Trishear: A New 3D Move-on-Fault Algorithm

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1 Trishear: A New 3D Move-on-Fault Algorithm The 3D Trishear algorithm in Move2015 provides new capabilities that more realistically simulate and restore complex deformation ahead of a fault tip. Trishear deformation was first used by Erslev (1991) to explain fault-related deformation in the Laramide orogeny. Since then, the algorithm has been further developed and used to model many fault systems in a variety of tectonic settings (e.g. Cardozo, 2008; Cardozo and Brandenburg, 2014). A 3D implementation of the trishear algorithm was developed for the Move2015 release and is included in the 3D Move-on-Fault toolbox. Trishear simulates distributed shear in a triangular zone ahead of a fault tip (Figure 1). Velocity vectors within this triangular trishear zone progressively decrease in magnitude towards the footwall. The 3D Trishear algorithm generates curved folds in the deformation zone. These differ from the angular kink bands predicted by the Fault-Propagation Fold algorithm, which is also used in Move to simulate deformation ahead of a fault tip. The Trishear algorithm is unique in Move because it can reproduce many commonly observed features of fault-related folds such as footwall folding, drag folding, thinning of forelimb strata and hanging wall synclines above normal faults. In the 3D view, the trishear zone is represented by translucent grey surfaces (Figure 2a). The width of the trishear zone perpendicular to the trace of the fault tip is controlled by adjusting the Trishear Angle parameter in the toolbox (Figure 2b). Narrower trishear zones with smaller angles intensify strain ahead of the fault tip; whereas wider zones with larger angles lead to the development of broader folds and a more diffuse distribution of strain. The distribution of the trishear zone between the hanging wall and footwall of the fault is controlled by the Trishear Angle Offset parameter. A Trishear Angle Offset of 0.5 places the trishear zone symmetrically between the hanging wall and footwall, distributing fault-related deformation in both. Values of 0 or 1 attach the trishear zone to the footwall or hanging wall, respectively. The starting position of the trishear zone is specified using the toolbox options for Fault Tip Position. This includes defining the starting position at a fault cut-off in the footwall or hanging wall. The toolbox parameter Propagation/Slip Ratio controls how far the fault tip propagates for a specific slip on the fault. This means that the trishear zone can move along the fault from the starting position, simulating deformation induced by a propagating fault. Natural faults can have Propagation/Slip Ratios of 0 to 9 (Hardy and Ford, 1997). Lower Propagation/Slip Ratios keep rock within the trishear zone for longer causing it to become more tightly folded.

2 In Move, it is possible to simulate both homogeneous and heterogeneous trishear deformation (Erslev, 1991) to control how displacement vectors vary across the trishear zone. When the number of Trishear Zones is set to 1, homogeneous trishear will be simulated and displacement vectors will decrease linearly across one trishear zone. Values > 1 signify that the main trishear zone should be sub-divided into an equivalent number of trishear zones and that heterogeneous trishear should be used. For heterogeneous trishear, variations in the displacement vectors are calculated across each of the trishear zones and typically results in the greatest displacement change occurring in the central portion of the main trishear zone. The 3D trishear algorithm generally requires a higher sampling density than the other 3D Move-on-Fault algorithms in Move (Simple Shear and Fault Parallel Flow). However, it is not always necessary to up-sample the entire surface prior to modelling. The Maintain level of detail option will automatically up-sample the areas of maximum complexity in the trishear zone; thereby minimizing the number of mesh artefacts generated by the trishear algorithm. Switching on Maintain level of detail will increase the computation time. As a result, our recommended workflow is to initially experiment without using the Maintain level of detail option; this will allow the most appropriate parameters for the Trishear Angle, Trishear Offset Angle, starting position of Trishear Zone, Propagation/Slip Ratio and the number of Trishear Zones to be identified. Then, we recommend that the Maintain level of detail option is selected for the final run using the identified optimum trishear parameters. To identify the most appropriate trishear parameters it is often easiest to use the 2D forward modelling capabilities of the Horizons from Fault toolbox. The ability to interactively adjust the Trishear Angle, Trishear Offset Angle and the starting position of Trishear Zone on-screen in Move2015 has greatly improved the efficiency of the 2D forward modelling workflow. The 3D Move-on-Fault algorithms in Move2015 offer increased levels of control on fault kinematics with the introduction of Variable Heave (Simple Shear) and Variable Slip (Fault Parallel Flow and Trishear). Along strike variations in fault displacement can be: Symmetric: the magnitude of displacement decreases linearly towards the fault s edges from a user-defined point; Asymmetric: the magnitude of displacement is defined at the edges of the fault and is linear extrapolated. Symmetric and asymmetric along strike variations can also be specified for the Trishear Angle, Trishear Offset Angle, Propagation/Slip Ratio and the number of Trishear Zones. The ability to control lateral variations in the geometry and development of the trishear zone allows complex faulting scenarios to be reproduced by forward modelling or sequential restoration.

