Statistical tests of scaling relationships for geologic structures

Displacement–length data from dilatant fractures (joints, veins, igneous dikes) and several varieties of deformation bands were analyzed statistically to investigate the applicability of mechanical models proposed for their formation. All 17 datasets are generally consistent with equilibrium or long-term power-law slopes on the displacement–length diagram of either 1.0 or 0.5. Similar to many faults, disaggregation deformation bands are consistent with a power-law scaling relation having a slope of approximately c = 1, implying a linear dependence of maximum displacement and discontinuity length (D_max = γL). In contrast, dilatant fractures, cataclastic deformation bands, and shear-enhanced compaction bands are consistent with a power-law scaling relation with a slope of approximately c = 0.5, implying a dependence of maximum displacement on the square root of length (D_max = αL^1/2). The scaling relations represent an average, or long-term equilibrium outcome of deformation for conditions such as length-scale, time-scale, temperature, chemistry, and an effectively homogeneous far-field stress field, allowing for variations such as rapid and/or localized behaviors. The displacement–length scaling of these geologic structures follows systematic relationships that provide information on host-rock properties and the physics of fracture and deformation-band propagation.     

A simple graphical method for estimating the components of the fault-slip vector

A simple calculation of the components of the total slip vector (D) on a fault plane allows the relationships between the magnitudes of the three slip components of D, the lateral horizontal displacement (L), the transversal horizontal displacement (T) and the vertical offset (V), to be determined. The contribution of each slip component to the total slip can be plotted jointly in a ternary diagram, assuming a unit length of the vector modulus and a suitable normalization for D. Each component equals the magnitude of D at the vertices of the diagram, hence it is possible to estimate the percentage contribution of each slip component to the total movement of a fault or a set of faults. The dip of the fault surface and the rake of the slickenlines are the input data required for displaying L, T and V relationships in these diagrams. This information may be useful in the analysis of movement geometry for different fault populations and in the determination of D by measuring just one of the fault-slip components, such as vertical slip associated with a fault scarp.     

Displacement-length scaling relations for faults on the terrestrial planets

Displacement-length (D/L)scaling relations for normal and thrust faults from Mars, and thrust faults from Mercury, for which sufficiently accurate measurements are available, are consistently smaller than terrestrial D/L ratios by a factor of about 5, regardless of fault type (i.e. normal or thrust). We demonstrate that D/L ratios for faults scale, to first order, with planetary gravity. In particular, confining pressure modulates: (1) the magnitude of shear driving stress on the fault; (2) the shear yield strength of near-tip rock; and (3) the Young's (or shear) modulus of crustal rock. In general, all three factors decrease with gravity for the same rock type and pore-pressure state (e.g. wet conditions). Faults on planets with lower surface gravities, such as Mars and Mercury, demonstrate systematically smaller D/L ratios than faults on larger planets, such as Earth. Smaller D/L ratios of faults on Venus and the Moon are predicted by this approach, and we infer still smaller values of D/L ratio for faults on icy satellites in the outer solar system. Collection of additional displacement-length and down-dip height data from terrestrial normal, strike-slip, and thrust faults, located within fold-and-thrust belts, plate margins, and continental interiors, is required to evaluate the influence of fault shape and progressive deformation on the scaling relations for faults from Earth and elsewhere.     

Implications of the fault scaling law for the growth of topography: mountain ranges in the broken foreland of north-east Tibet

A fault scaling law suggests that, over eight orders of magnitude, fault length L is linearly related to maximum displacement D. Individual faults may therefore retain a constant ratio of D/L as they grow. If erosion is minor compared with tectonic uplift, the length and along‐strike relief of young mountain ranges should thus reflect fault growth. Topographic profiles along the crests of mountain ranges in the actively deforming foreland of north‐east Tibet exhibit a characteristic shape with maximum height near their centre and decreasing elevation toward the tips. We interpret the along‐strike relief of these ranges to reflect the slip distribution on high‐angle reverse faults. A geometric model illustrates that the lateral propagation rate of such mountain ranges may be deciphered if their length‐to‐height ratio has remained constant. As an application of the model, we reconstruct the growth of the Heli Shan using a long‐term uplift rate of ～1.3 mm yr^?1 derived from ²¹Ne and ¹⁰Be exposure dating.     

