Propagation, interaction and linkage in normal fault systems

Earth-Science Reviews 58 (2002) 121 – 142 www.elsevier.com/locate/earscirev

Propagation, interaction and linkage in normal fault systems D.C.P. Peacock* Department of Geology, 876 Natural Science Complex, State University of New York, Buffalo, NY 14260, USA Received 19 September 2000; accepted 3 September 2001

Abstract Recent advances are reviewed in the understanding of the geometry and development of steep, planar normal faults with up to hundreds of meters throw in multilayered sedimentary rocks. This essential class of structures is of particular importance in basin formation and hydrocarbon development. The role of interaction and linkage between fault segments is emphasized. Such normal faults usually consist of complex zones of overstepping and linked segments, within which relay ramps are significant structures. Displacement is transferred between normal faults that overstep in map view and that dip in the same direction by tilting of beds to form a relay ramp and by the development of minor faults. Oversteps and bends also occur along normal faults in cross-section, these commonly being controlled by lithological variations. Damage zones are zones of fractures developed around faults as they initiate, propagate, link and build up displacement. Various models have been developed to account for the accumulation of slip and the finite displacement on faults. Recent models emphasize the importance of fault interaction and other mechanical effects in causing variations in the displacement characteristics of faults. A population of normal faults typically displays a linear length – displacement ratio and obeys a power – law-scaling relationship for displacement. It is likely, however, that complex networks of faults and reverse-reactivated normal faults do not obey simple scaling relationships, with the pattern and history of deformation changing with scale. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Normal faults; Propagation; Interaction; Linkage

1. Introduction There has been great interest in normal faults over the past few years because of their role in basin development (e.g. Gibbs, 1984) and because of their significance in mining (e.g. Rippon, 1985) and hydrocarbon exploration (e.g. Hardman and Booth, 1991). Since the early 1980s, attempts have been made to describe the geometry and development of normal faults using models for the development of thrust * Present address: Robertson’s Research International Ltd., Llandudno LL30 1SA, United Kingdom. Tel.: +44-0-1492-581811; fax: +44-0-1492-583416. E-mail address: [email protected] (D.C.P. Peacock).

systems (e.g. Wernicke, 1981; Wernicke and Burchfiel, 1982; Beach, 1984; Gibbs, 1984; Simony and Carr, 1997). This thin-skinned view of normal faulting has been successfully applied to several regions including the Basin and Range Province of western USA (e.g. Davis and Hardy, 1981; see review by Davis and Reynolds, 1996). Since the mid-1980s, however, models have been developed specifically for the type of normal fault that typically occur in sedimentary basins. Such normal faults are usually steep, planar and with displacements of up to hundreds of metres. This thick-skinned view of normal faults is based on detailed field observations (e.g. Barnett et al., 1987; Walsh and Watterson, 1987; Larsen, 1988; Peacock and Sanderson, 1991, 1994a; Dawers et al., 1993) and

0012-8252/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 5 2 ( 0 1 ) 0 0 0 8 5 - X

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on improved seismic data (e.g. Roberts and Yielding, 1994; Mansfield and Cartwright, 1996; Nicol et al., 1996a; Pickering et al., 1997). This is a key class of faults because of their effects on hydrocarbon exploitation in many sedimentary basins. Large, low-angle normal faults, for which thrust geometries may be appropriate, are not discussed here. This paper is a personal view of the substantial advances that have been made in the understanding of steep normal faults in multilayered sedimentary rocks over the last decade. These views have been strongly influenced by analyses of normal faults in the Jurassic sedimentary rocks of the Somerset coast (Peacock and

Sanderson, 1991, 1992, 1994a). Emphasis is placed on the primary role of segmentation in fault geometry and evolution. This paper is not intended as a literature review, but original references are used wherever possible and key references are given. Peacock et al. (2000) define most of the terms used.

2. The segmentation of normal faults in map view, cross-section and three dimensions It has long been recognized that normal faults are segmented (e.g. Goguel, 1952), but there has been

Fig. 1. Photographs of relay ramps exposed on limestone bedding planes at East Quantoxhead, Somerset, UK (Peacock and Sanderson, 1994a). Bedding is tilted between two normal faults that overstep in map view. (a) The relay ramp is not breached, but veins link between the overstepping faults. (b) The relay ramp has been partially breached by small connecting faults.

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increased understanding over the past few years of the vital role of segmentation in the propagation and geometry of faults. This section discusses some of these advances. A characteristic feature of faults is that they are composed of overstepping (e.g. Biddle and ChristieBlick, 1985) and linked segments (Fig. 1) over a wide range of scales (Tchalenko, 1970). Examples of fractures that overstep from the millimeter to the kilometer scale are given by Pollard and Aydin (1984, fig. 6), Nelson et al. (1992, fig. 3) and Peacock and Sanderson (1994a, fig. 14). Early models for normal faults considered them as simple, single planes (e.g. Gibbs, 1984; Barnett et al., 1987) although, in some cases, the segmented nature of faults was recognized (e.g. Goguel, 1952). Segmentation has a strong controlling influence on earthquakes and surface ruptures (e.g. Crone and Haller, 1991; dePolo et al., 1991; Zhang et al., 1991) and, therefore, on fault development. To understand the development and final geometry of normal faults, it is, therefore, vital to understand the role of segmentation (Peacock and Sanderson, 1996). Transfer zones that occur at oversteps between normal faults in map view are described in Section 3. Oversteps and bends along normal faults are commonly visible on seismic sections and in cliff exposures. For example, Chapman and Meneilly (1991, fig. 6) show a fault zone with oversteps on seismic cross-sections. Similarly, Peacock and Zhang (1994) and Childs et al. (1996) describe oversteps and bends along cross-sections through normal faults with less than 2-m displacement at Flamborough Head, Yorkshire, UK (Fig. 2). Lithological variations, particularly the relative proportions of brittle to less brittle layers, have significant effects on fault geometry (Peacock and Zhang, 1994). Pull-aparts (extensional bends) typically develop in brittle layers where there is a high proportion of less brittle layers in the rock sequence (Fig. 3). Faults initiate in the brittle layers where there is a greater thickness of brittle layers than less brittle layers, with contractional bends developing in less brittle layers where faults have gentler dips (Fig. 2b). Minor structures typically cause displacement minima at contractional bends including such structures as minor faults, brecciation, folds, compaction and pressure solution (Fig. 3c). Martel (1999) shows how a planar fault will tend to become curved as displacement increases because of varia-

