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‘Diffuse faulting’ in the Machu Picchu granitoid pluton, Eastern Cordillera, Peru

Stefano Mazzoli

a

,

*

, Stefano Vitale

a

, Giuseppe Delmonaco

b

, Vincenzo Guerriero

a

,

Claudio Margottini

b

, Daniele Spizzichino

b

a

Dipartimento di Scienze della Terra, Universita

`di Napoli ‘Federico II’, Largo San Marcellino 10, 80138 Napoli, Italy

b

ISPRA – Istituto per la Protezione e la Ricerca Ambientale, Servizio Geologico d’Italia, Dipartimento Difesa del Suolo, Via Curtatone 3, 00185 Roma, Italy

article info

Article history:

Received 14 January 2009

Received in revised form

3 August 2009

Accepted 9 August 2009

Available online 14 August 2009

Keywords:

Fracture analysis

Structural inheritance

Strain localization

Distributed deformation

Central Andes

abstract

A series of batholiths, forming part of the ‘roots’ of a Permo-Liassic rift system, are exposed in the high

Eastern Cordillera of central Peru as a result of tectonic inversion. Shortening of the Machu Picchu

granitoid pluton was accommodated by widespread shear reactivation of primary joints, by a process

termed here ‘diffuse faulting’. Fault-like reactivation of precursor joint surfaces, marked by chlorite,

epidote and quartz shear ﬁbres, is locally evidenced by few centimetres offsets within apparently

undeformed granite. Analysis of fault slip data indicates that shear reactivation of different joint sets was

kinematically consistent with ENE oriented shortening. Less frequent mylonitic shear zones appear to

have evolved from the common brittle precursors. Apart from rare phyllonitic shear zones, ﬂuid–rock

interaction along the brittle precursors was generally limited, and pluton deformation appears to be

mainly controlled by the geometry and distribution of primary joints. Three main sets of reactivated

joints can be recognized, characterized by oblique-slip kinematics with variable reverse and strike–slip

components of motion. Theoretical modelling based on quantitative fracture analysis (scan-line data)

and different displacement–length relationships applied to the main reactivated joint sets yield ﬁrst-

order estimates of pluton ﬁnite strain. The results suggest that bulk ﬁnite strain is oblate and essentially

coaxial, and is characterized by horizontal shortening not exceeding 10%. Relatively small ﬁnite strains,

integrated over the size of the pluton, still result in a few kilometres of crustal shortening.

Ó2009 Elsevier Ltd. All rights reserved.

1. Introduction

In the last twenty years, the process of basin inversion has

received considerable attention. Numerousstudies integrating basin

stratigraphy, structural analysis and/or analogue and numerical

modelling allowed geoscientists to obtain a progressively better

understanding of the geometry, modes and mechanisms of basin

inversion (e.g. Cooper and Williams, 1993; Buchanan and Buchanan,

1995; Glen et al., 2005 and references therein). However, little is

known about the deformation occurring at depth, in the ‘roots’ of rift

basins – often occupied by magmatic complexes – during tectonic

inversion. In the Eastern Cordillera of southern Peru, granitoid

plutons originally emplaced along a Permo-Liassic rift axis are

presently exposed at high elevationsas a result of strong inversion of

the axial zone of the rift system (Sempere et al., 2002). This provides

a unique opportunity to analyze the effects of Andean shortening

and basin inversion in homogenous rock bodies originally sitting in

the ‘roots’ of the rift system.

It is well known that, in homogeneous plutonic rocks, strain

tends to be partitioned and is mainly localized along shear zones.

Since the pioneering work of Ramsay and Graham (1970), these

represent widely investigated, ‘classic’ geological structures (e.g.

Vitale and Mazzoli, 2008, 2009 and references therein). A broad

literature exists on rheology-dependent strain localization in

homogenous plutonic rocks. In particular, the role of ﬂuids and

chemical softening has been intensely investigated (e.g. Christian-

sen and Pollard, 1997; Tourigny and Tremblay, 1997), as well as the

fundamental control exerted by brittle precursor structures in

shear zone nucleation; the interested reader is referred to the

papers by Pennacchioni (2005),Mancktelow and Pennacchioni

(2005) and Pennacchioni and Mancktelow (2007) for exhaustive

reviews and critical discussions of these issues.

Structural analysis of the Machu Picchu granitoid pluton, being

characterized by pre-existing, well-developed planar discontinu-

ities at the time of low-T deformation, conﬁrms the fundamental

role played by structural inheritance and brittle fracture reac-

tivation in shear zone nucleation. Furthermore, this study attempts

*Corresponding author.

E-mail address: stefano.mazzoli@unina.it (S. Mazzoli).

Contents lists available at ScienceDirect

Journal of Structural Geology

journal homepage: www.elsevier.com/locate/jsg

0191-8141/$ – see front matter Ó2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jsg.2009.08.010

Journal of Structural Geology 31 (2009) 1395–1408

to obtain an estimate of bulk ﬁnite strain and crustal shortening

associated with joint reactivation within a large pluton located at

the base of the upper crust at the time of basin inversion. The aim is

to provide new, quantitative insights into the modes of deformation

of common continental crust rock bodies such as plutonic

complexes involved in crustal shortening. Our results may hope-

fully also contribute to the more general debate on the roles of

localized (non-coaxial) vs. distributed (and essentially coaxial)

deformation in convergent tectonic settings (e.g. Butler and Maz-

zoli, 2006).