3 The forward model shown in Figure 3 uses asymmetric variations to simulate lateral variations in deformation ahead of both normal and reverse faults. Figure 3a shows a model with a buried normal fault. An episode of normal faulting is simulated causing a hanging wall syncline to develop (Figure 3b). The Moveon-Fault toolbox parameters for this normal faulting were set up to simulate asymmetric slip with the magnitude of displacement increasing towards the west. This along strike variation in displacement is mirrored in the thickness of the growth sequences infilling the accommodation space generated in the hanging wall of the normal fault (Figure 3c). Finally, the region experienced a phase of tectonic inversion resulting in the breakthrough of a footwall shortcut (Figure 3d). Trishear deformation ahead of this reverse fault is asymmetrically variable with greater displacement and Propagation/Slip Ratio in the west of the model. Geometries of this final forward model step could be compared to observed data to discriminate between fault evolution hypotheses. Figure 1. Illustration showing the parameters that can be used to control how a trishear zone is modelled ahead of a fault tip. Red elements can be interactively adjusted in a 2D section view in Move2015.

4 Figure 2(a) Figure 2(b) Figure 2. 3D trishear deformation ahead of flat-ramp fault. a) 3D model showing forward modelling of horizon deformation using trishear. Trishear zone shown as translucent grey surfaces. b) Trishear settings in the 3D Move-on-Fault toolbox.

5 3a) Trishear zone (shown in grey) displayed attached to a fault cutoff of a buried normal fault. 3b) Trishear deformation results in the development of a hanging wall syncline. Hanging wall syncline 3c) Asymmetric slip across buried normal fault has influenced distribution of infilling sediment (isopachs shown with coloured contours).

6 3d) Asymmetric trishear zone develops ahead of footwall short-cut with a reverse sense of slip following tectonic inversion of the region. Mesh has been up-sampled in the trishear zone using Maintain level of detail. Figure 3. Forward modelled scenario using the 3D Trishear Move-on-Fault algorithm, which involves initial normal faulting, accumulation of growth strata and finally inversion: a) Model initial state with trishear zone shown as translucent grey surfaces. The trishear zone is asymmetric with modelled offset increasing to the distal edge of the model. The trishear zone is concentrated in the hangingwall and attached to a fault cutoff; b) Model following trishear-modelled normal shear with development of an asymmetric hangingwall syncline; c) Model with addition of a growth unit, infilling the accommodation space created by the hangingwall syncline; d) Model with simulated regional inversion modelled by reverse fault breakthrough of a footwall shortcut and development of a complex asymmetric fault propagation anticline. References Cardozo, N Trishear in 3D. Algorithms, implementation, and limitations.journal of Structural Geology, 30(3), Cardozo, N., & Brandenburg, J. P. (2014). Kinematic modeling of folding above listric propagating thrusts. Journal of Structural Geology, 60, Erslev, E. A Trishear fault-propagation folding. Geology, 19(6), Hardy, S., & Ford, M Numerical modeling of trishear fault propagation folding. Tectonics, 16(5),