Spatial distribution of deformation bands in damage zones of extensional faults in porous sandstones: Statistical analysis of field data

The distribution of deformation bands in damage zones of extensional faults in porous sandstones has been analyzed using 106 outcrop scanlines along which the position and frequency of deformation bands have been recorded. The analysis reveals a non-linear relationship between damage zone width and fault throw, a logarithmic decrease in deformation band frequency away from the fault core, as well as a fractal spatial distribution associated with clustering of the deformation bands. Furthermore, damage zones appear wider in the hanging wall than in the footwall, although the deformation band density is similar on both sides. Statistical trends derived from the database imply that fault growth in porous sandstones can be considered as a scale invariant process. From an initial process zone, the damage zone grows by a constant balance between the development of new deformation bands in the existing damage zone and the creation of new bands outside. Moreover, as the width of the damage zone increases throughout the active lifetime of a fault, the distribution of the deformation bands in the damage zone remains self-similar. Hence band distribution and damage zone width for seismically mapped faults can be predicted from the relationships found in this paper.     

Transtensional deformation in the Lake Tahoe region, California and Nevada, USA

Dextral transtensional deformation is occurring along the Sierra Nevada–Great Basin boundary zone (SNGBBZ) at the eastern edge of the Sierra Nevada microplate. In the Lake Tahoe region of the SNGBBZ, transtension is partitioned spatially and temporally into domains of north–south striking normal faults and transitional domains with conjugate strike-slip faults. The normal fault domains, which have had large Holocene earthquakes but account only for background seismicity in the historic period, primarily accommodate east–west extension, while the transitional domains, which have had moderate Holocene and historic earthquakes and are currently seismically active, primarily record north–south shortening. Through partitioned slip, the upper crust in this region undergoes overall constrictional strain.Major fault zones within the Lake Tahoe basin include two normal fault zones: the northwest-trending Tahoe–Sierra frontal fault zone (TSFFZ) and the north-trending West Tahoe–Dollar Point fault zone. Most faults in these zones show eastside down displacements. Both of these fault zones show evidence of Holocene earthquakes but are relatively quiet seismically through the historic record. The northeast-trending North Tahoe–Incline Village fault zone is a major normal to sinistral-oblique fault zone. This fault zone shows evidence for large Holocene earthquakes and based on the historic record is seismically active at the microearthquake level. The zone forms the boundary between the Lake Tahoe normal fault domain to the south and the Truckee transition zone to the north.Several lines of evidence, including both geology and historic seismicity, indicate that the seismically active Truckee and Gardnerville transition zones, north and southeast of Lake Tahoe basin, respectively, are undergoing north–south shortening. In addition, the central Carson Range, a major north-trending range block between two large normal fault zones, shows internal fault patterns that suggest the range is undergoing north–south shortening in addition to east–west extension.A model capable of explaining the spatial and temporal partitioning of slip suggests that seismic behavior in the region alternates between two modes, one mode characterized by an east–west minimum principal stress and a north–south maximum principal stress as at present. In this mode, seismicity and small-scale faulting reflecting north–south shortening concentrate in mechanically weak transition zones with primarily strike-slip faulting in relatively small-magnitude events, and domains with major normal faults are relatively quiet. A second mode occurs after sufficient north–south shortening reduces the north–south S_hmax in magnitude until it is less than S_v, at which point S_v becomes the maximum principal stress. This second mode is then characterized by large earthquakes on major normal faults in the large normal fault domains, which dominate the overall moment release in the region, producing significant east–west extension.     