2. Geological setting

The Andean chain represents the paradigm of continental

orogeny resulting from the subduction of an oceanic slab beneath

a continental plate (e.g. Ramos and Aleman, 2000 and references

therein). The chain is classically divided into three main sectors

(Jaillard et al., 2002): (i) a forearc zone, including the Paciﬁc slope

and offshore areas; (ii) an arc zone, mainly represented by the

present chain (and the Altiplano); and (iii) a back-arc area, which

includes the Eastern Cordilleras and Amazonian slope and foothills

and the eastern lowlands underlain by the foreland basin. Since the

Tertiary, each zone is dominated by distinctive deformation styles.

Extension-related, tectonic and magmatic manifestations

affected the Andean margin (Eastern Cordillera) of Peru and Bolivia

between Permian and Jurassic times. According to Sempere et al.

(2002) this rift structure controlled the location and nature of

subsequent contractional deformation and allowed the individu-

alization of crustal blocks characterized by distinct tectonic

behaviour and evolution. The Machu Picchu granitoid pluton,

forming part of the larger ‘Quillabamba granite’ (a magmatic

complex exposed in the high Eastern Cordillera of central Peru NW

of Cusco; Fig. 1), is one of a series of plutons intruded along the axial

zone of such Permo-Liassic rift system. Available geochronological

(U–Pb) data provide an age of 257 3 Ma for the Quillabamba

granite (Lancelot et al., 1978), whereas Andean convergent defor-

mation affected the study area mainly in Eocene times (‘Inca 1

tectonic event’, which took place at 43–40 Ma according to Carlotto,

2002), although an early, weak tectonic inversion episode may have

occurred already in latest Jurassic–earliest Cretaceous times

(Sempere et al., 2002). Shortening produced strong tectonic

inversion of the axial zone of the rift system. As a result, the

granitoid plutons forming part of the rift ‘roots’ are now exposed at

the highest altitudes (Sempere et al., 2002) allowing studying the

effects, on these bodies, of the deformation associated with rift-

scale tectonic inversion.

The Machu Picchu granitoid pluton includes a variety of rock

types, dominantly granites and granodiorites (Carlotto et al., 1996).

The main plutonic body is a medium-grained (millimetre grain

size), rather equigranular granite to granodiorite composed of

quartz, plagioclase, biotite, K-feldspar muscovite. It includes

enclaves of more basic composition, being also crosscut by planar

Fig. 1. (a) Geological sketch map showing main Mesozoic elements of Peru and Bolivia (after Sempere et al., 2002). (b) Geological sketch map of the Cusco–Abancay area (after

Carlotto, 2002), showing location of ﬁeld study area. (c) Schematic stratigraphic transect (located in a) showing position of Permo-Triassic plutons of the Eastern Cordillera (after

Sempere et al., 2002).

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–14081396

intrusions consisting of porphyritic biotite-bearing lamprophyres

and aplitic dykes. The batholith, presently preserving intrusive

contacts with surrounding Lower Paleozoic pre-rift successions,

shows a general rounded shape in map view, with an average

diameter of ca.30km(Carlotto et al., 1996).

3. Structural analysis

Most of the plutonic body shows little macroscopic evidence of

deformation and metamorphism, igneous relationships being well

preserved (Fig. 2a). Although the igneous fabric is macroscopically

well preserved, in thin section (Fig. 2b) many investigated samples

display deformation microstructures and a variable low-T meta-

morphic overprint of the primary minerals. Typical is the alteration

and replacement of plagioclase by epidote–sericite–calcite assem-

blages, pervasively distributed within grains and/or concentrated

along plagioclase cleavage planes and intragranular fractures, as

well as the replacement of biotite by chlorite.

The most evident structures at the outcrop scale consist of

planar joint sets (Fig. 2c–f) that, as discussed in the following

sections, may be variably reactivated. The origin of these joint sets,

being it related to thermal and/or tectonic stresses acting during

cooling of the main plutonic body, is not a subject of this paper.

What is important in this context is that batholiths are commonly

characterized by variably oriented sets of primary joints (as we

shall term them throughout this paper), which form typical

networks of planar discontinuities within plutonic bodies (e.g. Price

and Cosgrove, 1990). Orientation data for these structures,

measured in the Machu Picchu pluton, are shown in Fig. 3.

3.1. Joints

Granitoid rocks showing no evidence of solid-state deformation

at the outcrop scale are commonly crosscut by isolated joints of

variable length, the larger of which (master joints) may extend for

several tens of metres (Fig. 2c–f). These fractures are segmented

and show en-echelon geometry, usually with a slight overlap at

Fig. 2. Plutonic rocks and joint sets. (a) Primary relationships among igneous rocks of different composition. (b) Microphotograph (crossed polars) of undeformed granite (note

plagioclase alteration, and quartz microstructures including undulose extinction, incipient grain boundary migration and subgrain development at grain margins). (c) Steeply SW-

dipping (Set 1) and moderately NE-dipping (Set 3) master joints. (d) Set 3 master joints and steeply NE-dipping secondary joints. (e) Detail of Set 3 joints, showing variable fracture

spacing at the outcrop scale. (f) NE-trending, vertical (Set 2) master joints intersecting Set 1 and Set 3 master joints.