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Fig. 2. Line drawings of normal faults in cross-sections through Cretaceous Chalk cliffs at Flamborough Head, UK (Peacock and Zhang, 1994). (a) An extensional overstep, in which a pull-apart is accommodated by folding of beds, extension fractures and by some brecciation. (b) A contractional overstep accommodated by thinning of beds, a network of small-scale synthetic and antithetic faults and, possibly, by a low-angle connecting fault.

tions in friction, fault strength, fault interaction and material heterogeneity. The model of Barnett et al. (1987) and of Walsh and Watterson (1987) idealized isolated normal faults as simple planes that have elliptical tip lines, with contours of equal displacement being elliptical about a maximum in the center of the fault (Fig. 4a). This model gives a good approximation of the shape and displacement patterns of isolated faults, but fieldwork and seismic data have shown that normal faults are almost always segmented in both map view and crosssection (e.g. Walsh and Watterson, 1987). This implies that normal faults have complex three-dimensional geometries, which has been proven using threedimensional seismic methods (e.g. Childs et al., 1995; Mansfield and Cartwright, 1996). Aydin and Schultz (1990) and Peacock and Sanderson (1991, 1994a,

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Fig. 3. The development of normal faults and relay ramps in a limestone-shale sequence (c.f. Peacock and Sanderson, 1992, fig. 9). (a) Veins initiate in the limestones (brittle), producing boudins. Cartwright and Mansfield (1998) also show the development of extension fractures at the tips of normal faults. The less brittle units extend without visible fracturing. (b) Extension continues, with shear developing. The faults propagate into the shales, allowing further displacement to occur and pull-aparts to develop. Relay ramps develop at oversteps between faults in map view. Displacement minima typically occur at oversteps (e.g. Ellis and Dunlap, 1988; Peacock and Sanderson, 1991). (c) Linkage occurs between segments, e.g. with breaching of relay ramps (Peacock and Sanderson, 1994a).

1996) show that mechanical interaction (e.g. Segall and Pollard, 1980) can influence fault propagation, modifying the idealized elliptical tip-line geometries of the segments. This would cause the type of complex three-dimensional geometry illustrated in Fig. 4b.

3. Relay ramps and transfer zones It is essential to understand the structures that occur at oversteps because they are so common and they

strongly influence normal fault development. A relay ramp (Fig. 1) is an area of tilting between two normal fault segments that overstep in map view and that have the same dip direction (Goguel, 1952; Larsen, 1988). Macdonald (1957) called these structures monoclinal ramps, with other synonymous terms being given by Peacock et al. (2000). A relay ramp connects the footwall of one fault or fault zone with the hanging wall of another and transfers displacement between the overstepping segments (Peacock and Sanderson, 1991, 1994a). Complex faulting can

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Fig. 4. Models for normal faults viewed perpendicular to the fault surfaces, illustrating how displacement varies on the fault plane. (a) The model of Barnett et al. (1987) and Walsh and Watterson (1987) for an isolated normal fault. The tip line is elliptical, with contours of equal displacement distributed around the displacement maximum in the center of the fault plane. Displacement decreases approximately linearly toward the fault tip line. (b) Model for a segmented fault zone. Segmentation occurs in both cross-section and map view, with interaction between segments causing deviations from the model of an elliptical tip line (a). The individual fault segments and the fault zone as a whole have less regular displacement characteristics than predicted by the model shown in (a).

occur in a relay ramp to accommodate the tilting of beds and to link the overstepping faults (Griffiths, 1980; Stewart and Hancock, 1991, figs. 4a and 5a). A transfer zone (Fig. 5) is a general term for an area of deformation between two normal faults that overstep in map view (Morley et al., 1990), so includes relay ramps. Transfer zones include antithetic transfer zones, where the overstepping faults have different dip directions, which are characterized by complex warping of beds (Morley et al., 1990). See Faulds and Varga (1998) and Peacock et al. (2000) for various definitions of transfer zone and accommodation zone. 3.1. The evolution of relay ramps A wide variety of relay ramp geometries occur, but these can be classified into four groups based on the

degree of interaction and linkage between the fault segments. Peacock and Sanderson (1994a, fig. 3) interpreted these four groups as evolutionary stages. At Stage 1, the subparallel, noncoplanar, possibly underlapping fault segments do not interact. Stage 2 involves the tilting of beds between two interacting faults to produce a relay ramp (e.g. Peacock and Sanderson, 1994a, fig. 5). The overstepping faults may be unconnected (Peacock and Sanderson, 1991) or connected (e.g. Huggins et al., 1995) at depth, as discussed by Willemse (1997) and by Walsh et al. (1999). At Stage 3, connecting fractures start to break the relay ramp (e.g. Peacock and Sanderson, 1994a, figs. 7 and 10); thus, the relay ramp is breached (Childs et al., 1993, 1995). Stage 4 is when the relay ramp is destroyed to produce a single, irregular fault that has an along-strike bend (e.g. Peacock and

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Fig. 5. The classification of transfer zones, from Morley et al. (1990, fig. 1). Types of transfer zone are shown in map view. In this scheme, relay ramps are approaching or overlapping synthetic transfer zones.