Brittle normal faulting in the highest-grade Sambagawa metamorphic rocks of central Shikoku, southwest Japan: Indication of the exhumation into the upper crustal level

Analysis of fault system in the high-P/T type Sambagawa metamorphic rocks of central Shikoku, southwest Japan, shows that conjugate normal faults pervasively developed in the highest-grade biotite zone (upper structural level) in three study areas (Asemi river, Oriu and Niihama areas). These conjugate normal faults consist of NE–SW to E–W striking and moderately north-dipping (set A), and NNW–SSE striking and moderately east dipping (set B) faults. The fault set A is dominant compared to the fault set B, and hence most of deformation is accommodated by the fault set A, leading to non-coaxial deformation. The sense of shear is inferred to be a top-to-the-WNW to NNW, based on the orientations of striation or quartz slickenfibre and dominant north-side down normal displacement. These transport direction by normal faulting is significantly different from that at D₁ penetrative ductile flow (i.e. top-to-the-W to WNW). It has also been found that these conjugate normal faults are openly folded during the D₃ phase about the axes trending NW–SE to E–W and plunging west at low-angles or horizontally, indicating that normal faulting occurred at the D₂ phase. D₂ normal faults, along which actinolite breccia derived from serpentinite by metasomatism sometimes occurs, perhaps formed under subgreenschist conditions (ca. 250 °C) in relation to the final exhumation of Sambagawa metamorphic rocks into the upper crustal level. The pervasive development of D₂ normal faults in the upper structural level suggests that the final exhumation of Sambagawa metamorphic rocks could be caused by “distributed extension and normal faulting (removal of overburden)” in the upper crust.     

Structural controls on gold mineralisation and the nature of related fluids of the Paiol gold deposit, Almas Greenstone Belt, Brazil

Chemical analyses suggest that the metavolcanic rocks of the Almas Greenstone Belt (AGB), Tocantins State, Brazil have a continental affinity, possibly related to a continental rift environment. They were metamorphosed to amphibolite facies during a regional tectono-metamorphic event (D_n), retrogressed to greenschist facies assemblages and then hydrothermally altered within dextral strike–slip shear zones (D_n+1). Fracture sets related to D_n+2 intersect S_n+1.The Paiol Gold Mine is one of several mineralised zones within metabasic and meta-intermediate rocks of the AGB. It exploits shoots of sulphide–Au–quartz mineralisation that occupy dilational zones approximately perpendicular to an elongation lineation (L_n+1) within mylonitic foliation S_n+1 (S_n+1=S within the S–C fabric). The dilational zones probably formed due to dextral displacement on sinistrally en echelon C surfaces. Minor amounts of gold may have been introduced or remobilised during D_n+2.Coexisting primary and pseudosecondary fluid inclusions in mineralised quartz veins from ore shoots comprise a high-salinity three-phase type (Type II) and a lower salinity two-phase type (Type I). Homogenisation temperatures for Type II inclusions range from 200 to 410 °C and Type I from 90 to 320 °C. The inclusions and their temperature ranges are believed to reflect heat exchange and some mixing between the two fluid types under relatively constant ambient temperatures, but variable (though broadly declining) fluid temperatures. This took place late in D_n+1 in conjunction with greenschist facies retrogression and localised hydrothermally induced metasomatism.     

Analysis of faulting in porous sandstones

Faults in porous sandstones occur in three forms: deformation bands about 1-mm thick and tens of m long and across which offsets are a few mm; zones of deformation bands constituted of many closely spaced deformation bands across which offsets are a few cm or dm; and slip surfaces, that is, distinct surfaces within zones of deformation bands across which offsets are a few m to a few tens of m. Deformation bands represent highly localized deformation; analogous localization within a field of homogeneous deformation is theoretically possible in inelastic materials with certain ranges of constitutive parameters. Crushing and consolidation of sandstone within a band cause the material there to become stiffer than the surrounding porous sandstone. A zone of deformation bands behaves mesoscopically much as a stiff inclusion in a soft matrix. According to the constitutive model assumed to investigate the formation of deformation bands, an instability can develop, and strain increments within the zone of deformation bands can become boundlessly large when the far-field stresses reach critical values. This instability is here associated with the formation of slip surfaces.     