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408 1397

their terminations. They generally show no evidence of cataclasis

and also little or no alteration by ﬂuid–rock interaction (in fact the

typical bleached haloes are uncommon here). The joints show

variable spacing, from several centimetres to few metres, and

a wide range of attitudes (Fig. 3a). However, four dominant sets can

be recognized (Fig. 3b). These, also coinciding with the master joint

sets, include: (i) a steeply SW-dipping set; (ii) a N to NE-trending,

vertical set; (iii) a moderately NE-dipping set; and (iv) a gently NW

dipping set. In the following, they will be indicated as Set 1, Set 2,

Set 3, and Set 4, respectively.

Rare maﬁc dykes occur, parallel to the main joint systems

(Fig. 4a). This feature suggests that the joints formed early, most

probably during cooling of the main plutonic body, and were

intruded by late-magmatic dykes. The lamprophyres also show

evidence of lower greenschist facies metamorphism. Fluid inﬂux is

suggested by intense low-T overprinting, with widespread

replacement of biotite by chlorite (Fig. 4b). Maﬁc dykes also display

common evidence of shear along the contact with wall-rock

granite, testiﬁed by surfaces coated with mineral shear ﬁbres and

local development of gouge bands (Fig. 4c).

3.2. Brittle shear zones

Planar structures forming part of the joint sets described in the

previous section (Fig. 3) may show evidence of fault-like reac-

tivation, marked by chlorite, epidote and quartz shear ﬁbres

(Fig. 4d and e). Fault offsets cannot usually be obtained, due to the

general lack of suitable markers. However, displacements can

sometimes be measured at the intersection between different

reactivated joint sets within apparently undeformed granite. Such

Fig. 3. Orientation data (b–e are lower hemisphere, equal area projections). (a) Rose diagram for all measured planar structures. (b) Poles to planes (all measured structures).

(c) Contour plot of data shown in (b); main joint sets are labelled as in text. (d) Contour plot of poles to shear planes. (e) Contour plot of striae/shear ﬁbre lineation data.

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–14081398

joint intersections provide relevant information. For example, in

Fig. 5a NE-dipping (Set 3) fractures are shown, offsetting a steep

SW-dipping (Set 1) surface, producing a series of steps associated

with the reverse component of motion of Set 3 fractures. However,

the stepped surface also appears to have been reactivated, the steps

tending to be smoothed out by oblique shearing along the steep

SW-dipping surface (Fig. 5b). These features suggest that: (i) the

different fracture sets were reactivated more or less synchronously,

during a shortening event; and (ii) the displacements were small

(of a few centimetres), so that slip along a reactivated joint set

produced asperities that could be smoothed out by shearing along

another set at a high angle to the ﬁrst one.

A straight foliation is sometimes developed at an angle of ca.45

to the reactivated joint, extending for a few centimetres into the

adjacent country rock (Fig. 5c), particularly at compressive jogs

between stepped terminations of en-echelon fractures. The fact

that the foliation is straight and at ca.45

to the bounding reac-

tivated joint segments conﬁrms that the shear displacement is

generally small, leading to a correspondingly low ﬁnite strain

within the compressive bridges, as discussed in Mancktelow and

Pennacchioni (2005). According to the latter Authors, the

displacement rates on the reactivated joints must have been

sufﬁciently low for strain to be accommodated within the jog zones

in a distributed fashion and local cleavage development.

Away from compressive jogs, the wall rock to fault-like reac-

tivated joints generally consists of apparently undeformed granite,

macroscopically showing no evidence of alteration by ﬂuid–rock

interaction. In thin section, wall-rock granite shows no major

differences, in terms of alteration and fabric development, with

respect to country rock granite (Fig. 5d). Only in a sub-millimetre

thick zone in contact with the fault plane, the breakdown of

plagioclase and of iron–magnesium-bearing minerals becomes

more intense (Fig. 5e and f). This appears to represent an incipient

stage of reaction softening and development of phyllosilicate-rich

assemblages that are important for the next group of structures.

3.3. Mylonitic shear zones

Mylonitic shear zones consist of several centimetres to tens of

centimetres thick bands of sigmoidally shaped foliation, typical of

heterogeneous ductile shear zones, ﬂanking the brittle precursor

fracture (Fig. 6a). The latter also shows clear evidence of slip, in the

form of mineral shear ﬁbres, consistent with shear zone kinematics.

Ductile bands show a mylonitic fabric, including typical S-C struc-

tures and shear bands (Fig. 6b), and dynamic recrystallization of

quartz dominated by subgrain rotation recrystallization (Fig. 6c).

Several tens of centimetres thick phyllonites also occur within

the study area, although they are rare, representing <1% of the

reactivated joints. They show a mylonitic fabric and replacement of

the original mineral assemblage of the granite, dominated by

quartz and plagioclase, by one consisting of quartz, epidote–sericite

and chlorite (Fig. 6d). These phyllonitic levels appear to represent

more evolved shear zones that nucleated along the common brittle

precursors, but underwent more intense reaction softening,

allowing strain localization.