Sanderson, 1994a, fig. 10; Walsh et al., 1999). Ferrill et al. (1999) show that the ‘‘corrugation’’ of large faults results from the linkage of small fault segments. The evolutionary stages may develop through time (Fig. 3), but can also occur spatially, down the dip of the fault zone (Fig. 6). Fault segments and linked faults show characteristic variability in displacement –distance profiles that accompanies the interaction and linkage of the segments (see Section 5). Displacement transfer by a relay ramp is accompanied by steep displacement gradients along fault segments at the overstep (e.g. Peacock and Sanderson, 1991; Contreras et al., 2000; Gupta and Scholz, 2000). Tilting of beds within a relay ramp typically contributes to a minimum in total fault displacement at a linkage point (Peacock and Sanderson, 1991, 1994a, fig. 9). 3.2. The significance of relay ramps and transfer zones Relay ramps are common in extensional basins, where they can be key locations for hydrocarbon

migration (Larsen, 1988; Morley et al., 1990; Peacock and Sanderson, 1994a, fig. 16). Fluid flow can occur from a basin in the hanging wall, up the ramp to the footwall and, thereby, out of the basin. The faults and tilting of beds that occur in relay ramps may also cause hydrocarbon entrapment. For example, the Beryl Embayment in the North Sea is a relay ramp that occurs at a left step between the east-dipping faults that form the boundary between the East Shetland Platform and the South Viking Graben (Peacock and Sanderson, 1994a, fig. 16a). The Beryl Embayment relay ramp lies between two main fault traces, separated by about 30 km and is represented by an area of generally NE-dipping strata that connects the platform with the graben. Synthetic and antithetic faults occur in the Stage 3 relay ramp and appear to isolate blocks of rock to control the position of several oil fields, including Beryl and Gryphon. Classic examples of relay ramps are exposed in the Liassic rocks of the Somerset coast (e.g. Peacock and Sanderson, 1991, 1994a) and in Devils Lane, Canyonlands National Park, Colorado (e.g. Moore and Schultz, 1999).

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(2) Rupture patterns and sequences (Crone and Haller, 1991; dePolo et al., 1991; Zhang et al., 1991; Gupta and Scholz, 2000); (3) Topography, erosion and drainage (Morley et al., 1990; Roberts and Jackson, 1991; Gawthorpe and Hurst, 1993; Leeder and Jackson, 1993; Jackson and Leeder, 1994); (4) Basin development (Anders and Schlische, 1994; Contreras et al., 2000); (5) Stratigraphy (Gawthorpe and Hurst, 1993; Schlische and Anders, 1996; Gupta et al., 1998; Dawers and Underhill, 2000); (6) Outcrop patterns (Wu and Bruhn, 1994); (7) The location of volcanic activity (Acocella et al., 1999).

4. Fault damage zones

Fig. 6. Block diagram of the possible three-dimensional geometry of a relay ramp (also see Peacock and Sanderson, 1994a, fig. 12; Peacock and Parfitt, in press). Different levels have different displacements and different stages of relay ramp evolution, with a spatial development occurring from stage 4 at the branch line (Butler, 1982) to stages 3 and 2 up or down the dip of the fault. It is possible that such faults pass vertically into stage 1 relay ramps, i.e. apparently isolated, noninteracting segments. Huggins et al. (1995) and Walsh et al. (1999, fig. 1) show a model in which a relay ramp is nucleated at an irregularity on a tip line of an isolated fault.

Active relay ramps have been described from many regions including the Basin and Range Province, western USA (e.g. Crone and Haller, 1991; dePolo et al., 1991; Machette et al., 1991; Dawers and Anders, 1995), the East African Rift (Griffiths, 1980; Morley et al., 1990), Greece (Jackson et al., 1982; Roberts and Jackson, 1991; Stewart and Hancock, 1991), Hawaii (Macdonald, 1957; Peacock and Parfitt, in press) and Iceland (Acocella et al., 2000, fig. 3). Morley et al. (1990) and Gawthorpe and Hurst (1993) give descriptions of active relay ramps from various other locations around the World. Active relay ramps can control: (1) Slip and finite displacement patterns (e.g. Zhang et al., 1991; Anders and Schlische, 1994; Dawers and Anders, 1995) (see Section 5);

Early models for normal faults, based on models for thrusts and on two-dimensional seismic data, assumed the simple propagation of a single fault plane (e.g. Gibbs, 1984). Detailed fieldwork has shown that fault planes and fault tips are typically associated with complex zones of fracturing and that this fracturing plays a crucial role in fault development (e.g. Cowie and Scholz, 1992c). A fault damage zone (Fig. 7) is an area of fracturing and strain around and related to a fault (Wu and Groshong, 1991; Cowie and Scholz, 1992c; McGrath and Davison, 1995; Cowie and Shipton, 1998; Vermilye and Scholz, 1998). Damage zones are the products of pre-faulting strain, fault propagation, displacement and linkage processes operating during the growth of the fault zone (Fig. 8). A damage zone is, therefore, the final product of the total history of strain accumulation in the volume around the fault. The increase in frequency of fractures around large normal faults (i.e. those faults that would be seen on a seismic survey) is a ubiquitous characteristic of the cores studied from the North Sea (e.g. Knipe et al., 1996; Fossen and Hesthammer, 2000). The frequency of deformation features can increase from background levels of less than 50 per 100 m of core to more than 1000 per 100 m of core close to faults with tens of metres of throw. The size of the damage zone is dependent upon the lithologies that have been faulted, the deformation conditions and the distribution of

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Fig. 7. Example of a fault damage zone in an extensional step between two normal faults in cross-section, in the Cretaceous Chalk at Flamborough Head, Yorkshire (Peacock and Zhang, 1994). A damage zone at an overstep between normal faults in map view is shown by Antonellini and Aydin (1994, fig. 16).

strain between the hanging wall and footwall (see Knipe et al., 1996).

