or as splaysalong large fault segments. The differences in the lengthproperties and in the timing of formation of short (mostlyjoints) and long (sheared joints and faults) fractures mayexplain the observed multiscale distributions.

7. Discussion

7.1. Damage Zone Classification

[43] Our classification of fault damage zones into innerand outer damage zones differs from the geometric ap-

proach taken by Kim et al. [2004], which defines thedifferent components of damage zones by their locationalong the faults (tip, wall, and linking damage zones). Thegeometric approach has the virtue of applicability to a widerange of fault configurations, but it has crucial limitationsthat make it difficult to apply to fault networks thatdeveloped in a sequential manner, such as those in theValley of Fire. The first difficulty in this type of situation isthat it is hard to distinguish among the classes of damagezones as defined by Kim et al. [2004]. For example, the walldamage zone in the central part of a mature fault may becomposed of structures related to earlier relay zones (linkingdamage zone) or tip zones (tip damage zone) of prior faultsegments that linked together over time to form the present-day fault. The second complication is that the geometricclassification does not take into account the progressiveevolution of the structures forming the damage zones.Splays formed at the tips of a fault (and classified as a tipdamage zone) may, for instance, later on evolve into faultswith their own tip, wall, and linking damage zones.

7.2. Damage Zone Models

[44] Field studies and models of slip distribution alongfaults both indicate that the largest amount of slip occursnear the center of fault segments and that it decreases insome fashion to zero at the fault tips [Walsh and Watterson,1987, 1988; Cowie and Scholz, 1992; Dawers et al., 1993;Schlische et al., 1996]. For faults growing by the linkage ofseveral individual segments, the slip distribution is per-turbed by the process of fault interaction and becomessomewhat skewed [Willemse et al., 1996]. However, asthe segments coalesce, the total slip progressively catchesup and eventually exhibits a regular distribution along the

Figure 12. (a and b) Plots showing cumulative fracturespacing frequency distributions for scan line 1 (Figure 12a)and scan line 2 (Figure 12b). Distributions are bifractal forscan line 1 and, perhaps, lognormal fractal for scan line 2.The slopes of the fractal segments are provided.

Figure 13. (a) Map showing the main faults along scanline 3 (modified from Myers [1999]). (b) Plot showing thecumulative fracture spacing frequency distribution for scanline 3. This distribution is trifractal with the slopes of thefractal segments as shown.

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new fault system, with the maximum slip again found nearthe center of the fault and decreasing to zero toward the tips[Cartwright et al., 1995; Dawers and Anders, 1995; Guptaand Scholz, 2000]. If the slip distribution is tied to thedamage zone distribution along a fault, the broadest damageshould be found in the middle part of the fault with little orno damage to be found near its tips. This should hold truefor individual fault segments as well as for fault systemsformed by the coalescence of several individual fault seg-ments (stages 1 to 3, Figure 15a).[45] A different model in which the thickness of the

damage zone is determined by the static stress distributionand, more specifically, by the geometry of the extensionaland contractional fields around the faults (Figure 15b) wasproposed by Knott et al. [1996]. This model predicts a wide

damage zone in the extensional fields near the fault tips anda narrow damage zone in the contractional fields near thecenter of the faults, with an asymmetrical distribution ofdamage on both sides of the faults.[46] Our field observations and our conceptual model for

damage zone evolution with fault growth suggest that bothof these models have merits, but neither can fully accountfor the observed distributions of fault damage by itself. Inthe early stages of fault development, slip is greatest nearthe center of the fault segments and decreases to zerotoward their tips. On the other hand, the damage is localizedmostly around the fault segment tips because of stressconcentration (stage 1, Figure 15c), which follows themodel proposed by Knott et al. [1996]. However, as thefault segments mechanically interact and link, the slip

Figure 14. Conceptual model of damage zone evolution with fault growth (see text for explanations).

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increases significantly along the central part of the newcoalesced system, promoting the development of newsplays and the growth of preexisting splays in this centralzone (stage 2, Figure 15c). At this stage of evolution, thedistribution of damage around the fault is what would beexpected in the models of slip distribution, as the damage iswidest near the center of the new fault system where slip isthe greatest. However, in this case, a significant amount ofdamage is also present at fault tips, which is not expected inthe slip distribution models, because slip vanishes at faulttips by definition. Finally, when the fault segments eventu-

ally coalesce to form a new, longer fault entity, the mech-anism of stress concentration at fault tips dominates andresults in the formation of new, much longer splays at thefault tips, due to increased fault size and slip (stage 3,Figure 15c). In the meantime, the inner damage zoneprogressively develops along the fault by the mechanismof fracture infilling, as in the conceptual model presented insection 6.1. The damage zone distribution along the faultresembles that in the model proposed by Knott et al. [1996],with the widest damage occurring around the fault tips but,unlike in that model, the damage zone is also rather wide in

Figure 15. (a) Conceptual model for damage zone distribution around a fault, based on models of slipdistribution by Gupta and Scholz [2000] and others. (b) Conceptual model for damage zone distributionaround a fault, based on models of static stress distribution (modified from Knott et al. [1996]). (c) Newconceptual model for damage zone distribution around a fault integrating the slip distribution, stressperturbations and evolution of the fault system.