3.4. Brittle shear zone kinematics and paleostress analysis

Three out of four main sets characterizing the whole joint

population have been preferentially reactivated (Fig. 3). Set 1

Fig. 4. (a) Maﬁc dyke (arrowed) intruded parallel to primary joints at Huayna Picchu Mt. (b) Thin section view (crossed polars) of lamprophyre, showing composition dominated by

feldspars and biotite (largely replaced by chlorite as a result of low-T metamorphic overprint). (c) Fault gouge (brown) along the contact between lamprophyre and wall-rock

granite. (d) Reactivated joint surface showing quartz shear ﬁbres and chlorite. (e) Reactivated joint surface showing epidote shear ﬁbres. (For interpretation of the references to

colour in this ﬁgure legend, the reader is referred to the web version of this article.)

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408 1399

(steeply SW-dipping) joints and Set 3 (moderately NE-dipping)

joints are generally reactivated as reverse-sinistral, oblique-slip

faults (the reverse component being dominant for Set 3), whereas

Set 2 (vertical, N to NE trending) joints are characterized by dextral

strike–slip (Fig. 7). These three joint sets appear to have acted as

independent slip systems during convergent deformation (Fig. 8).

Two methods have been used for paleostress analysis, and the

results compared (Fig. 9). The right dihedra method (Angelier and

Mechler, 1977) provides the following attitudes for the principal

stress axes:

s

1

¼246/07;

s

2

¼155/12;

s

3

¼008/76. A second

method involves estimating the orientation of the principal stress

axes (or P-B-Taxes; Turner,1953) using a value of

Q

(angle between

the shear plane and the Paxis, i.e.

s

1

) deﬁned by the maximum

clustering of Pand Taxes (Wallbrecher, 1986). In our instance, a

Q

value of 50

is obtained. The contour plots indicate a well-deﬁned P

axis showing an ENE–WSW horizontal compression, consistent

with the

s

1

axis obtained by the right dihedral method. On the

other hand, the Band Taxes tend to be more distributed along

a great circle (

s

2

–

s

3

plane).

The lack of reactivation of Set 4 joints is most probably

controlled by their orientation, as these fractures are striking

roughly parallel to the maximum compression direction (i.e. they

experienced only minor or no shear stress). It is worth noting that,

on the contrary, joint Sets 1–3 are suitably oriented for reactivation,

the maximum compression direction forming an angle close to 50

with respect to all three joint set mean planes (therefore, the

s

1

axis approaches the bisector of the trihedral angle formed by the

three quasi-orthogonal joint sets).

3.5. Fracture analysis (scan-line data) for the main reactivated

joint sets

The basic structure detection technique used for quantitative

fracture analysis consisted of measuring fractures along linear

traverses (scan lines). Eighteen scan lines were carried out, their

length ranging between 5 and 20 m. The following characteristics

have been recorded for each detected planar feature: (i) type (joint,

reactivated joint, vein, dyke), (ii) distance from scan-line origin,

Fig. 5. Brittle shear zones. (a) Stepped surface developed at the intersection between two reactivated joint sets. (b) Detail of previous picture, showing steps (produced by the

reverse component of motion along NE-dipping, Set 3 fractures) being smoothed out by oblique shearing along the steep SW-dipping surface. (c) Straight foliation (arrowed) at

dextral strike–slip fault termination (reactivated, NNE striking, Set 2 joint; large arrow to the left shows strike–slip motion). (d) Thin section view (crossed polars) of hanging-wall

granite 2 cm away from NE-dipping, reactivated Set 3 joint surface. (e) Thin section view(crossed polars) of hanging-wall granite in contact with reactivated Set 3 joint surface. Note

intense plagioclase alteration and breakdown of biotite. (f) Sketch showing location of previous thin sections with respect to NE-dipping, Set 3 joint reactivated as oblique-slip fault

with a dominant reverse component of motion.

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408140 0

Fig. 6. Mylonitic shear zones developed along NE dipping, Set 3 brittle precursors (sense of shear is top-to-the-SW for all diagrams). (a) Heterogeneous ductile shear zone, showing

sigmoidally shaped foliation (hatched line) and shear bands (thin arrows; note deﬂected foliation along shear bands), ﬂanking reactivated (thick arrow) primary joint surface. (b)

Thin section view of mylonite showing shear bands. (c) Thin section view (crossed polars) of mylonite showing sigmoidally shaped foliation and dynamic recrystallization of quartz

(dominated by subgrain rotation recrystallization). (d) Thin section view (crossed polars) of phyllonite. The mineral assemblage is dominated by quartz, sericite, ﬁne-grained epidote

and chlorite.

Fig. 7. Orientation data for the three main brittle shear zone sets (reactivated joints). In the upper row (lower hemisphere, equal area projections), fault planes are plotted as great

circles, with striae/shear ﬁbre lineation on shear surfaces. Rose diagrams refer to fault planes (medium row) and lineation data (lower row).