5. Accumulation of displacement on normal faults Muraoka and Kamata (1983) use displacement – distance (d – x) graphs to show how displacement can vary along normal faults (Fig. 9a). More recent field studies of displacements along normal faults that emphasize the roles of interaction and linkage include Peacock and Sanderson (1991, 1994a), Walsh and Watterson (1991), Dawers et al. (1993), Cartwright et al. (1995), Childs et al. (1995), Cartwright and Mansfield (1998) and Cowie and Shipton (1998). Various models have been developed to account for the displacement geometry of normal faults and to show how faults develop by the accumulation of many discrete seismic-slip events (Walsh and Watterson, 1987; Sibson, 1989). Recent two-dimensional models (Bu¨rgmann et al., 1994; Peacock and Sanderson, 1996) have illustrated the crucial role played by fault

segmentation and interaction in controlling d– x profiles. Models to explain the displacement geometry of faults are summarised in Table 1. The development of an accurate three-dimensional model for the accumulation of displacement on faults would aid the interpretation and prediction of the displacement geometries of faults. This would be particularly useful when only limited data are available with which to make predictions, as in a seismic survey (Pickering et al., 1997). 5.1. Model for a single-slip event in an ideal elastic material Pollard and Segall (1987) describe a model for a crack subject to mode III loading in an elastic material. Displacement (d) is given by: d ¼ Aðr2  x2 Þ0:5 ,

ð1Þ

where A = a constant dependent on the driving stress and on the elastic properties of the rock, r = the crack half-length and x = the distance from the crack centre.

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Fig. 8. The evolution of a normal fault system in cross-section, showing the locations of damage zones (see Kim et al., in review). (a) The fault system initiates as a zone of fracturing. (b) Damage occurs at irregularities as displacement builds up. Damage also occurs in the process zone at the tips of a fault as it propagates. A process zone is defined by Vermilye and Scholz (1998, 1999) as a zone of microfracturing (slip surfaces and comminuted material) associated with growth of a shear plane. Relict process zones occur along the length of a fault as it propagates through the previous tip zones. More distributed, background damage may occur in the extending rocks. (c) Damage occurs as the fault links with other faults. Relict damage zones occur around the fault as it propagates.

Maximum displacement (dMAX) occurs at the crack centre (x = 0) and is proportional to crack length. There are three problems with this model. Firstly, it implies infinitely high stresses at crack tips, which is unrealistic because rocks have a finite strength (Cowie and Scholz, 1992a). Secondly, the model does not account for the propagation of faults or for multipleslip events (Walsh and Watterson, 1987). Thirdly, it does not take fault interaction and linkage into account. Data for normal fault segments usually lie below this theoretical profile (Fig. 9).

5.2. The cumulative slip model The model of Walsh and Watterson (1987) assumes that a propagating, isolated, planar fault accumulates displacement according to the model for a single slip event in an elastic material, but the final d– x profile results from the accumulation of many slip events (Fig. 10a). The model predicts: D ¼ 2ð1  X Þ f½ð1 þ X Þ=22  X 2 g0:5 ,

ð2Þ

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where D = normalised displacement (d/dMAX) and X = normalised distance from the point of maximum displacement (Fig. 9b). The cumulative-slip model does emphasize the role of multiple slip events. The model does not, however, account for the variability of d –x profiles that occur. Such variability is illustrated by Walsh and Watterson (1987, fig. 5a) and by Fig. 9b,c. Also, the model uses equal amounts of fault propagation for each slip event (Walsh and Watterson, 1987, figs. 3 and A1). This means that there is the same amount of propagation for early small slip events as for later large slip events; thus, displacement would continually increase in proportion to fault length. 5.3. Recent models that use modifications of the model for slip in an ideal elastic material Various papers, mostly by members of the Rock Fracture Project at Stanford University, have been published that use modifications of Pollard and Segall (1987) model for a single slip event in an ideal elastic material (Section 5.1). Bu¨rgmann et al. (1994) show that the d –x profile of a single slip event can be modified by changes in frictional strength along a fault, spatial variations in the stress field, inelastic deformation at fault tips and by variations in the elastic modulus of the wall rocks. They emphasize the role of segment interaction in causing stress variations and inelastic deformation. Willemse et al. (1996), Willemse (1997) and Crider and Pollard (1998) present three-dimensional modelling of relay ramps using similar techniques to those of Bu¨rgmann et al. (1994). Willemse (1997) uses the model to explain observations that interacting faults have complex d– x profiles, steep displacement gradients occur at oversteps and points of maximum Fig. 9. (a) Schematic displacement – distance (d – x) profile along the strike of a fault (Muraoka and Kamata, 1983; Williams and Chapman, 1983), showing the maximum displacement (dMAX) and the distance between the maximum displacement point and the tip (r). Note that dMAX is not at the centre of the trace, so r1 > r2. (b) D – X (normalised) data for a normal fault zone at Kilve, Somerset (n = 245 from 29 fault segments). The D – X (normalised) profiles for a single slip event in an elastic material (A) and for the Walsh and Watterson (1987) model (B) are also shown. (c) Examples of D – X (normalised) plots for individual fault segments in the fault zone at Kilve, Somerset (Peacock and Sanderson, 1991). Differences in these d – x profiles are related to their linkage characteristics (Peacock and Sanderson, 1991).

