J. Watterson

Analysis of the relationship between displacements and dimensions of faults

Displacement gradients on single fault surfaces are a function of the maximum displacement on a fault and the dimensions of the fault surface. Data on the maximum lateral dimensions (widths) and maximum displacements on normal faults and thrusts, with maximum displacements from 4 mm to 40 km, are used to derive an expression relating width, displacement and material properties. The basis of this expression is a fault growth model in which width is proportional to the square root of displacement. Width/displacement ratios vary systematically with the size of a fault from values of ca 30,000, which are characteristic of a single slip event, to about 10 in the case of thrusts with displacements of 40 km. Rocks from which the fault data are derived have a likely range of shear moduli from ca 0.1 to ca 30 GPa, which is sufficient to account for the range of data. Data on widths and maximum displacements of 308 fault traces recorded on British coalmine plans are shown to be consistent with variation of shear modulus of about half an order of magnitude. Data on 58 further fault traces are shown to be consistent with the fault growth model. Synsedimentary faults may have growth curves characteristically different from those of other faults. It is suggested that the increase in dimensions of a fault is a postseismic process of subcritical crack propagation for which the significant material property is fracture toughness.

Fault overlap zones within developing normal fault systems

Overlap zones between normal faults have been studied using a variety of 2D and 3D seismic reflection datasets. The overlaps are of two types, (i) relay zones in which displacement is transferred between the overlapping faults and (ii) non-relay overlaps in which displacement is not transferred. Overlap zones are continually formed and destroyed during the growth of a fault system. Overlap zones are formed either by interference between initially isolated faults or as a result of bifurcation of a single fault. The mode of overlap formation is reflected in the 3D geometry of the overlapping faults which may be either unconnected or linked at a branch-line or branch-point. Seismic reflection data from regions of growth faulting, and also sandbox analogue data, allow analysis of fault development through time. Reconstructions of the displacement distribution on some faults with sharp bends and associated hanging-wall splays, show that the bends originated as overlap zones which were later breached to form through-going faults. Depending on the displacements of relay-bounding faults, the effect of relay zones on hydrocarbon reservoirs may be to (a) provide structural closure, (b) form gaps in otherwise sealing faults or (c) increase reservoir connectivity.

Displacement geometry in the volume containing a single normal fault

Fault displacements measured in coal mines and from seismic data are used to develop a model describing the near-field displacements associated with an ideal, single normal fault. Displacement on a fault surface ranges from a maximum at the center of the fault to zero at the edge or tip-line. The tip-line is elliptical, with the shorter axis of the ellipse parallel to the displacement direction. Contours of equal displacement form concentric ellipses centered on the point of maximum displacement. Displacement gradients vary with fault size and with mechanical properties of host rock; fault radius to maximum displacement ratios range from 5 to 500. Plotting of displacement contour diagrams and knowledge of displacement gradients are useful in interpreting seismic reflectio data, both for quality control of interpretations and for quantitative extrapolation of limited data. Displacements associated with faulting decrease systematically with increasing distance along the normal to the fault surface; this decrease is seen as reverse drag in both hanging wall and footwall. Hanging-wall rollover and tilting of the reflectors cannot be used to distinguish listric from planar normal faults; even where fault-block rotation can be demonstrated, neither listric fault geometry nor a flat detachment surface is geometrically necessary. Because faulting is accommodated by ductile deformation, rigid fault-bounded blocks cannot exist except in some special circumstances related to a free surface. The displacements within the rock volume affected by a single fault are not simply related to regional extension. Apparent horizontal extension by faulting varies from one layer to another, and a significant proportion of the extension in a basin may be due to ductile deformation.

Distributions of cumulative displacement and seismic slip on a single normal fault surface

Abstract Displacement profiles (normalized displacement vs normalized distance from the point of maximum displacement) have been plotted for 34 horizontal radii from 25 normal faults with maximum displacements ranging from 1.0 to 37.5 m. The composite displacement profile for these faults, when corrected for systematic inaccuracies of the data, is significantly different from the theoretical slip profile for a single seismic slip event. The integration of slip displacement profiles of many slip events on a growing fault shows that a steady-state displacement profile will be established. This theoretical displacement profile is similar to the composite profile derived from the fault data. Analysis of displacement data from 488 fault traces, which do not necessarily pass through the point of maximum displacement of their respective faults, shows that although displacement measurements are strongly influenced by ductile drag the theoretical distribution can still be identified in the data. Although the slip distribution on a fault during a single slip event, or during a period of stable sliding, is not simply related to the distribution of cumulative displacement on the fault, a knowledge of both characteristics places firm constraints on fault growth models.