(iii) attitude, (iv) length, (v) aperture (or opening displacement),

(vi) shear displacement (when measurable), (vii) morphology, (viii)

crosscutting relationships, (ix) composition and texture of fracture

ﬁll. As the purpose of the present study is to analyze the role of

reactivated primary fractures in pluton deformation, only the

results concerning the joints belonging to the three main reac-

tivated families (i.e. Sets 1–3) will be presented.

In order to obtain correct fracture density estimates, for each of

the three main reactivated fracture sets the data have been pro-

jected onto a section normal to the mean joint plane. The ratio (r)

between the standard deviation and the mean of spacing values is

of 0.84, 0.55 and 0.50 for joint Sets 1, 2, and 3, respectively. Values of

r<1 point out a clustered spatial distribution of joints (Gillespie

et al., 1993): compared with a random distribution (characterized

by r¼1), ‘small’ and ‘large’ spacing values are more frequent with

respect to the mean. Fig. 10a and b shows the cumulative distri-

butions of spacing values and related best-ﬁt diagrams. The latter

display the standard normal distribution inverse function of

observed cumulative distributions as a function of spacing (S).

Using these diagrams allows one verifying whether an analyzed

aleatoric variable (AV) is characterized by a normal or log-normal

distribution and, in the latter instance, to obtain the equation of the

Fig. 8. The three main brittle shear zone sets. (a) Mean slip planes and associated slip vectors (based on orientation data in Fig. 7). (b) Cartoon showing reactivation pattern.

Fig. 9. (a) Plot of all fault planes (including the three sets of Fig. 7), showing striae/shear ﬁbre lineation on shear surfaces. (b) Results of paleostress analysis for faults in (a), carried

out using the right dihedra method (Angelier and Mechler, 1977). (c) Contour plot of P-B-Tdistribution, showing orientation of

s

1

,

s

2

and

s

3

determined by the right dihedra method

for comparison. (d) Contour plots of P,Band Taxes separate distributions. Plots and paleostress analysis were performed using TectonicsFP (software by F. Reiter and P. Acs for

Microsoft Windows).

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–14081402

theoretical distribution best ﬁtting the data. In case the data points

are well aligned, the AV is a linear function of the standard normal

AV and consequently is characterized by a Gaussian distribution. In

our instance, the data points plot along a logarithmic curve, i.e.

their distribution is well approximated by a linear function of ln(S).

Therefore, ln(S) has a normal distribution (i.e. Sis characterized by

a log-normal distribution). By calculating the least squares curve on

the semi-logarithmic diagram, a function is obtained of the type

u¼aln(S)þb(shown in Fig. 10b), where uis the standard normal

AV, while aand bare constants. Applying the standard Gaussian

distribution function to the variable u, the log-normal distribution

function is obtained as the best ﬁt for the data points included in

the diagrams of Fig. 10a. Mean fracture densities are of 3.47, 1.85,

and 2.1 fracturesm

1

for joint Sets 1, 2, and 3, respectively.

The analysis of joint length distributions (Fig. 10c and d) has

been carried out with a method similar to that used for the analysis

of fracture spacing. Also in this instance, the best-ﬁt diagrams

appear to outline a log-normal distribution. Such a distribution of

fracture length values – as well as fracture spacing – has been

observed in several studies where, however, normal and power-law

distributions are also frequently reported (e.g. Gillespie et al., 1993;

Odling et al., 1999). As for the evaluation of ﬁnite strain associated

with joint reactivation we shall use the cumulative distribution

function of fracture length (see Section 4.1), a more accurate

statistical analysis concerning this parameter is relevant. Such an

analysis is essentially devoted at deﬁning whether fracture length

data actually conform to a log-normal – rather than normal or

power-law – distribution. To this purpose, in Fig.10e the cumulative

distributions of fracture length values are plotted for the three main

reactivated joint sets, together with the 90% conﬁdence intervals

for each estimated cumulative frequency value (such intervals have

been calculated by considering a uniform spatial distribution of

joints, using the method outlined in Guerriero et al., in press). As it

can be observed in the diagrams, the best-ﬁt log-normal

Fig. 10. Fracture analysis (scan-line data) for the main reactivated joint sets. (a) Cumulative frequency distribution of fracture spacing values. (b) Best-ﬁt plots of the standard

normal distribution inverse function of observed cumulative distributions vs. spacing. (c) Cumulative frequency distribution of fracture length values. (d) Best-ﬁt plots of the

standard normal distribution inverse function of observed cumulative distributions vs. length. (e) Semi-logarithmic plots of fracture length cumulative frequency, showing 90%

conﬁdence intervals and curves of normal, log-normal, and power-law distributions.

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408 1403

Fig. 10. (continued).

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408140 4

distribution – obtained using the best-ﬁt diagrams of Fig. 10d by

calculating the standard normal distribution of the least squares

logarithmic function – is more consistently contained, with respect

to both normal and power-law curves, within the conﬁdence

intervals of the cumulative frequency sampling estimates. Mean

joint lengths are of 2.2, 2.65, and 1.7 m for joint Sets 1, 2, and 3,

respectively.