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Table 1 Summary of the main features of various models for the accumulation of displacement on faults (see Section 5) Model

Rationale

d – x Profile

Length – displacement ratio

Single slip event in an ideal elastic material (Pollard and Segall, 1987)

Displacement depends on the driving stress, the elastic properties of the rock, fault length and the distance from the fault center

Semicircular

Controlled by the driving stress and the elastic properties of the rock

Cumulative slip model (Walsh and Watterson, 1987)

Displacement builds up by a series of slip events, each obeying the ideal elastic model

Approximately linear after about 100 slip events

Length2 ~ maximum displacement

Modelling of Bu¨rgmann et al. (1994) Displacement is controlled by several mechanical factors (frictional strength along faults, spatial stress variations, inelastic deformation at fault tips and variations in the elastic modulus of the wall-rocks)

d – x profiles can be modified Ratios vary, depending on by mechanical factors mechanical factors

Post-yield fracture mechanics model Inelastic deformation occurs (Cowie and Scholz, 1992a,c) at fault tips

Approximately semicircular, but tapering at fault tips

Varying propagation ‘‘rate’’ (Peacock and Sanderson, 1996)

Varies depending on the Varies depending on the propagation history, which propagation history, commonly is commonly related to fault controlled by fault interaction interaction

Displacement builds up by a series of slip events, each with displacement proportional to fault length. Propagation ‘‘rate’’ can vary during fault development

displacement away from the centre of fault traces. Crider and Pollard (1998) model the geometry of relay ramps and predict locations of relay ramp breaching. A problem with the models for relay ramps of Willemse (1997) and of Crider and Pollard (1998, fig. 9) is that the modelled dip direction of the relay ramp is different from the field examples used. Maerten et al. (1999) use an elastic model to calculate three-dimensional displacement distributions on normal faults that intersect either in map view or cross-section. They show that intersections cause variability in d –x profiles, with steep displacement gradients tending to occur near fault branches. The models are similar to the field examples of conjugate normal faults described by Odonne and Massonnat (1992), Nicol et al. (1995) and by Watterson et al. (1998), which show high displacement gradients near where they intersect. A potential problem with these models (Bu¨rgmann et al., 1994; Willemse et al., 1996; Willemse, 1997; Crider and Pollard, 1998; Maerten et al., 1999) is that

Length~maximum displacement

they do not include the crucial effects of the accumulation of displacement by multiple slip events or of fault propagation. They are limited to individual-slip events (c.f. Walsh and Watterson, 1987; Peacock and Sanderson, 1996) (Section 5.5). 5.4. The post-yield fracture mechanics model The Cowie and Scholz (1992c) model involves inelastic deformation at fault tips during fault growth (also see Cowie and Scholz, 1992a; Dawers et al., 1993; Scholz et al., 1993; Cowie and Shipton, 1998; Moore and Schultz, 1999; Gupta and Scholz, 2000). Inelastic deformation occurs if the yield strength is exceeded at the fault tip, with yield continuing until stress at the tip just equals the yield strength. The d –x profile for a single slip event in an ideal elastic material is thereby modified into a bell shape, with displacement tapering gradually to the tip. There are three problems with the model. Firstly, Cowie and Scholz (1992a,c) do not demonstrate their

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Fig. 10. d – x graphs for four slip events (numbered 1 to 4), illustrating how displacement may build up on a fault by a succession of slip events, and how the d – x profile changes during fault development. (a) The Walsh and Watterson (1987) model, where fault length increases by the same amount after each slip event. (b) Model using Eq. (3), in which the amount of propagation is proportional to fault length. In this case, the propagation ‘‘rate’’ ( p) = 1.5 (Peacock and Sanderson, 1996, fig. 3).

conclusion that faults maintain self-similar d– x profiles. Secondly, the model does not deal with fault interaction. For example, Cowie and Scholz (1992a, fig. 8a) describe the Wasatch Fault, which shows the start of inelastic deformation at an overstep; thus, inelastic deformation may have been caused by the overstep. The best exposed, and the only apparently unsegmented, example they give (Cowie and Scholz, 1992a, fig. 8c) has a linear d – x profile. Most of the faults described by Dawers et al. (1993, fig. 2) have asymmetric d– x profiles, indicating that such factors as fault interaction and lithological variations play a role (Peacock, 1991; Peacock and Sanderson, 1991; Cartwright and Mansfield, 1998; Maerten et al., 1999). Gupta and Scholz (2000) use the Cowie and Scholz (1992c) model to model how fault interaction affects rupture sequences and d – x profiles. Their summary model for the evolution of relay ramps and the build up of displacement on interacting normal faults is similar to the model of Peacock and Sanderson (1991, fig. 12). Thirdly, Cowie and Shipton (1998) present detailed measurements of a normal fault that has a linear d– x profile. They suggest that the model of Cowie and Scholz (1992c) for bellshaped d –x profiles would only occur in the special case of a slip event occurring on a whole fault surface. Cowie and Shipton (1998) also predict periods of displacement build up with limited propagation, caus-

ing variations in length –displacement ratios during fault growth (see Peacock and Sanderson, 1996). 5.5. Model using variations in fault propagation ‘‘rate’’ The variability in d– x profiles (Fig. 9) and length– displacement ratios (Fig. 11a) of normal fault segments illustrate that fault development is typically more complex than predicted by the models for ‘‘isolated’’ faults. The length– displacement ratio is the trace length of a fault divided by the maximum displacement (e.g. Barnett et al., 1987). Peacock and Sanderson (1996) consider fault interaction and model the development of a fault using: d¼

N X

ðð pn c1 Þ2  x2 Þ0:5 ,

ð3Þ

n¼0

where d = finite displacement on a fault, c1 = initial half-length of the fault, n = number of slip events and x = distance from fault centre. The function p is a parametric representation of fault growth, referred to here as propagation ‘‘rate’’. Note, however, that it is not measured with respect to time, but is a function that gives the ratio of propagation to length for each slip event. When p = 1, there is no propagation, but when p>1, the fault propagates (Fig. 10b). Eq. (3)

