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_Journal of Structural Geology 32 (2010) 1668–1676_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _Using empirical geological rules to reduce structural uncertainty in seismic interpretation of faults_ _Brett Freeman a,*, Peter J. Boult b, Graham Yielding a, Sandy Menpesc a Badley Geoscience Ltd., North Beck House, North Beck Lane, Hundleby, Lincolnshire PE23 5NB, UK; b GINKGO ENPGNG, 57, Seventh Avenue, St. Morris SA 5068, Australia; c Palaeosearch, 41 Walker Avenue, Heath?eld SA 5153, Australia_ _article info_ _Article history: Received 3 February 2009; Received in revised form 21 October 2009; Accepted 2 November 2009; Available online 23 November 2009_ _Keywords: Normal fault Displacement Displacement gradient Wall-rock strain Seismic interpretation_ _abstract_ _Good seismic interpretation of faults should include a workflow that checks the interpretation against known structural properties of fault systems. Estimates of wall-rock strains provide one objective means for discriminating between correct and incorrect structural interpretations of 2D and 3D seismic data – implied wall-rock strain should be below a geologically plausible maximum. We call this the strain minimisation approach. Drawing on the large body of published data for strike dimension and maximum displacement for faults, we suggest a realistic upper limit of wall-rock shear strain of 0.05, and 0.1 for maximum longitudinal strain when measured in the displacement direction. Small-scale variation of fault wall-rock strain also adheres to this rule, except in specific areas of strain localisation such as relay zones. As a case study we review an existing structural interpretation of 2D seismic surveys. Mapping of shear and longitudinal strain on the fault planes show values commonly greater than 0.05 and 0.1 respectively. Thus the model is deemed inadmissible. We then reinterpreted the area in an iterative manner using the strain minimisation approach. By using regions of implied high wall-rock strain as an indicator of high uncertainty in the interpretation, we were able to break out two self-consistent fault sets, each of which had geologically plausible wall-rock strains, where previously there had only been one fault set with highly implausible wall-rock strains._ _? 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ _It has been established for more than twenty years that the displacement on geological fault surfaces varies in a smooth, continuous and consistent manner. Rippon (1985) and Barnett et al. (1987) first demonstrated this for isolated normal faults from the English coal?elds. They used precise survey data from coal mine plans to measure the throw (vertical component of dip separation) for a number of coal seams at varying spatial locations. When the throw values were plotted on a strike projection of the fault surface, the contours of throw were concentric and sub-parallel, with a maximum throw close to the centre of the fault surface. Moreover, the boundary, or tip, of the fault surface was approximately elliptical. These important observations have stimulated an enormous amount of research into the form and scaling relationships of displacement distributions, the quantitative systematics of fault geometry and speculation on fault growth mechanisms. The simplicity of the observations implies both a consistency and a limit._ _? Corresponding author. Tel.: ?44 (0) 1754 890390; fax: ?44 (0) 1790 753527. E-mail address: brett@badleys.co.uk (B. Freeman)._ _0191-8141 $ – see front matter ? 2009 Elsevier Ltd. All rights reserved. doi:10.1016 j.jsg.2009.11.001_ _to the strain in the wall rocks. Barnett et al. (1987), Bouvier et al. (1989) (normal faults) and then Chapman and Meneilly (1991) (reactivated normal fault with net reverse displacement) demonstrated similar patterns from seismic interpretation. Although the precision of the structural information from seismic data is considerably poorer than the surveyed data of Rippon (1985), these early examples of displacement distributions are also characteristically continuous and smooth._ _A priori knowledge of the shape form of the displacement distribution and its gradients can be useful as an aid to seismic interpretation. Barnett et al. (1987) suggested that it could serve both as a quality control metric and a means to predict quantitatively the location of lithological layers (horizons) and faults where data is limited. In other words, it can be used to manage interpretation uncertainty. In faulted reservoirs, structural uncertainty arises from two major sources of error: the systematic error of the seismic method, and the human error of the interpreter. For good quality 3D seismic data, the order of error in lateral positioning of structures is approximately the same as the error in the vertical dimension and both are dominantly systematic. However, when the spacing between fault traces from line samples (e.g., seismic lines) is closer than the spacing between the line samples themselves, the lateral correlation of faults is equivocal (e.g., Freeman et al., 1990). So for 2D seismic data, reconnaissance mapping, poor quality 3D seismic data and for small faults in 3D seismic data, the pattern of faulting becomes a serious interpretive issue. The balance of the error, or uncertainty, is then strongly one-sided and the effects of systematic errors become secondary to those inherent in the interpreter’s ‘‘model’’. Freeman et al. (1990) introduced a methodology that used displacement patterns to distinguish likely fault plane correlations from possible and impossible correlations. In a similar vein, Needham et al. (1996) showed how this kind of analysis was valuable for validating three-dimensional structural models. Traditionally the analytical part of the process has taken the form of visual inspection of the throw contours. If the resulting pattern