4. Discussion

Tectonic inversion of the Eastern Cordillera Permo-Liassic rift

system and shortening of the rift ‘roots’ produced widespread shear

reactivation of primary joints within the Machu Picchu granitoid

pluton. Analysis of fault slip data indicates that shear reactivation of

different joint sets is kinematically consistent with ENE oriented

shortening (Fig. 11). Therefore, although contractional deformation

of the pluton may have resulted from a long history of tectonic

inversion (Sempere et al., 2002), it appears that the shortening

direction remained essentially constant during such a tectonic

evolution. Lower greenschist facies metamorphic conditions during

joint reactivation are indicated by the growth of chlorite, epidote

and sericite, with a lack of higher-grade minerals. Such conditions

are consistent with the microstructure of quartz observed in

mylonitic shear zones, indicating dynamic recrystallization domi-

nated by subgrain rotation recrystallization. The related deforma-

tion took place at depth, as the pluton was probably located toward

the base of the upper crust. Therefore, it may be envisaged that

most of the joint reactivation occurred during the early shortening

stages, prior to the ﬁnal ascent of the granitoid body as a result of

strong inversion of the rift system. The lack of cataclastic over-

printing of the more evolved, mylonitic shear zones suggests that

slip along reactivated joints essentially ceased at shallower crustal

levels, during pluton exhumation.

This work conﬁrms that both brittle and mylonitic shear zones

(Hull, 1988) can develop from precursor joints in plutonic rocks. In

the study area, the transition from initial joints to faults, to mylo-

nitic shear zones can be carefully documented. Shear zone types

reﬂect the inﬂuence of ﬂuid inﬁltration and the degree of ﬂuid–rock

interaction along the primary fracture. Fluid–rock interaction

appears to have occurred along a great number of primary joints.

However, both non-reactivated joints and brittle shear zones

commonly display only limited (microscopically observable) wall-

rock alteration by ﬂuid–rock interaction. Mylonitic shear zones

show a larger degree of ﬂuid–rock interaction and substantial

reaction softening. However, only <1% of observed shear zones

(including both brittle and mylonitic types) consists of several tens

of centimetres thick phyllonites. This, together with little wall-rock

alteration and the lack of mineral-ﬁlled extension fractures and

shear-related tension gashes, suggests minor dilatancy and limited

ﬂuid inﬂux along precursor joints. This probably led to minor

reaction softening and limited strain localization along individual

(‘weak’) shear zones. Finite strain appears to have been mainly

accommodated by a form of ‘distributed shear’ within the pluton,

probably involving relatively small displacements accumulating

over a very large number of primary fractures, which form

a pervasive network at the batholith scale. Therefore, even though

strain localization occurs at the metre scale, at the km (or pluton)

scale strain can be considered as essentially distributed. This

process of widespread reactivation of precursor joints is termed

here ‘diffuse faulting’.

4.1. How much strain at the pluton scale?

Faults and shear zones within the Machu Picchu pluton origi-

nated from reactivation of precursor fractures. Therefore, scan-line

data analysis (Section 3.5) and related scaling relationships (Fig. 10)

refer to structures that originated as joints. Numerous studies have

shown that parameters such as aperture or length of tensional

fractures display fracture-size relationships that are effectively

described by log-normal or power-law distributions (e.g. Das

Gupta, 1978; Mandelbrot,1983; Nelson, 1985; Gudmundsson,1987;

Heffer and Bevan, 1990; Barton and Zoback, 1992; Gillespie et al.,

1993; Sanderson et al., 1994; Barton, 1995; Gross and Engelder,

1995; Johnston and McCaffrey, 1996; Marrett, 1997; Odling et al.,

1999; Ortega and Marrett, 2000; Ortega et al., 2006). On the other

hand, joint spacing appears to be controlled by a series of param-

eters including (Nelson, 1985): (i) rock composition; (ii) rock

texture, grain size, porosity; (iii) structural position; and (iv)

mechanical layer thickness (a parameter that, in principle, should

not apply to homogenous, roughly isotropic plutonic rocks,

although early master joint sets are likely to control the develop-

ment, in terms of size and spacing, of later joints).

The bulk ﬁnite strain associated with joint reactivation essen-

tially results from the shear strain components produced by the

three main reactivated joint Sets 1–3. In order to obtain the ﬁnite

strain associated with each of the three main joint sets it would be

necessary to know the statistic distribution f(D)of displacements

(D), that we deﬁne as the product between the probability density

function (PDF)ofD(e.g. Dekking et al., 2005) and mean fracture

density (F

m

): f(D)¼PDF(D)$F

m

. The shear strain (

g

) could then be

obtained by the following integration:

g

¼Z

N

0

D$fðDÞdD(1)

where f(D)dDis the number of fractures per m having displace-

ment comprised between Dand (DþdD). In our instance, as

a systematic measurement of displacements was hindered by the

common lack of suitable markers, a statistically meaningful sample

is unavailable. However, our ﬁeld observations point out that

displacements of few centimetres generally characterize fractures

of metric size. Several studies (e.g. Cowie and Scholz, 1992; Schli-

sche et al., 1996) unravelled a linear relationship between fault

displacement (D) and fault length (L), the coefﬁcient of pro-

portionality being comprised between 10

3

and 10

1

. On the other

hand, Wilkins et al. (2001) demonstrated that the D/Lrelationship

appears to be rather weak in the case of reactivated joints, for

which it is characterized by low values of the correlation coefﬁ-

cient. According to these Authors, since reactivated joints attain

considerable length prior to slip, their D/Lratios are initially much

smaller than those for primary faults. Furthermore, as magnitude of

slip is not a consequence of fault growth, displacement across

reactivated joints in certain cases may be independent of length.

