Constrained Fault Construction Providing realistic interpretations of faults is critical in hydrocarbon and mineral exploration. Faults can act as conduits or barriers to subsurface fluid migration and can define the geometry and extent of stratigraphic units (Figure 1). Accurate prediction of fault shape in 2D and 3D is therefore crucial to the evaluation of economic resources. However, geological and geophysical datasets can often be of variable quality or limited availability and the interpreter is commonly required to make a series of informed decisions based on their training and expertise. The constrained model building techniques in Move allow for the creation of geometrically valid fault interpretations, thereby reducing the risk and uncertainty in exploration. This Move Feature will focus on the fault construction techniques available in the Fault Geometry tool, which can be used to predict the geometry and detachment depth of faults in 2D space. Figure 1: An example of how fault geometry can influence the prediction of economic reserves (adapted from Dula, 1991). A) The available data reveals the geometry of a stratigraphic unit and an initial fault segment. The depth of the reservoir and area of uncertainty is marked, B) Interpretation 1 the fault detaches above target reservoir. No trap is formed. C) Interpretation 2 the fault detaches below the target reservoir. A structural trap is formed allowing oil to accumulate in the hanging wall anticline. Fault construction methods Assuming plane strain with no movement of material in or out of a 2D section, geometric fault construction techniques use the geometry of a deformed hanging wall horizon and an inferred regional level (i.e. the predeformation elevation of the hanging wall) to predict the location and shape of a fault at depth (e.g. Chamberlin 1910; Davison 1986; Gibbs 1983; Verrall 1981; Wheeler 1987). These techniques work on the principle of area balance and assume that the hanging wall fold geometry is controlled by the underlying fault geometry, and that the footwall remains rigid. The Fault Geometry tool is located on the Model Building panel and the methods available are:
Constant Heave Constant Slip Constant Bed Length Simple Depth to Detachment Area-depth Calculation Constant Heave method The Constant Heave method approximates a simple shear deformation mechanism (White et al 1986). Internal strain in the hanging wall is analogous to that of a pack of cards sliding past each other on shear planes. The shear angle can be varied to simulate vertical or inclined shear, and antithetic or synthetic shear. Construction lines are used to divide the inferred regional into equal lengths based on the heave (h) (Figure 2). The orientation of the construction lines are defined by the shear angle and between each line a displacement vector is drawn to connect the regional with the hanging wall horizon. The vectors are parallel to the fault trajectory and are projected down to construct the fault at depth. This method is strongly controlled by the elevation of the regional. Figure 2: Cross-section showing the theory behind the Constant Heave method. Constant Slip method The Constant Slip method approximates the Move-on-Fault Fault Parallel Flow algorithm (Wheeler 1987) and the theory that the hanging wall beds follow displacement trajectories parallel to the fault. The slip (s) is measured and used to divide the fault into equal lengths. A perpendicular bisector is constructed at a 90 angle from the fault and used to construct the displacement vector (Chapman and Williams, 1986). The length of the displacement vector is measured as the distance between the hanging wall fault cut-off and the regional, and is then projected at an orientation parallel to the bisector to construct the fault at depth (Figure 3).
Figure 3: Cross-section showing the theory behind the Constant Slip method. Constant Bed Length method This method assumes that flexural slip folding occurs in the hanging wall. It implies that net slip on the fault decreases with increasing depth. The fault is constructed by dividing the hanging wall horizon into equal intervals based upon the heave, and vertical construction lines are drawn at these intervals. Vectors connecting the hanging wall to the regional at the heave intervals provide the fault angle at this position, and this angle is projected down to join the fault at depth. Figure 4: Cross-section showing the theory behind the Constant Bed Length method. Case study example A case study from the Gulf of Suez shows how the seismic quality is good at shallow depths, allowing for the interpretation of a horizon in the hanging wall and footwall, as well as the first ~1000 m of a fault (Figure 5). As the seismic quality decreases with depth, so too does the level of confidence in predicting the normal fault geometry. The Constant Heave, Constant Slip and Constant Bed Length methods can collect the hanging wall interpretation and first segment of the fault, and define a regional elevation into the Fault Geometry toolbox (Figure 6).
Figure 5: Fault stick top horizon interpretation at the surface. The geometry of the fault at depth is ambiguous. Seismic provided courtesy of BP. Figure 6: Construct Fault Geometry toolbox showing the input parameters (hanging wall, fault, and regional elevation). Please note that for the Constant Heave method it is also possible to edit the shear angle.
