M. Scott Wilkerson

Predicting the orientation of joints from fold shape: Results of pseudo–three-dimensional modeling and curvature analysis

We treat layers of sedimentary rock as elastic plates and predict the orientations of joints by assuming that they open parallel to the maximum instantaneous stretch of a layer. Because the direction of maximum instantaneous stretch is parallel to the maximum curvature of a surface, we hypothesize that joints will trend parallel to the minimum curvature of an elastically deformed layer. After constructing pseudo–three-dimensional trishear models of Laramide-style uplifts that grow self-similarly, we calculated the direction of minimum-curvature axes during the evolution of the fold. Our analysis of minimum-curvature axes in evolving folds suggests several important characteristics for fold-related joint sets: (1) joints that are neither parallel nor perpendicular to the fold axis may be induced by local fold-related strains; (2) at any time during folding, joint orientations may vary according to the structural position on a fold; (3) at any location on a fold, joint orientation may depend on when a joint forms during the evolution of the fold; and (4) joint patterns in trishear folds may vary with stratigraphic position. Natural folds that evolve along simple geometric pathways may develop fold-related joint sets, the orientation, dominance, abutting relationships, spacing, and continuity of which will vary systematically throughout the structure. This variation in joint-system architecture may reflect the history of fold growth.

Interpreting the geologic map expression of contractional fault-related fold terminations: lateral/oblique ramps versus displacement gradients

Abstract Fault-related folds in contractional settings do not extend indefinitely, but rather commonly terminate as plunging anticlines near the tips of the genetically-related fault. Geologists often attribute the formation of such terminations to loss of slip on the underlying fault (i.e. a displacement gradient), to changes in fault geometry in which the fault laterally changes stratigraphic position along strike (i.e. a lateral/oblique ramp), or to some combination of these mechanisms. Discerning between these formative mechanisms solely through the interpretation of the geologic map expression of the termination can be difficult because of the subjective nature of the criteria used (e.g. lateral/oblique ramps often are interpreted at terminations where folds plunge at ‘steep’ angles, where hanging wall cutoff lines trend at ‘high’ angles to fault strike, where stratigraphic contacts trend at ‘high’ angles to fault strike, etc.). We created pseudo-three-dimensional model terminations of individual fault-related folds using both displacement gradients and lateral/oblique ramps to determine if unique characteristics in their map expressions exist. We show that map patterns of folds produced by a displacement gradient along a thrust fault of constant geometry are similar to map patterns of folds produced by constant slip on a thrust fault with a lateral/oblique ramp. Specifically, our modeling results suggest that (1) simple fault-bend folds that plunge less than 20° and simple fault-propagation folds that plunge less than 50° at their terminations can be created by both displacement gradients and lateral/oblique ramps; angles greater than these values suggest that a lateral/oblique ramp may be involved in forming the termination, (2) hanging wall cutoff lines at terminations that trend at angles less than about 35° to fault strike for simple fault-bend and fault-propagation folds also may be produced by both displacement gradients and lateral/oblique ramps; higher angles likely indicate the presence of a lateral/oblique ramp at the termination, (3) the angle at which stratigraphic contacts trend to the fault strike cannot be used to uniquely identify displacement gradients or lateral/oblique ramps for simple fault-related folds, (4) stratigraphic separation diagrams can indicate the presence of ramps in the thrust sheet, but do not uniquely differentiate between frontal ramps with displacement gradients and lateral/oblique ramps, and (5) actual changes in fault orientation (after topographic influences have been taken into account), by definition, indicate a lateral/oblique ramp. In reality, most natural fault-related fold terminations probably share components of both displacement gradients and lateral/oblique ramps, with each structure possessing contributions from each mechanism.

Quick-look techniques for evaluating two-dimensional cross sections in detached contractional settings

For more than 30 yr, geologists and geophysicists have used balancing techniques to constrain their cross-sectional interpretations in detached contractional settings. The quality of the resulting interpretations commonly directly correlates to the quality of the data, the balancing and interpretational experience of the interpreter, and the time allotted for the interpretation. We demystify the balancing process and present quick-look techniques for quickly and effectively detecting and preventing common cross section balancing errors in detached contractional settings. Common balancing problems are highlighted through close scrutiny of hanging-wall and footwall ramps and flats; such analysis helps identify inconsistencies in the numbers of ramps and flats, in the strata and stratal thicknesses in corresponding ramps, and in displacement along the fault. These techniques possess the additional advantages of being useful at any stage of the interpretational process for time or depth sections and being easily comprehensible by students, geologists, geophysicists, and managers alike. The quick-look techniques, however, are not an all-encompassing panacea. They do not guarantee a unique and/or correct cross-sectional interpretation; instead, they serve to focus the interpreters attention on potentially problematic areas in the cross section that might require explanation and/or reinterpretation.

Seismic expression and kinematics of a fault-related fold termination: Rosario structure, Maracaibo Basin, Venezuela

Abstract Fold terminations are primary features of deformed belts and are critical elements in understanding the 3-D kinematics of fault-related folds. Typically, such terminations form due to loss of displacement on the genetically-related thrust fault and/or to along-strike change in fault attitude, forming a lateral or oblique ramp. To unambiguously determine the mechanism responsible for a given fault-related fold termination, footwall cutoffs and along-strike displacement variation must be constrained. Reflection seismic data can provide the detail necessary to uniquely describe these features. The Rosario structure in the Maracaibo Basin, Venezuela is an example of a natural fault-related fold that possesses a southern termination whose fold/fault geometry and along-strike displacement variation are constrained by industry reflection seismic and well data. We interpret that the fold plunge near the southern termination is due to an along-strike decrease in displacement. The fault geometry associated with the southern termination changes from a flat–ramp–flat at the crest of the structure where displacement is greatest to simply a ramp near the lateral fault tip, without forming a lateral or oblique ramp. We combine these observations regarding displacement and fault geometry with the assumption that along-strike spatial variations reflect temporal variations during development of a fault-related fold to propose a kinematic model for the Rosario structure. Specifically, we suggest that the structure first initiated as an isolated fault ramp within the ‘stiff’ carbonate and clastic units. With increased shortening, the fault grew to link with upper and lower detachments in the weaker shale units to create a hybridized fault-bend fold. Our model suggests a possible explanation for the evolution of the Rosario structure, and also provides an alternative to existing pseudo-three-dimensional models for fault-related fold growth that relaxes the rigidity in the assumption of along-strike self-similarity.

DETACH: an Excel spreadsheet to simulate 2-D cross sections of detachment folds

Structural geologists now recognize detachment folds as fundamental structural features in many contractional settings. Several two-dimensional geometric and kinematic models exist to describe the development of such detachment folds; however, most are not available in a computer-based format that permits the forward-modeling and graphical representation of the detachment fold geometry. We developed DETACH, a Microsoft Excel(TM) spreadsheet, to construct simple cross sections of detachment folds using published geometric and kinematic models. DETACH allows users to assess the range of possible fold geometries and detachment depths that can be constructed using a prescribed set of fold kinematics, and to quickly evaluate and select a best-fit kinematic model for folds of known geometry. We illustrate DETACHs capabilities by modeling a two-dimensional cross section of a natural detachment fold and by constructing pseudo-three-dimensional models of detachment fold terminations with the assistance of Geosec2D(TM) and Gocad(TM) structural modeling software.