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

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.

Full text

‘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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