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assumes that a fault builds up displacement by a series of slip events (Fig. 10b), each of which has the d –x characteristics of a fracture in an ideal elastic material (Eq. (1)). Propagation and displacement are proportional to fault length. Cowie and Scholz (1992c) believe that faults usually grow by 0.25% to 2.5% of their previous length during an individual seismic event, i.e. p = 1.0025 to 1.025. Variations in propagation rate can be caused by fault interaction, fault bends, conjugate relationships and lithological variations (see Peacock, 1991). The model of Peacock and Sanderson (1996) indicates the following: (1) When p is large, faults develop approximately linear d – x profiles after relatively few slip events and have relatively high length – displacement ratios. (2) Interaction with nearby, overlapping faults tends to decrease the rate of propagation (Segall and Pollard, 1980), causing d –x profiles to rise toward those expected for a single slip event and causing length –displacement ratios to decrease. Interaction in only one direction typically causes maximum displacement away from the centre of the fault trace (e.g. Fig. 9a). (3) The finite d – x profile is strongly influenced by the propagation history of a fault; hence, the finite profile gives little information about the d– x profiles of the individual slip events. (4) Variations in p can cause much of the variability observed in length – displacement ratios (Fig. 11a). Fig. 11. Graphs of fault-scaling relationships. (a) r (distance between the point of maximum displacement and the fault tip) against dMAX (the maximum displacement on the fault trace). The scatter of points illustrates the variability in length – displacement ratios. E, Normal fault segments (Peacock and Sanderson, 1991); n, Normal fault zone from Kilve, Somerset (Peacock and Sanderson, 1991); +, British coalfield normal faults (Walsh and Watterson, 1987). The segments have much lower mean length – displacement ratios than the ‘‘isolated’’ British coalfield normal faults (Walsh and Watterson, 1987), probably because interaction decreases the ratio (Peacock, 1991). (b) Cumulative frequency against fault displacement for normal faults along the 6-km-long cliff section on the south coast of Flamborough Head (n = 1340) (Peacock and Sanderson, 1994b, fig. 9). Faults with more than 20mm displacement follow an approximate straight line and, hence, show a power-law scaling relationship. The power-law is particularly apparent when the censoring effect is removed by adding two faults of more than 6-m displacement to the data (5 on graph), which may occur in the two breaks of section along the coast (Peacock and Sanderson, 1994b).

5.6. Problems with the existing models and the need for further work The model of Peacock and Sanderson (1996) and the existing models for the build-up of displacement on faults suffer from the same problem: the exact d –x profile for each slip event is poorly constrained. As pointed out by Sibson (1989), more work is needed to relate the slip events to finite displacement on faults. More detailed work is being carried out on fault evolution. For example, Nicol et al. (1997) provide evidence for the growth rate of normal faults in the Aegean, while Contreras et al. (2000) describe fault growth and relay ramps in the East African Rift. Contreras et al. (2000) use seismic data to look at sediment infill and, thereby, determine temporal evo-

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lution of fault system. Contreras et al. (2000) show that the point of maximum displacement is not fixed with time and that the largest fault does not necessarily have the highest rates of displacement in any particular time interval. This results in complex d –x profiles. Schultz (1999) lists twelve factors that can control displacement distributions on faults and gives references. These are: (1) fault length (in map view and cross-section); (2) fault aspect ratio; (3) fault shape (e.g. elliptical tip line vs. rectangular tip line); (4) proximity to the free surface and other boundaries; (5) configuration of far-field stresses; (6) frictional and constitutive properties of the fault; (7) variations in elastic properties and lithology along the fault; (8) time-dependent faulted rheologies; (9) interfault plate deformation; (10) near-tip processes; (11) interaction with other faults; and (12) fault segment linkage. The roles of interaction and linkage are emphasized here, but these other factors need to be fully incorporated if realistic models for normal faults are to be developed.

scaling relationship of fault displacements (Fig. 11b) is given by:

6. Effects of interaction and reactivation on fault scaling relationships

An example of the self-similarity of faults is the ratio of fault trace length to maximum displacement (Fig. 11a). There has been debate on the relationship between the maximum displacement and the length of faults (Fig. 11a). Cowie and Scholz (1992b) state a fault population will obey a constant ratio between maximum displacement and trace length, while Gillespie et al. (1992) state that that the ratio is not constant. Peacock (1991) and Peacock and Sanderson (1991, 1996) show, however, that the ratio is strongly controlled by the factors that effect fault propagation, particularly fault interaction. As interaction occurs, propagation tends to be hindered, but displacement increases (see Section 5). The ratio between maximum displacement and fault length will, therefore, increase with increasing fault interaction. Cartwright et al. (1995) surmise how the displacement to length ratio varies as fault segments link. Linkage between two similar-sized faults will approximately double the length – displacement ratio. Much of the scatter of data in the displacement to length graph shown in Fig. 11a could, therefore, be a result of the interaction and linkage of fault segments. Similarly, Moore and Schultz (1999) and Poulimenos (2000) show that the

Recent work has not only concentrated on individual normal faults or fault zones. There has also been considerable interest in populations of faults, i.e. how the faults of all scales in a region are related to each other (see Cowie et al., 1996; Yielding et al., 1996). This section discusses how fault interaction can influence fault scaling and discusses how fault reactivation can modify the displacement characteristics of a fault population. Tchalenko (1970) shows that the geometries and mechanics of microscopic fault zones closely resemble those of continental scale fault zones. Faults are, therefore, described as being self-similar, with the geometry at one scale being identical to the geometries at other scales. The development of the concept of fractals (e.g. Mandlebrot, 1982; Turcotte, 1990) has provided a method for describing the selfsimilarity of different scales of faults within a population. For example, Childs et al. (1990), Scholz and Cowie (1990), Marrett and Allmendinger (1992) and Walsh and Watterson (1992) show that the power-law

N ¼ c U D ,

ð4Þ

where N = number of faults with a displacement greater than U, c = a constant and D = the power-law exponent. The power-law scaling relationship for fault displacements has been used to estimate the numbers of faults above and below the scale of resolution of a particular survey and, hence, to estimate the total deformation in a region (e.g. Marrett and Allmendinger, 1992; Walsh and Watterson, 1992; Poulimenos, 2000). One use of this is the prediction of the number of faults to be encountered in mining and hydrocarbon exploration (e.g. Childs et al., 1990; Gauthier and Lake, 1993), but care is needed with such methods. For example, the style of deformation may change with scale (e.g. Fossen and Hesthammer, 2000). 6.1. Effects of fault interaction on length – displacement ratios of faults

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ratio of fault trace length to maximum displacement tends to decrease as strain increases. Poulimenos speculates that faults tend to increase in displacement at a proportionally greater rate than they increase length when an area becomes ‘‘saturated’’ in faults; thus, the ratio between maximum displacement and trace length is not equal to 1.

