Three-dimensional distinct element modelling of relay growth and breaching along normal faults

Abstract

Three-dimensional numerical models of neutral (i.e. slip-parallel) relay zones on normal faults that cut massive sandstone host rocks have been constructed using the distinct element method code, Particle Flow Code in 3-D (PFC^3D). The models successfully reproduce the geometries, displacement profiles and strains observed in natural relay zones. In contrast to boundary element method simulations, the modelled relay ramps dip towards the hanging wall, consistent with observations of most natural relay zones. The modelling shows that relay zones are stable structures that ‘grow’ by progressive rotation of an approximately planar relay ramp without significant propagation of the relay-bounding faults prior to breaching. Stable growth is terminated when a breaching fault propagates across the top or bottom of the relay ramp. Breaching fault propagation is not instantaneous and the ramp continues to rotate, and therefore transfer displacement between the relay-bounding faults, until they become fully hard linked. Following hard linkage, displacement is accommodated by slip on the through-going fault surface. The modelling results confirm previous conceptual models of relay growth and breaching based on geometric and kinematic analysis of natural relay zones.

Introduction

Displacements on normal faults are rarely accommodated on a single well-defined slip surface, but are partitioned between interacting fault segments (Walsh and Watterson, 1990, Walsh and Watterson, 1991, Peacock and Sanderson, 1991, Peacock and Sanderson, 1994, Cartwright et al., 1995, Cartwright et al., 1996, Childs et al., 1995, Childs et al., 1996, Willemse, 1997). Fault segmentation occurs across a wide range of length scales (Stewart and Hancock, 1991, Trudgill and Cartwright, 1994, Walsh et al., 2003).

The transfer of displacement from one fault segment to another segment that dips in the same direction most often occurs through relay structures (Chadwick, 1986, Ramsay and Huber, 1987, Larsen, 1988), which are zones of high fault-parallel shear strain that provide soft linkage (Walsh and Watterson, 1991) between two interacting fault segments (Fig. 1a–c). Breaching occurs when the fault segments are replaced by a single, through-going fault surface. Typically, breaching faults propagate across either the top or bottom of the relay ramp (e.g. Peacock and Sanderson, 1991, Peacock and Sanderson, 1994, Childs et al., 1995; Fig. 1a and d) though, in previously jointed rocks, breaching faults may reactivate pre-existing joint sets to cut across the centre of the relay zone (Peacock, 2001). Intact relay zones are suggested to be important sediment entry points into fault-bounded extensional basins (Gawthorpe and Leeder, 2000), and both intact and breached relays can influence the sealing capacities and/or flow properties of faults in hydrocarbon reservoirs (Morley et al., 1990, Childs et al., 1995). Thus, knowledge of relay growth and breaching is important to understand the kinematics of fault growth and segment linkage, fault zone development (Cartwright et al., 1995, Walsh et al., 2003) and has direct relevance to hydrocarbon exploration and production (Peacock, 2002).

Conceptual models of relay growth and breaching are most often based on detailed geometric analyses of outcrop- to seismic-scale relays (Peacock and Sanderson, 1991, Peacock and Sanderson, 1994, Trudgill and Cartwright, 1994, Childs et al., 1995, Huggins et al., 1995, Cartwright et al., 1996, Walsh et al., 1999). These models suggest that breaching occurs when strain can no longer be accommodated by continuous deformation within the relay zone (e.g. Fig. 1a). There are, however, few published kinematic (as opposed to purely geometric) studies of natural relays that provide direct observational support for such conceptual models. A notable exception is the work of Childs et al., 1993, Childs et al., 1995 who examined the growth and breaching of relay zones on syn-sedimentary normal faults from 3-D seismic datasets and analogue models. These authors applied displacement backstripping methods (Chapman and Meneilly, 1991, Petersen et al., 1992, Childs et al., 1993, Clausen and Korstgård, 1994) to reconstruct the pre-breaching fault displacements and relay ramp geometries. These kinematic studies support the simple geometric models in which relays are established, maintain a stable configuration and then eventually breach. The conditions required for accurate application of the displacement backstripping method (Childs et al., 1993, Childs et al., 1995) are rarely met and, even where they are, the lateral resolution of many seismic datasets does not permit kinematic analysis of relay zones where the fault separation is less than a few tens of metres. Similarly, the imperfect (i.e. <3-D) exposure of relays in outcrop and the absence of growth strata in most cases preclude kinematic analysis. Numerical models that capture the mechanics of fault segment interaction therefore provide a useful tool to examine growth and breaching of sub-seismic relays.

The aims of this study are twofold. The first is to show that three-dimensional (3-D) numerical simulations based on the distinct element method (DEM; Cundall and Strack, 1979) can be used to model the kinematics of a small, neutral (i.e. ‘slip-parallel’) relay zone (Peacock and Sanderson, 1991, Walsh et al., 1999; Fig. 1a) in a massive, intact sandstone from the time the overlapping faults first become geometrically coherent (i.e. conserving and transferring displacements between the segments; see Walsh and Watterson, 1991), to the point of relay breaching and beyond. The second aim is to understand better the stability and breaching of relay ramps. Crucially, the DEM as implemented in the program ‘Particle Flow Code in 3-D’ (PFC^3D; Itasca Consulting Group, 1999a) allows realistic modelling of fracture propagation and accumulation of large fault displacements and inelastic strains (e.g. Strayer and Suppe, 2002), difficult feats using continuum numerical schemes (Morgan and Boettcher, 1999). Our work therefore complements previous studies into the mechanics of fault segment interaction using boundary element method simulations based on the theory of linear elasticity (Section 2). We should emphasize, however, that the question of how relay zones initiate was not addressed by our modelling. Relay zones can form through bifurcation of a propagating fault tip-line, propagation of a segmented fault array or through lateral propagation and subsequent interaction of previously independent structures (Mandl, 1987, Peacock and Sanderson, 1991, Peacock and Sanderson, 1994, Childs et al., 1995, Childs et al., 1996, Huggins et al., 1995, Cartwright et al., 1996; see Walsh et al., 2003 for discussion). Though a distinction between these mechanisms is not always clear from natural data (Childs et al., 1995) our modelling results are believed to be valid for all neutral relay zones regardless of how they initiated.