is smooth and continuous, the fault may be judged as a valid interpretation; otherwise, the correlation is deemed to be suspect. Although ostensibly objective, the effectiveness of the above approach is dependent on the skill or experience of the interpreter in being able to identify bad contour patterns. We know of no published work that actually quantifies what constitutes either a good or a bad contour pattern. In this paper we suggest that the above basic validation procedure can be improved by (1) quantifying the strains that are implied by the contour patterns and (2) setting out reasonable limits for the magnitudes of these strains._ _We show that there is a simple relationship between strain and the displacement gradient. Drawing from a large database of published information on the shapes of displacement profiles and the scaling relationship between displacement and fault dimension, we can suggest reasonable limits on the amount of strain that is admissible in the walls of a fault. Implied strains that exceed these empirical limits indicate flaws in the structural model. The resulting strategy for interpretation leads to a structural model that minimizes the strain attributable to faulting._ _As an example, we show how an analysis of a 2D seismic interpretation from South Australia consistently implies erratic and unrealistically large strains. An iterative structural reinterpretation using our minimum strain approach provides a solution that is geologically more feasible._ _Fig. 1. (a) Schematic of an idealized fault plane (strike dimension L, dip dimension L 2) showing the absolute displacements from a horizontal, unfaulted layer to the faulted, upthrown and downthrown positions. The element E in the unfaulted state is translated and strained to E0. (b) Analysis of the change in shape of the rectangular element E. x is the strike direction of the fault and y is the dip direction, uq and us are absolute, dip–slip displacements._ _2. Displacement and wall-rock strain_ _There is a simple relationship between the displacement gradient and the strain of the wall rocks in the plane parallel to the fault._ _Fig. 1a shows the deformation associated with the faulting of a preexisting uniform horizontal layer (i.e., the fault is not a growth fault). The element, E (Fig. 1a and b), is defined by the position of the layer in the undeformed state with the top of the layer at p and the base of the layer at q (Fig. 1b). For the sake of argument we assume that displacement is in the dip direction of the fault, and that strain is partitioned equally in the two walls of the fault. The layer is then faulted such that, in the dip direction (parallel to y), p moves to p0 and q moves to q0. The stretch in the dip direction is then_ _?? 1?e? uq ? q ? up ? p ?q ? p?, (1) where e is the unit extension, up and uq are the absolute displacements for one side of the fault (half the total, relative displacement). This can be re-written as _?? 1_ _?? e_ _?? 1_ _?? 1?2_ _Du Dy_, (2) where the factor of 1/2 means that u refers to the total relative displacement across the fault. At the limit as Dy approaches zero, _?? 1?e_ _?? 1_ _?? 1?2_ _vu vy_, (3) In other words the unit extension is equal to half the displacement gradient. Using an alternative formulation it is easy to show that the stretch in the upthrown layer is the reciprocal of the stretch in the downthrown layer and that the undeformed layer thickness is the average of the upthrown and downthrown thicknesses (cf. figure 1 from Barnett et al., 1987)._ _Referring back to Fig. 1b we can also see that, for each wall of the fault, the strain g for shear in the dip direction is given by _g_ ?? _us_ ?? ? up _?s ? p?, ?? 1 Du 2 Dx_, (4) then as Dx approaches zero, _g_ ?? 1 vu 2 vx_. (5) Eqs. (3) and (5) are useful results because (1) they are independent of the form of the displacement distribution, and (2) they give us a direct way to measure and represent strain from information that is almost universally available from seismic interpretations._ Ключевые слова: surface, continuous, fracture, isolated fault, freeman journal, lee, close vicinity, observation, gradient, colour, longitudinal strain, lie, longitudinal, magnitude, simple relationship, downthrown, fault surface, seismic data, implied, small, wall rock, eds, implied strain, walsh, separation, picked persistently, maximum, australia, horizon cutoff, shear, increase, high, limit, fault, data, wibberley, scale, nicol, strain, isolated, badley geoscience, cutoff, dmaxl, map, displacement gradient, wall, displacement prole, view, upthrown, unrestricted fault, geology, unrestricted, seismic interpretation, dimension, contour, model, normal fault, wall-rock strain, structural geology, ha, lovibond, horizon, slip, strike, eshelby, geophysical, journal structural, layer, approach, correlation, joint, published, structure, dip direction, twt range, basin, scaling relationship, published data, willemse, gambier embayment, aspect, dip separation, perspective view, absolute displacement, slip direction, fault plane, ratio, break, downthrown layer, element, dip dimension, freeman, strike projection, pattern, analysis, fault trace, journal structural geology, upper, london, large, interpretation, simple, rock, aspect ratio, schultz, soliva, seismic, wall-rock, growth, reservoir, direction, picked, otway, uncertainty, shape, plane, error, embayment, strike dimension, natural, geological, raw data, structural, fault geometry, gambier, quality, yielding, boult, maximum displacement, dmax, otway basin, shear strain, report, dip, journal, pick, objective, ncs, lateral, relationship, structural model, form, imaged, unit extension, systematic error, rippon, normal, displacement, displacement distribution, south, measured, upper limit, throw, trace, upper bound, geologically, set, distribution, reasonable limit, small fault, range, displacement pattern, area, method