Solution transfer syn-S2: an inferred means of deriving fault fill in the lake Moondarra area, Mt. Isa, Queensland, Australia, based on oxygen isotope results

Many of the faults within the Lake Moondarra area cropout as wide zones which are filled with massive or fibrous milky quartz. Additionally, a variety of rock fragments from the surrounding metasediments are present in the fault zones. The second regional slaty cleavage, S₂, is locally observed through the quartz and country rock fragments within some of the zones, indicating that these fault fills originated pre- or early syn-S₂. The absence of the first regional slaty cleavage, S₁, suggests that the fault fills developed post or late syn-S₁. Evidence supporting an early syn-S₂ timing for the development of these fills is provided by the results of oxygen isotope analysis carried out on quartz specimens collected from the faults and also by the nature of the quartz. Specimens of quartz taken from the various fault zones have δ¹⁸O values between 12.4 and 14.5‰. This suggests that metamorphic water isotopically equilibrated with connate formation water was the aqueous fluid which transported the silica. δ¹⁸O values for the silica in the quartz-rich, sometimes dolomitic, metasediments of the Mount Isa and Haslingden Groups within the Lake Moondarra area are similar to the quartz within the fault fills. The lack of any metamorphic event between the first and second deformation, together with the sometimes fibrous nature of the fault-filling material with fibres parallel to the mineral elongation in S₂ (i.e. L₂²), suggests that the quartz in the faults was derived syntectonically at grain to grain contacts in the metasediments within the Lake Moondarra area, early in the development of S₂. The quartz is believed to have moved by the process of solution transfer to the faults as they underwent dilation during D₂. Subsequently the quartz was precipitated as a result of a chemical potential gradient.     

Collision leading to multiple-stage large-scale extrusion in the Qinling orogen: Insights from the Mianlue suture

The geologic framework of the Phanerozoic Qinling–Dabie orogen was built up through two major suturing events of three blocks. From north to south these include the North China craton (including the north Qinling block), the Qinling–Dabie microblock, and the South China craton (including the Bikou block), separated by the Shangdan and Mianlue sutures. The Mianlue suture zone contains evidence for Mesozoic extrusion tectonics in the form of major strike–slip border faults surrounding basement blocks, a Late Paleozoic ophiolite and a ca. 240–200 Ma thrust belt that reformed by 200–150 Ma thrusts during A-type (intracontinental) subduction. The regional map pattern shows that the blocks are surrounded by complexly deformed Devonian to Early Triassic metasandstones and metapelites, forming a regional-scale block-in-matrix mélange fabric. Five distinct tectonic units have been recognized in the belt: (1) basement blocks including two types of Precambrian basement, crystalline and transitional; (2) continental margin slices including Early Paleozoic strata, and Late Paleozoic fluviodeltaic sedimentary rocks, proximal and distal fan clastics, reflecting the development of a north-facing rift margin on the edge of the South China plate; (3) out of sequence oceanic crustal slices including strongly deformed postrift, deep-water sedimentary rocks, sheeted dikes, basalts, and mafic–ultramafic cumulates of a Late Paleozoic ophiolite suite, developing independent of the rift margin in a separate basin; (4) out-of-sequence island-arc slices; (5) accretionary wedge slices. All the tectonic units were deformed during three geometrically distinct deformation episodes (D₁, D₂ and D₃ during 240–200 Ma). Units 2–4 involved southward thrusting and vertical then southward extrusion of about 20 km of horizontal displacement above the autochthonous basement during the D₁ episode. Thrust slices 20 km south of the Mianlue suture are related to this vertical extrusion due to the same rock assemblages, ages and kinematics. The D₂ and D₃ episodes folded all the units in a thick-skinned style about east–west (D₂) and west–northwest (D₃) axes in the Mianlue suture zone. An early foreland propagating sequence of accretion of Late Paleozoic rocks deposited above the Yangtze craton is not involved in D₁ deformation but is temporally equivalent to the D₂ and D₃ deformation in the Mianlue suture. Two stages of strike–slip faulting mainly occurred at the end of D₂ and D₃, respectively. During D₂ deformation, the Bikou block was obliquely indented to the ESE into the Mianlue suture, rather than being thrust over the Mianlue suture from the north as a part of the Qinling–Dabie microblock. During D₃ deformation, however, the Bikou block was bounded by the south boundary fault of the Mianlue suture, and the Yangpingguan fault on the south. These faults are coeval strike–slip faults, but of opposite senses, and accommodated minor southwestward extrusion of the Bikou block into Songpan–Ganze orogen. The other basement blocks north of the Mianlue suture were extruded eastward by about 20 km of lateral displacement, based on the offset of the Wudang dome, during the D₃ episode due to the northeastward indentation of the Hannan complex of the South China craton. Post-D₃ emplacement of granite, cutting across the strike–slip faults such as the Mianlue suture, provides a minimum age of 200 Ma for D₃ deformation. Therefore, based on insights from the evolution of the Mianlue suture, the D₂ and D₃ episodes in the Mianlue suture and its neighbors are not responsible for and associated with the two-stage extrusion of the Dabie UHP-HP terranes from the Foping dome to the present erosional surface (more than 350 km).     