Fig. 11. Cartoon showing pluton deformation by widespread joint reactivation (‘diffuse

faulting’). Drawing of batholith fracture network was inspired by similar diagrams in

Price and Cosgrove (1990), here adopted with orientation consistent with structures

exposed in the Machu Picchu pluton.

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408 1405

Assuming that slip is independent of length, a constant value of

slip (D*) may be used for fractures having lengths larger than

a threshold value (L

0

) below which reactivation is supposed not to

occur. In this case, the shear strain is given by:

g

¼D

*

$Z

N

L

0

fðLÞdL¼D

*

$Z

N

L

0

PDFðLÞ$F

m

dL¼D

*

$FðL

0

Þ(2)

where f(L) dL is the number of fractures per m having length

comprised between Land (LþdL), F(L

0

) is the product between the

integral R

N

L

0

PDFðLÞdL(given by 1 CDF, where CDF is the cumula-

tive distribution of L

0

; e.g. Dekking et al., 2005) and mean fracture

density F

m

, i.e. F(L

0

)¼(1-CDF(L

0

))$F

m

.

An alternative approach involves displacements varying as

a function of length. It is worth noting that the data of Wilkins et al.

(2001) on reactivated (stratabound) joints suggest a signiﬁcant role

of mechanical layering in controlling the dispersion of D/Lratios. In

fact, stratabound – therefore constant-length – fractures contained

within a single bed tend to accumulate a roughly constant

displacement; however, different displacement values characterize

stratabound fracture sets contained in beds of different thickness.

Despite the control exerted by bedding, D/Lratios for the reac-

tivated joints analyzed by Wilkins et al. (2001) are all in the range of

0.01 <D/L<0.04. As we are dealing with homogenous plutonic

rocks for which there is no effect of mechanical layering, at a ﬁrst

approximation a linear relationship between Dand Lmay be

assumed in our variable displacement model. This would imply

that: (i) larger fractures are able to accommodate larger displace-

ments, and/or (ii) fracture growth occurred during joint

reactivation. The relationship is of the type:

D¼c$L(3)

where cis a constant. In this instance, equation (1) takes the form:

g

¼Z

N

0

D$fðLÞdL(4)

since a displacement D¼c$Lis associated with the number of

fractures per m having length comprised between Land LþdL

(given by f(L)dL). Therefore, equation (2) becomes:

g

¼c$Z

N

0

L$fðLÞdL¼c$Z

N

0

L$PDFðLÞ$F

m

dL¼c$L

*

(5)

where L* represents the product between mean fracture length

(given by: R

N

0

L$PDFðLÞdL) and mean fracture density (F

m

). Finite

strain associated with joint reactivation may be tentatively evalu-

ated using this constant aspect ratio (D/L) model, as well as the

previous constant slip model. For the constant aspect ratio model,

c¼10

2

is assumed as a representative ﬁrst-order approximation

(Scholz, 1990). For the constant slip model, a value of D¼3cmis

assumed as a representative ﬁrst-order approximation based on

ﬁeld observations (refer to Section 3.2); in this instance, a threshold

length value of 1 m is used (i.e. it is assumed that joints of length

below 1 m do not contribute to deformation at all). In both cases,

the same constant aspect ratio and constant slip values are

assumed for the three main reactivated joint sets. This seems

a reasonable approximation taking into account that the three joint

sets are at a similar angle (ca.50

) with respect to the maximum

compression direction associated with fracture reactivation. Finite

strain calculations involve a series of steps described below.

For each joint set, the ﬁnite strain tensor is obtained using

a reference frame having the xaxis parallel to the slip vector, the z

axis normal to fracture plane, and the yaxis normal to both xand z.

For the constant aspect ratio model, the strain tensors for joint Sets

1–3, obtained using equation (5), are:

T

1

¼2

6

4

100:08

01 0

00 1

3

7

5;T

2

¼2

6

4

100:05

01 0

00 1

3

7

5;

T

3

¼2

6

4

100:04

01 0

00 1

3

7

5ð6Þ

whereas for the constant slip model the strain tensors for joint Sets

1–3, obtained using equation (2), are:

T

1

¼2

6

4

100:08

01 0

00 1

3

7

5;T

2

¼2

6

4

100:04

01 0

00 1

3

7

5;

T

3

¼2

6

4

100:04

01 0

00 1

3

7

5ð7Þ

The strain tensors above are then referred to a common refer-

ence frame (arbitrarily chosen), and the composition of ﬁnite strain

components is carried out for each model by multiplying the three

matrices. As we are dealing with small ﬁnite strain values (of the

order of few points percent), the order of matrix multiplication has

a negligible effect.