Each method has several important theoretical differences and will extend the fault to a different detachment depth (Figure 7). The accuracy of the result depends on the accuracy of the predicted regional and hanging wall geometry; the depth to detachment will increase if the elevation of the regional increases. The regional can be picked using a pre-existing line in the cross-section or defined interactively by dragging a horizontal line up/down. The shear angle (Constant Heave method only) can also be defined by dragging an interactive green arrow (see Figure 2) or by typing a specific value from within the Construct Fault Geometry toolbox. The fault interpretation will automatically update to reflect any interactive adjustments, allowing for increased workflow efficiency. Figure 7: Normal fault modelled down to its detachment depth using the Constant Heave, Constant Slip and Constant Bed Length methods. The Constant Heave fault has been modelled with a vertical shear angle. The remaining two methods in the Fault Geometry tool are outlined below. These use notably different construction techniques. Simple Depth to Detachment method The Simple Depth to Detachment method in Move works by carrying out an area balance between the regional, the hanging wall and an interpreted fault stick (Area A in Figure 8). This method can be used to calculate the excess area (uplift) to model compressional faults, lost area (subsidence) to model extensional faults or net area (uplift subsidence).
Figure 8: Diagram explaining the Simple Depth to Detachment method in an extensional system. Area-Depth method The Area-Depth calculation is a powerful way of validating the depth to detachment and horizon interpretation, without having to perform multiple restorations to fine tune the model. The method uses the concept (from Groshong, 1994) of pure shear deformation above a detachment and constant displacement down through the section. The amount of area pushed above the detachment relative to the original height increases for shallower horizons (Figure 9). This trend is plotted to predict the detachment. Figure 9: Diagram explaining the theory behind the Area-Depth method. As with Simple Depth to Detachment, this method can work on extensional and contractional faults. Input parameters include the pin location and the deformed horizons (this may also include faults). The pin location marks the predicted regional level for each collected horizon and must be chosen carefully. The input horizons should also be considered carefully, do not collect any horizons that have been eroded as their true area will not be calculated. A cross-section interpretation of the Wheeler Ridge anticline, California, shows how the area calculation of the deformed horizons has been used to predict the detachment depth of a flat-ramp-flat fault by using an Area- Depth graph to linearly calculate the depth at which deformation is zero (Figure 10).
Figure 10: Construct Fault Geometry toolbox showing the Area-Depth Calculation parameters and the predicted depth to detachment (Calculated Intersect) from plotting the excess area of each horizon against its depth (intersection with the right pin). The results are also plotted on the cross-section (Figure 11).
Figure 11: Cross-section interpretation of the Wheeler Ridge Anticline. Gathering information on fault shape at depth is often difficult but constrained fault prediction methods in the Fault Geometry tool of Move can be used to provide geometrically accurate fault shapes based on the hanging wall deformation and inferred regional. This in turn reduces the level of uncertainty when going on to complete a restoration. Additional work Within Move it is also possible to reverse the workflow and use the Horizons from Fault tool to construct horizons in poorly constrained in areas. The horizons can be constructed from the fault geometry using a range of algorithms e.g. Simple Shear, Fault Parallel Flow, Trishear, and matched to the visible seismic reflectors. Fault geometries can then be iteratively edited and fine-tuned. References Chamberlin, R. T., 1910. The Appalachian folds of central Pennsylvania. Journal of Structural Geology, 18, p.228-251. Davison, I., 1986. Listric normal fault profiles: calculation using bed-length balance and fault displacement. Journal of Structural Geology, 8 (2), p.209 210. Dula, W., 1991. Geometric models of listric normal faults and rollover folds. AAPG Bulletin, 75, p.1609-1625. Gibbs, A., 1983. Balanced cross-section construction from seismic sections in areas of extensional tectonics. Journal of Structural Geology, 5 (2), p.153-160.
Groshong, Jr, R. H., 1994, Area balance, depth to detachment and strain in extension. Tectonics, 13, p.1488-1497. Verrall, P., 1981. Structural interpretation with application to North Sea problems. Joint Association for Petroleum Exploration Courses, Course Notes 3, London. Wheeler J., 1987. Variable-heave models of deformation above listric normal faults: the importance of area conservation. Journal of Structural Geology, 9 (8), p.1047-1049. White, N. J., Jackson J. A., and McKenzie, D. P., 1986, The relationship between the geometry of normal faults and that of the sedimentary layers in their hanging wall. Journal of Structural Geology, 8, p.897-910. If you require any more information about constrained fault construction, then please contact us by email: enquiries@mve.com or call: +44 (0)141 332 2681.