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the center of the fault because of the presence of splaysassociated with the tips of earlier fault segments andbecause of the high slip values across the segments locatedat or near the center of the fault.

7.3. Implications of the Statistical Properties of theFault Networks

[47] The shift in the statistical properties of damage zonesthat occurs with increasing fault length and slip has impor-tant consequences for the assessment of fault zone perme-ability. The damage zone usually is a permeable componentof fault zones [Caine et al., 1996; Aydin, 2000; Odling etal., 2004]. For faults formed by sequential shearing [Jourdeet al., 2002], its permeability may be up to 4 orders ofmagnitude greater than that of the host rock. Our resultsindicate that on the basis of knowledge of the physicalmechanism of faulting and the amount of slip along a fault,it should be possible to estimate the geometrical andstatistical properties of the faults and the associated damagezones and to compute realistic, upscaled fault zone perme-ability values to be used in fluid flow simulations. Forexample, for damage zones at intermediate and relativelymature stages of fault development, the fracture lengthdistributions have different parts which relate to differentstructural elements (joints, slightly sheared joints andfaults). This conclusion has important implications for fluidflow because of the different hydraulic properties of joints,slightly sheared joints and faults.[48] Finally, the multifractal length and spacing properties

of well-developed fault networks in the study area haveimportant implications for the prediction of the properties ofother fault networks in the subsurface. The classicapproaches to the estimation of the parameters of small-scale structures are to define one fractal element [see, e.g.,Watterson et al., 1996] or to make projections based on theslope of the first fractal segment identifiable in a statisticaldistribution [Yielding et al., 1992]. However, our resultsshow that the statistical distributions at relatively maturestages of fault development have several fractal segments

with slopes decreasing toward the small-scale features. Oneshould also be aware of the potential existence of anunidentified flatter fractal segment well below the resolutionlimit in a distribution. Neglecting or being unable torepresent such segments may lead to significant overesti-mations of small-scale features, as demonstrated inFigure 16.

8. Conclusions

[49] The basic premise of this study is that fault initiationand fault growth by linkage of individual segments deter-mine the characteristics and statistical properties of faultdamage zones. Incipient faults are sheared joints with smallpockets of damage localized to the fault tips and irregular-ities at the fault surface. As fault slip increases (>5 m), amore continuous fault core appears and the surroundingdamage zone becomes organized into two components withdifferent architecture and characteristics. The first compo-nent of the damage zone is the inner damage zone, directlyflanking the fault core. It is a zone with very high fracturefrequency and a thickness that increases with increasingamounts of fault slip. This inner zone develops throughprogressive fracture infilling from many generations ofsplays and it contributes to the progressive widening of thefault core as slip increases. The second component of thedamage zone is the outer damage zone, which is adjacent tothe inner damage zone and has a varying thickness and alow fracture frequency. It is defined by different generationsof long splays, related to the progressive stages of thegrowth of the faults by segment linkage. This mechanismis described in a new conceptual model for damage zoneevolution with fault growth. This model illustrates how thesegmentation of the main fault systems impacts both theproperties of the associated damage zone and the occurrenceof large-scale secondary faults. Such faults enhance fractureconnectivity and play a role in the compartmentalization ofthe medium.[50] The length and spacing statistical properties of fault

damage zones, determined by scan line surveys, show asystematic evolution with fault growth, attributable to theprogressive saturation of the fault networks. Well-developed,saturated fault networks commonly exhibit multifractalstatistical distributions, with important consequences for theprediction of the properties of fault populations in the subsur-face. We propose that these multifractal distributions reflectdifferent structural elements and different properties related tothe temporal and spatial framework for the evolution of faultdamagezones.Given thekinematicsof thestructuralelements,the statistical data together with the conceptual model can beused to better characterize fault populations associated withlarge faults that have remotely resolvable slip magnitudes inthe subsurface and, in turn, to providemore accurate informa-tion for subsurface fluid flow simulations.

[51] Acknowledgments. We acknowledge support from the Depart-ment of Energy, Basic Energy Sciences, Geosciences Research Program(grant DE-FG03-94ER14462 to Atilla Aydin and David D. Pollard). Weacknowledge reviews by Nancye Dawers, Ian Main, and Zoe Shipton andbenefited from discussions with, and suggestions by, Jef Caers and AndreJournel during the project as well as in the revision of this manuscript.Ghislain de Joussineau acknowledges the assistance and preliminary workdone by Nicholas Davatzes on one of the intermediate fault zones and theassistance in the field of Ann-Laure Moreau, Joseph Gonzales, Christopher

Figure 16. Conceptual diagram illustrating the impact ofmultifractal distributions on the estimation of the number ofsmall-scale features (fracture spacings or fracture lengths).

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Wilson, and Ramil Ahmadov. He would also like to express appreciation tothe Rock Fracture Project at Stanford University for providing a stimulatingworking environment.

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�����������������������A. Aydin, Rock Fracture Project, Department of Geological and

Environmental Sciences, 450 Serra Mall, Building 320, Stanford University,Stanford, CA 94305, USA. (aydin@pangea.stanford.edu)G. de Joussineau, Beicip-Franlab, 232 Avenue Napoleon Bonaparte,

F-92502 Rueil-Malmaison Cedex, France. (ghislain.dejoussineau@beicip.com)

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