The shapes, major axis orientations and displacement patterns of fault surfaces

Abstract Displacement contour diagrams constructed using seismic reflection data and coal-mine plans are analysed to establish the factors determining the dimensions, shapes and displacement patterns of normal faults. For blind isolated normal faults in layered sequences the average aspect ratio is 2.15, with sub-horizontal major axes. Earthquake slip-surface aspect ratios range from 0.5 to 3.5 and are independent of slip orientation. The principal control on the shape of blind isolated faults is mechanical anisotropy associated with rock layering, resulting in layer-parallel elongation of fault surface ellipses. Faults that intersect the free surface and/or interact with nearby faults have aspect ratios ranging from 0.5 to 8.4, and are referred to as restricted. Restriction of fault growth has various effects including: (i) reduced curvature of the tip-line and of displacement contours; and (ii) increased displacement gradients in the restricted region. Many faults are restricted at more than one place on their tip-line loop and so have highly irregular shapes and displacement patterns. Subsequent linkage of interacting faults produces combined faults with aspect ratios within the normal range for unrestricted faults. Lateral interaction between faults does not necessarily lead to a change in the power-law exponent of the fault population.

Measurement and characterisation of spatial distributions of fractures

Abstract A variety of line sample (1-D) and map (2-D) datasets of faults and joints has been used to investigate the spatial distributions of fractures and to test techniques of fractal analysis. The natural fracture datasets have been supplemented by synthetic datasets with known characteristics. The fault datasets investigated range in scale from regional to outcrop and the joint datasets are derived from outcrop. 1-D datasets were analysed by the spacing population, interval counting and fracture number interval counting techniques. 2-D datasets were analysed by box-counting and fracture number box-counting techniques. Results indicate that fracture spacing can be characterised in line samples using either the 1-D interval counting technique or, more simply, by measuring the spacing population as the cumulative frequency distribution of spaces between adjacent fractures. Tectonic faults frequently show a power-law spacing population, indicating fractal dimensions of between 0.4 and 1.0 but, except for outcrop data, truncation effects degrade the analysis. Unrefined joint datasets commonly show negative exponential or lognormal spacing-cumulative frequency distributions. However, single orientation joint sets are characterised by a regular spacing and are therefore non-fractal. For both fault and joint map data, box-counting techniques do not yield the power-law relationship between box size and the number of boxes that is expected of fractal geometries. It is concluded that 2-D box-counting techniques are too insensitive to characterise the many different parameters of a fracture array. The fracture density technique appears not to discriminate between very different fracture patterns and therefore does not provide useful results. A fracture pattern incorporates several attributes, e.g., size distribution, orientation, linkage, density, roughness, each of which may scale independently and each of which may be fractal with its own fractal dimension. Full characterisation of fracture patterns will therefore require independent analysis of each of these attributes.

Stretching fabrics, folds and crustal shortening

Abstract A simple shear model is proposed for mobile belts characterised by L-S tectonite fabrics in which the planar element dips at a low angle away from the foreland and the linear (stretching) element is transverse to the boundary of the belt. Reorientation of fold axes towards parallelism with the stretching direction appears to be a common feature consistent with this model. The geometry described is consistent with crustal shortening normal to the strike of the active belt, notwithstanding the transverse orientation of stretched elements.

Fault dimensions, displacements and growth

AbstractMaximum total displacement (D) is plotted against fault or thrust width(W) for 65 faults, thrusts, and groups of faults from a variety of geological environments. Displacements range from 0.4 m to 40 km and widths from 150 m to 630 km, and there is a near linear relationship betweenD andW2. The required compatibility strains (es) in rocks adjacent to these faults increases linearly withW and with

Limitations of dimension and displacement data from single faults and the consequences for data analysis and interpretation

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