Effects of Young's modulus on fault displacement

Elastic crack models predict a linear relationship between displacement (u) and rupture (trace) length (L) during slip in a fault zone. Attempts to find universal-scaling laws for L/u, however, have generally failed. Here I propose that these attempts have failed because they do not take into account the changes in the mechanical properties, in particular Young's modulus (stiffness), of the fault zone as it evolves. I propose that Young's modulus affects fault displacement both spatially and temporally: spatially when the trace of a fault at a given time dissects host rocks of different stiffnesses, and temporally when the stiffness of the fault zone itself changes. During the evolution of an active fault zone, the effective Young's modulus of its damage zone and fault core normally decreases, and so does the L/u ratio of the fault. By contrast, during inactive periods sealing and healing of the damage zone and core may increase the stiffness, hence the L/u ratio in subsequent slips. This model predicts that not only will the scaling of L/u within a given fault population vary in space and time, but also that of individual faults. To cite this article: A. Gudmundsson, C. R. Geoscience 336 (2004).     

Faulted joints: kinematics,displacement–length scaling relations and criteria for their identification

Structural geometries and kinematics based on two sets of joints, pinnate joints and fault striations, reveal that some mesoscale faults at Split Mountain, Utah, originated as joints. Unlike many other types of faults, displacements (D) across faulted joints do not scale with lengths (L) and therefore do not adhere to published fault scaling laws. Rather, fault size corresponds initially to original joint length, which in turn is controlled by bed thickness for bed-confined joints. Although faulted joints will grow in length with increasing slip, the total change in length is negligible compared to the original length, leading to an independence of D from L during early stages of joint reactivation. Therefore, attempts to predict fault length, gouge thickness, or hydrologic properties based solely upon D–L scaling laws could yield misleading results for faulted joints. Pinnate joints, distinguishable from wing cracks, developed within the dilational quadrants along faulted joints and help to constrain the kinematics of joint reactivation.     

Mechanisms of thrust faulting in the gran sasso chain, central apennines, italy

The Gran Sasso chain in Central Italy is made up of an imbricate stack of eight thrust sheets, which were emplaced over the Upper Miocene—Lower Pliocene Laga Flysch. The thrust sheets are numbered from 1 to 8 in order of their decreasing elevation in the tectonic stack, and their basal thrusts are numbered from T₁ to T₈, accordingly. On the basis of their different deformation features, the major thrust faults fall into three groups: (1) thrust faults marked by thick belts of incoherent gouges and breccia zones (T₁, T₂, T₃); (2) thrust faults characterized by a sharp plane which truncates folds that had developed in the footwall rocks (T₅, T₆); and (3) thrust faults truncating folds developed in both the hangingwall and footwall units, and bordered by foliated fault rocks (T₇). The deformation features observed for the different faults seem to vary because of two combined factors: (1) lithologic changes in the footwall and hangingwall units separated by the thrust faults; and (2) increasing amounts of deformation in the deepest portions of the imbricate stack. The upper thrust sheets (from 1 to 6) are characterized by massive calcareous and dolomitic rocks, they maintain a homoclinal setting and are truncated up-section by the cataclastic thrust faults. The lowermost thrust sheets (7 and 8) are characterized by a multilayer with competence contrasts, which undergoes shear-induced folding prior to the final emplacement of the thrust sheets. Bedding and axial planes of folds rotate progressively towards the T₅, T₆, T₇ and T₈ thrust boundaries, and are subsequently truncated by propagation of the brittle thrust faults. The maximum deformation is observed along the T₇ thrust fault, consistent with horizontal displacement that increases progressively from the uppermost to the lowermost thrust sheet in the tectonic stack. The axial planes of the folds developed in the hangingwall and footwall units are parallel to the T₇ thrust fault, and foliated fault rocks have developed. Field data and petrographic analysis indicate that cleavage fabrics in the fault rocks form by a combination of cataclasis, cataclastic flow and pressure-solution slip, associated with pervasive shearing along subtly distributed slip zones parallel to the T₇ thrust fault. The development of such fabrics at upper crustal levels creates easy-slip conditions in progressively thinner domains, which are regions of localized flow during the thrust sheet emplacement.     