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Fig. 12a illustrates a maximum displacement to length distribution of a population of normal faults. If this population is subject to a contractional epi-

6.2. Fault reactivation as an example of the difficulties of using fault scaling relationships Various factors may influence fault scaling relationships. For example, Wojtal (1996) discusses the changes in scaling relationships that occur during fault linkage, while Steen and Andresen (1999) show the effects of lithology on fault scaling. The reactivation of normal faults is discussed here as an example of how simple power-law scaling relationships may break down in the analysis of fault populations. A fault is reactivated if it undergoes renewed displacement after a prolonged period of inactivity; the fault has, therefore, been affected by at least two distinct tectonic events (e.g. ShephardThorn et al., 1972; Sibson, 1985). Fault reactivation is a key factor in modifying fault displacement geometries and in controlling the pattern of deformation in cover sequences above previously deformed basement (e.g. Allmendinger et al., 1987; Jackson, 1987; McClay, 1989; Williams et al., 1989). Kinematic reconstructions of tectonic domains usually invoke ‘‘major’’ fault zones to accommodate several deformation episodes, with reactivation being a function of the stress regime and the orientation, frictional strength and location of the pre-existing faults (e.g. Sassi et al., 1993). The reactivation of a population of faults will not reactivate all orientations or scales of faults equally. Kelly et al. (1999) show that common features of a fault system during a reactivation episode include: (1) The largest faults alter their geometry to accommodate the change in the imposed stress. (2) Reactivation will commonly be concentrated on the largest faults in the population. The smallest faults, which were the product of an earlier deformation episode, remain largely unaffected. (3) A new set of faults may be formed to accommodate the new stress state and the reactivation of the largest faults.

Fig. 12. Graphs illustrating the effects of reverse reactivation on a population of normal faults. (a) Throw against fault length (Eddie McAllister, personal communication). When the normal faults are reverse-reactivated, the throw decreases and the length may increase. If the normal faults are reactivated as strike – slip faults, the throw will not change, but the length may increase. (b) Cumulative frequency against displacement for a population of normal faults. If the largest faults are preferentially reversereactivated, the graph will steepen for the largest displacement faults. Kelly et al. (1999) observed this phenomenon in populations of normal faults. The number of faults in the population will tend to increase as a result of the increase of damage around the major faults.

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sode with maximum shortening orthogonal to the strike of the faults, then the displacements on the largest faults will decrease. The number of faults in the population will tend to increase as a result of the increase of damage around the major faults. If the largest faults are preferentially reverse-reactivated (Kelly et al., 1999), the population may not obey a simple power-law distribution (Fig. 12b). Strike –slip reactivation of the population of normal faults will increase the length of the faults, while the throw remains constant.

7. Fault networks and triaxial strain Most work on normal faults and fault populations has concentrated on parallel-striking faults in map view or in cross-section (e.g. Davison, 1986; Williams and Vann, 1987). More complex fault networks (e.g. Stoces and White, 1935) are needed, however, to accommodate triaxial strain (Reches, 1983; Krantz, 1988; Nieto-Samaniego, 1999). This section discusses such networks to illustrate some of the complexity that can occur in normal fault systems. Local and regional networks of normal faults can

occur. For example, Griffiths (1980) describes local networks of ‘‘box’’ faults developed in relay ramps in the East African Rift (Fig. 13). Morewood and Roberts (2000) also describe a complex three-dimensional strain, in a neotectonic relay ramp in central Italy. As pointed out by Angelier (1984), the palaeostresses implied by such three-dimensional fault systems in relay ramps may not be compatible with the regional, far-field stresses. Cartwright and Lonergan (1996) and Lonergan et al. (1998) describe patterns of more widespread, regional, layer-bound polygonal faults from the North Sea, while Watterson et al. (2000) describe polygonal fault systems in South Australia. There is an example of a complex fault network at Flamborough Head, UK, where faults occur with a wide range of orientations and with displacements of less than 6 m occur (Peacock and Sanderson, 1994b). A model for the development of the faults at Flamborough Head is illustrated in Fig. 14. This network of normal faults is complicated by reverse reactivation, thus is not a simple, classic example of a fault network. Flamborough Head does, however, illustrate the sorts of complexity that can occur in a natural population of normal faults. The normal faults at

Fig. 13. Block diagram showing an example of a local network of faults. The ‘‘box faults’’ are developed in a relay ramp in the East African Rift (Griffiths, 1980).

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Fig. 14. Block diagram illustrating the fault pattern at Flamborough Head (Peacock and Sanderson, 1994b). E – W striking faults extend from the basement to the Cretaceous Chalk cover rocks. Onshore seismic sections (e.g. Kirby and Swallow, 1987) show that the basement faults have a much larger displacement in the Carboniferous rocks than in the Chalk, and illustrate that they are at least as old as the Carboniferous. The basement faults were reactivated during N – S extension, probably at the end of the Cretaceous, and a network of small normal faults developed to accommodate a triaxial stress system. The basement faults (e.g. the Selwicks Bay Fault Zone) were reverse-reactivated, probably during the Tertiary, but the small normal faults were not reactivated (Kelly et al., 1999). For simplicity, the fault network is only shown in the graben between the basement faults.