For convenience – and obviously maintaining the concepts of

strain and stress clearly distinct – a reference frame is adopted here

whose axes lye parallel to the principal stress orientations deter-

mined by paleostress analysis (refer to Section 3.4). By referring the

calculated ﬁnite strain to such a reference frame, the following

tensors are obtained:

for the constant aspect ratio model;

T¼2

6

4

0:92 0:02 0:02

0:02 1:04 0:01

0:01 0:01 1:05

3

7

5ð8Þ

whereas for the constant slip model;

T¼2

6

4

0:92 0:01 0:01

0:02 1:03 0:01

0:01 0:01 1:05

3

7

5ð9Þ

Finally, orientation and magnitude of the principal ﬁnite

strain axes may be obtained for the two cases of constant aspect

ratio (Table 1) and constant slip (Tab le 2). The results are very

similar for the two models. In both cases the ﬁnite strain

ellipsoid is markedly oblate. The axis of maximum shortening

(Z) is roughly horizontal and parallel to that of maximum

compression (

s

1

) determined by paleostress analysis. The ﬁnite

strain tensors (8) and (9) also show that the bulk deformation

resulting from reactivation of different joint sets is very close to

coaxial, the non-diagonal components of the two matrices

attaining very minor values. Considering an average pluton

Table 1

Parameters of the ﬁnite strain ellipsoid obtained by the constant aspect ratio (D/L)

model (see text).

X;(1þe

1

)Y;(1þe

2

)Z;(1þe

3

)

Trend 346 162 254

Plunge 40 50 2

(1 þe) 1.054 1.033 0.920

S. Mazzoli et al. / Journal of Structural Geology 31 (2009) 1395–1408140 6

diameter of ca.30km(Carlotto et al., 1996), the ﬁnite strain

values obtained by both models would result in ca.2.5kmof

horizontal shortening across the granitoid body. Of course this

value represents just a ﬁrst-order approximation, as it depends

on the input parameters of fracture displacement and the

assumptions on D/Lrelationships for reactivated joints. In this

study, a conservative approach has been chosen in the evalua-

tion of bulk ﬁnite strain. For instance, the contribution of slip

along fractures not belonging to the main joint Sets 1–3 has

been neglected. For the constant slip model, the contribution to

deformation by fractures having length <1 m has also been

neglected. Furthermore, larger displacements likely associated

with mylonitic shear zones have not been taken into account.

Considering the rather subordinate occurrence of ductile shear

zones (and even more rare phyllonites), as well as the likely

amounts of displacements associated with tens of centimetres

thick ductile shear zones (being of the order of the tens of

metres according to Hull, 1988), the contribution of mylonitic

shear zones to bulk ﬁnite strain at the pluton scale is likely to be

minor. Nevertheless, our modelling most probably yields

minimum ﬁnite strain estimates. Yet these are likely to repre-

sent reasonable approximations for bulk pluton deformation in

terms of: (i) order of magnitude of ﬁnite strains; (ii) principal

ﬁnite strain axes orientation; (iii) reciprocal proportions of

principal ﬁnite strain axes magnitudes; and (iv) proportions of

coaxial vs. non-coaxial strain components.

5. Concluding remarks

– The Machu Picchu pluton displays different stages of shear

zone evolution, from (dominant) fault-like reactivation of

primary joints to (subordinate) mylonitic shear zone develop-

ment – with rare formation of more retrogressed phyllonites –

apparently reﬂecting the inﬂuence of ﬂuid inﬂux along

precursor fractures.

– Paleostress analysis indicates that shear reactivation of

different joint sets is kinematically consistent with ENE

oriented shortening associated with tectonic inversion of the

Permo-Liassic rift system in the high Eastern Cordillera.

– Deformation was accommodated by a form of distributedshear –

here termed ‘diffuse faulting’ – probably involving relatively

small displacements occurring over a very large number of

primary fractures, which form a pervasive network within the

pluton. Therefore, although strain localization occurs at the

metre scale, at the kilometre(or pluton) scale strain is essentially

distributed.

– Theoretical modelling based on fracture analysis and on the

application of various displacement–length relationships

suggests that reactivation of different master jointsets resulted

in pluton deformation dominated by markedly oblate, bulk

coaxial strain.

– Our modelling suggests that the process of ‘diffuse faulting’ is

likely to have accommodated relatively limited ﬁnite strains in

terms of percent shortening (8% according to our conservative

estimates); yet, this yields a signiﬁcant crustal shortening

(of a few kilometres) when deformation is integrated across the

whole granitoid body.

Acknowledgments

The paper greatly beneﬁted from thoughtful and constructive

critical comments by JSG Reviewer Fernando Hongn and Editor Joao

Hippertt. ISPRA co-authors of this paper gratefully acknowledge the

ﬁnancial support from their institution (formerly ENEA). ISPRA co-

authors carried out the present activities under the project

INTERFRASI, funded by the Italian Ministry of University and

Scientiﬁc Research and coordinated by Paolo Canuti and Claudio

Margottini. Field activities greatly beneﬁted from the support of the

Instituto Nacional de Cultura (INC) in Machu Picchu, for which the

Director Ferdinando Astete is thanked sincerely.

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