Microstructural evolution of the Seridó Belt, NE-Brazil: the effect of two tectonic events on development of c-axis preferred orientation in quartz

The polyphase evolution of the Seridó Belt (NE-Brazil) includes D₁ crust formation at 2.3–2.1 Ga, D₂ thrust tectonics at 1.9 Ga and crustal reworking by D₃ strike-slip shear zones at 600 Ma. Microstructural investigations within mylonites associated with D₂ and D₃ events were used to constrain the tectono-thermal evolution of the belt. D₂ shear zones commenced at deeper crustal levels and high amphibolite facies conditions (600–650 °C) through grain boundary migration, subgrain rotation and operation of quartz c-prism slip. Continued shearing and exhumation of the terrain forced the re-equilibration of high-T fabrics and the switching of slip systems from c-prism to positive and negative a-rhombs. During D₃, enhancement of ductility by dissipation of heat that came from syn-D₃ granites developed wide belts of amphibolite facies mylonites. Continued shearing, uplift and cooling of the region induced D₃ shear zones to act in ductile-brittle regimes, marked by fracturing and development of thinner belts of greenschist facies mylonites. During this event, switching from a-prism to a-basal slip indicates a thermal path from 600 to 350 °C. Therefore, microstructures and quartz c-axis fabrics in polydeformed rocks from the Seridó Belt preserve the record of two major events, which includes contrasting deformation mechanisms and thermal paths.     

A geometric model for the formation of deformation band clusters

Arrays of closely-spaced (approximately <70 mm) sub-parallel cataclastic deformation bands are common structures in deformed, high-porosity (∼10–35%) sandstones. The distribution of strain onto many small-displacement deformation bands is thought by some to result from strain-hardening of the cataclasite within individual bands. Examination of both normal and strike-slip faults with displacements ≤7 m from southeastern Utah, USA, and the North Island of New Zealand suggests, however, that clusters of deformation bands systematically develop at fault geometric irregularities (e.g., fault bends, steps, relays, intersections and zones of normal drag). The strain-hardening model does not account for clustering of deformation bands at fault geometric irregularities or the associated widespread coalescence of bands, and is not unequivocally demonstrated by post-peak macroscopic mechanical responses in laboratory rock deformation experiments. A geometric model is proposed in which individual bands within clusters develop sequentially due to migration of incremental shear strains at fault geometric irregularities as part of a slip localisation, asperity removal and strain weakening process. The geometric model, which does not require strain hardening of the fault rock, applies for the duration of faulting and a range of rock types in the brittle upper crust.     

Structural similarity and variety at the tips in a wide range of strike–slip faults: a review

Strike–slip faults are often accompanied by a variety of structures, particularly at their tips. The zones of additional fracturing are classified as tip‐damage zones. These zones can be subdivided into several different damage patterns based on the nature and orientation of faults and fractures developed. Damage zones at the ends of small strike–slip faults (mode II tips) develop wing cracks, horsetail splays, antithetic faults, synthetic branch faults and solution surfaces. Similar tip‐damage patterns are also commonly observed at larger (regional) scales, but with a dominance of faulting over tensile cracks and solution surfaces. Wing cracks and horsetail splays developed at small‐scale faults are replaced by normal faults in large‐scale faults. Antithetic faults and synthetic branch faults are observed at small and large scales. Thrust faults are developed at large scales, in a similar pattern to solution surfaces at a small scale. All these structures may show slightly different angular relationships to the master fault at small and large scale, but develop in response similar stress distribution and mechanics around the fault. Thus, mode II tip‐damage zones show similar patterns over a wide range of fault scales.     