Flamborough Head indicate two serious problems with the simple idea of power-law scaling relationships presented by Childs et al. (1990), Scholz and Cowie (1990), Marrett and Allmendinger (1992), Walsh and Watterson (1992) and by Nicol et al. (1996b). Firstly, the faults that are large enough to be resolved on seismic sections strike dominantly E – W (e.g. Rawson and Wright, 1992, fig. 2), while the smaller faults exposed at Flamborough Head have a much wider range of orientations. The pattern of deformation, therefore, changes with scale (Peacock and Sanderson, 1994b) and it would be impossible to predict the pattern of large faults from the pattern of smaller faults and vice versa. Secondly, the larger (basement-controlled) faults have a longer, more complex history than the small faults including a phase of reverse reactivation (Peacock, 1996). The simple scaling relationship of a population of normal

faults will, therefore, break down, as illustrated in Fig. 12.

8. Conclusions Detailed fieldwork and improvements in seismic data over the past decade have enabled more sophisticated models to be developed for normal faults in multilayered sedimentary rocks. Recent advances in the understanding of such normal faults include the following: (1) Normal faults are composed of segments and bends at all scales, both in map view and in crosssection. The cross-sectional geometry of normal faults is commonly controlled by lithological variations. This three-dimensional complexity must be taken into account in any model for normal fault development.

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(2) A relay ramp is an area of tilting between two normal faults that overstep in map view and that dip in the same direction. They can develop from two initially noninteracting faults and can evolve into a single fault with a bend characterised by apparent drag folding. Relay ramps can be significant locations for hydrocarbon migration and entrapment. Antithetic transfer zones are areas of warped bedding that develop between overstepping faults that dip in opposite directions. (3) Fault damage zones are areas of fracturing that accommodate strain around faults. The fracturing is related to fault initiation, propagation, displacement and linkage. Damage zones can act as barriers or as conduits to fluid flow. (4) Various models have been proposed to account for the accumulation of displacement on normal faults, but it is only recently that models have been developed that incorporate fault interaction and other mechanical effects (e.g. Bu¨rgmann et al., 1994; Peacock and Sanderson, 1996). Fault interaction strongly affects fault growth and the final displacement – distance profile of faults. Interacting faults are characterised by steep displacement gradients near their interacting tips by the point of maximum displacement away from the centre of the fault trace. (5) The relationship between displacement and length of faults is strongly influenced by fault interaction and linkage. The displacement on a particular fault segment becomes proportionately larger as interaction increases because fault propagation is inhibited (Peacock, 1991; Peacock and Sanderson, 1996). (6) Normal faults typically obey power-law scaling relationships for cumulative number against displacement (e.g. Scholz and Cowie, 1990; Marrett and Allmendinger, 1992; Walsh and Watterson, 1992). Knowledge of the power-law exponent enables predictions to be made about the numbers of faults with sizes above and below the resolution of the survey and, therefore, about the total strain in a region. (7) Simple fault scaling relationships can be modified, however, by fault reactivation, especially because the largest faults are preferentially reactivated (Kelly et al., 1999). (8) Complicated fault networks can develop that represent triaxial strain. These networks may not obey simple power-law scaling relationships, with fault patterns commonly changing with scale. This compli-

cates attempts to make predictions from one scale of fault to other scales. Normal faults show a wide variety of geometries and displacement patterns. This indicates that a wide range of factors influence fault development, with faults, therefore, having complex evolutions. As pointed out by Schultz (1999) and by Tikoff and Wojtal (1999), more work is needed, especially to link detailed field observations with realistic models. Acknowledgements Funding for this work was provided by Shell and by a Natural Environment Research Council ROPA award to Rob Knipe. Discussions with Greg Jones, Rob Knipe, Eddie McAllister and Dave Sanderson were very useful. Richard Groshong is thanked for clarifying usage of the term damage zone. Gary Axen, Ernest Duebendorfer and James Evans are thanked for giving detailed comments of an earlier version of this paper. I am grateful to two anonymous reviewers, whose comments greatly improved this paper. References Acocella, V., Salvini, F., Funiciello, R., Faccenna, C., 1999. The role of transfer structures on volcanic activity at Campi Flegrei (southern Italy). Journal of Volcanology and Geothermal Research 91, 123 – 139. Acocella, V., Gudmundsson, A., Funiciello, R., 2000. Interaction and linkage of extension fractures and normal faults: examples from the rift zone of Iceland. Journal of Structural Geology 22, 1233 – 1246. Allmendinger, R.W., Nelson, K.D., Potter, C.J., Barazangi, M., Brown, L.D., Oliver, J.E., 1987. Deep seismic-reflection characteristics of the continental-crust. Geology 15, 304 – 310. Anders, M.H., Schlische, R.W., 1994. Overlapping faults, intra-basin highs, and the growth of normal faults. Journal of Geology 102, 165 – 180. Angelier, J., 1984. Tectonic analysis of fault slip data sets. Journal of Geophysical Research 89, 5835 – 5848. Antonellini, M., Aydin, A., 1994. Effect of faulting on fluid flow in porous sandstones: petrophysical properties. Bulletin of the American Association of Petroleum Geologists 78, 335 – 377. Aydin, A., Schultz, R.A., 1990. Effect of mechanical interaction on the development of strike – slip faults with echelon patterns. Journal of Structural Geology 12, 123 – 129. Barnett, J.A.M., Mortimer, J., Rippon, J.H., Walsh, J.J., Watterson, J., 1987. Displacement geometry in the volume containing a single normal fault. Bulletin of the American Association of Petroleum Geologists 71, 925 – 937.

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