Effect of sampling and linkage on fault length and length–displacement relationship

The power-law exponent (n) in the equation: D=cL ⁿ , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10⁻²–10⁵ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n _d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.     

Correlation between distribution and shape of VMS deposits and regional deformation patterns,Skellefte district,northern Sweden

The Skellefte district in northern Sweden is host to abundant volcanogenic massive sulphide (VMS) deposits comprising pyritic, massive, semi-massive and disseminated Zn–Cu–Au ± Pb ores surrounded by disseminated pyrite and with or without stockwork mineralisation. The VMS deposits are associated with Palaeoproterozoic upper crustal extension (D₁) that resulted in the development of normal faults and related transfer faults. The VMS ores formed as sub-seafloor replacement in both felsic volcaniclastic and sedimentary rocks and partly as exhalative deposits within the uppermost part of the volcanic stratigraphy. Subsequently, the district was subjected to deformation (D₂) during crustal shortening. Comparing the distribution of VMS deposits with the regional fault pattern reveals a close spatial relationship of VMS deposits to the faults that formed during crustal extension (D₁) utilising the syn-extensional faults as fluid conduits. Analysing the shape and orientation of VMS ore bodies shows how their deformation pattern mimics those of the hosting structures and results from the overprinting D₂ deformation. Furthermore, regional structural transitions are imitated in the deformation patterns of the ore bodies. Plotting the aspect ratios of VMS ore bodies and the comparison with undeformed equivalents in the Hokuroko district, Japan allow an estimation of apparent strain and show correlation with the D₂ deformation intensity of the certain structural domains. A comparison of the size of VMS deposits with their location shows that the smallest deposits are not related to known high-strain zones and the largest deposits are associated with regional-scale high-strain zones. The comparison of distribution and size with the pattern of high-strain zones provides an important tool for regional-scale mineral exploration in the Skellefte district, whereas the analysis of ore body shape and orientation can aid near-mine exploration activities.     

Tectonic geomorphology of the easternmost extension of the Gulf of Corinth (Beotia, Central Greece)

The easternmost sector of the Gulf of Corinth, the Beotia area in Central Greece, is an area with active normal faults located between the two major rift structures of Central Greece, the Gulf of Corinth and the North Gulf of Evia. These active normal faults include WNW to E–W and NE to ENE-trending faults affect the landscape and generate basin and range topography within the Beotia. We study four normal fault zones and drainage basin geometry in the easternmost sector of the Gulf of Corinth to document the impact of active tectonics on the landscape evolution. Fault and drainage geometry are investigated based on detailed field mapping and high-resolution digital elevation models. Tectonic geomorphic analysis using several parameters of active tectonics provides information concerning the relative tectonic activity and fault growth. In order to detect areas of lateral stream migration that could indicate recent tectonic activity, the Transverse Topographic Symmetry Factor and the Asymmetry Factor are used to analyse drainage basin geometry in six large drainage basins and a drainage domain covering the study area. Our results show that vertical motions and tilting associated with normal faulting influence the drainage geometry and its development. Values of stream-gradient indices (S_L) are relatively high close to the fault traces of the studied fault zones suggesting high activity. Mountain-front sinuosity (S_mf) mean values along the fault zones ranges from 1.08 to 1.26. Valley floor width to valley height ratios (V_f) mean values along the studied fault zones range between 0.5 and 1.6. Drainage basin shape (B_S) mean values along the fault zones range from 1.08 to 3.54. All these geomorphic parameters and geomorphological data suggest that the analyzed normal faults are highly active. Lateral fault growth was likely produced by primarily eastward propagation, with the WNW to E–W trending faults being the relatively more active structures.