John Wickham

Fault displacement-gradient folds and the structure at Lost Hills, California (U.S.A.)

Abstract Geometric models of fault-propagation folds require that the underlying fault tip propagate upward across layering. However, related folds can be generated if the tip remains stationary, or even moves back along the ramp as a pre-existing fault is reactivated. Fault-propagation folds, detachment folds, as well as those produced when there is no propagation are generated by a displacement gradient along the underlying fault, and, as a general class, can be called fault displacement-gradient folds. New geometric equations are derived which relate fold shape to displacement gradient, and fault-propagation folds are a special case of these more general equations. Growth sequences associated with these structures have been used to distinguish fault-propagation folds from fault-bend folds when the underlying structure is obscured. A displacement-gradient fold in which the fault tip retreats back down the ramp generates a growth sequence that in some cases could be confused with that of a fault-bend fold. The structure at Lost Hills, in the San Joaquin Valley of California (U.S.A.) has been interpreted as a fault-bend fold, but it may be a displacement-gradient fold which formed as a pre-existing fault was reactivated during a Pliocene change in plate motion.

Plate tectonics models for the Ouachita foldbelt

Plate tectonics models proposed for the Ouachita foldbelt include cordilleran models, flip models, and collision models. Upper-plate cordilleran models and flip models fail because (1) no Paleozoic plutonic rocks or high-temperature, low-pressure metamorphic rocks have been found, (2) volcanic and metamorphic components are rare in the Carboniferous Ouachita flysch, and (3) the subsidence history of the craton suggests an Atlantic-type margin during part of the Carboniferous flysch interval. Collision models fit the known geologic data best. An oceanic part of the North American plate was consumed beneath a southern continental mass (South America?), which contained the magmatic arc. Collision began in Early Pennsylvanian time, with postcollision convergence through earliest Permian time.

Experimental analysis of folding in simple shear

Abstract Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded. Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks. Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater. Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions. The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.

Finite-element simulation of asymmetric folding

Abstract Fold shapes and strain distributions produced in stiff single layers inclined up to 20° to the direction of principal shortening were investigated using finite-element computer models. The finite-element model was formulated for constant-strain quadrilaterals using the constitutive equation for a compressible, linearly viscous fluid. The model of a stiff layer imbedded in a less viscous medium was designed to accommodate 2 1 2 Biot wavelengths. Inclinations of the stiff layer to the shortening direction were 0°, 5°, 10°, 15° and 20°. At each inclination folds were produced with viscosity ratios of 17 : 1, 24 : 1 and 42 : 1. Folds were initiated by prescribing symmetric sinusoidal perturbations with limb dips of 2°. Results from models with 0° initial inclinations are similar to results obtained by others. Folds are sinusoidal and symmetric, and strain distributions are symmetrically disposed about axial planes in both the matrix and stiff layer. As layer inclination is increased, these features change. The folds become asymmetric (as measured by the ratio of limb lengths), and the amount of asymmetry increases with inclination. Finite-strain distributions in both the stiff layer and matrix are not symmetrically disposed about the axial plane. Principal strains in the matrix tend to parallel the long limb of the stiff layer, and are “refracted” through the long limb at a larger angle than through the short limb.

Strain paths and folding of carbonate rocks near Blue Ridge, central Appalachians

Two-dimensional incremental and accumulating strain paths have been calculated from displacement paths preserved by syntectonic, fibrous growths of calcite in ten specimens from limbs of various folds of the Conococheague Formation. The folds are asymmetric, possess a slaty cleavage, and consist of multilayers of mechanically stiff dolomite interlayered with less stiff limestone in which displacement paths were measured. The strain paths are referred to a local, rotating coordinate frame which is approximately defined by the strata as they rotate during folding. The calculated strain paths give an estimate of the change in orientation of the principal directions of strain with respect to layering on fold limbs. As expected, the principal extensional strain begins at a high angle to layering and rotates toward layering as folding progresses. The sense of rotation reverses on opposite fold limbs, and one limb tends to have smaller magnitudes of rotation than the other. Similar strain paths occur on the limbs of finite-element computer models of asymmetric folds produced by buckling single layers inclined as much as 15° to the direction of boundary shortening. Although the natural folds are multilayers, comparison with the computer models indicates that strata near Blue Ridge were locally inclined as much as 15° to the direction of bulk shortening. If this direction was nearly horizontal, some strata may have had dips as high as 15°NW prior to late Paleozoic deformation.

Restoration of structural cross-sections

Abstract Cross-section restoration transforms deformed stratigraphic boundaries (the cross-section) into a less deformed state at an earlier time in the structural history. It is best described by transformation equations which incorporate rigid translation and rotation plus deformation. These equations can be linear (affine) or non-linear. Strain is a function of the transformation constants, and linear transformation equations produce homogeneous strain. Most existing restorations use linear transformations, and many assume simple shear strain, a special case of linear transformation. Linear transformations (such as simple shear) cannot, in general, preserve both area and continuity in cross-section restoration: i.e. if area is constrained, there will be gaps and overlaps between different regions of the restored cross-section. If gaps and overlaps are eliminated, area cannot be constrained. Cross-section restoration can be achieved by solving a geometric boundary value problem using quadrilateral domains with non-linear transformations. The geometric boundary conditions are specified by knowlege of the position of an undeformed layer boundary and the pin line. Strain measured in the field can be incorporated as an initial condition. Discontinuities (faults) can be incorporated into the solution by treating them as an internal boundary without gaps or overlaps.

Structural History of a Portion of the Blue Ridge, Northern Virginia

The Front Royal area is on the west flank of the Blue Ridge uplift in northern Virginia. The rocks include Precambrian gneisses nonconformably overlain by Precambrian clastic and volcanic rocks and Cambrian to Ordovician siliceous clastic rocks, carbonate rocks, and graywacke-slate. Regional metamorphism of greenschist grade affected all of these rocks during the Paleozoic. Deformation accompanied metamorphism producing folds, slatey cleavage, and mineral lineation. Cleavage locally cuts across hinge surfaces of folds suggesting that cleavage formed late in the folding process after folds were well defined. The cleavage normal is interpreted as paralleling the short axis of a finite strain ellipsoid, and the lineation as paralleling the long axis. Both of these directions line in a northwest-southeast plane approximately perpendicular to the fold hinges. Pressure solution surfaces and quartz deformation lamellae also indicate that maximum compressive stress was at some time nearly perpendicular to cleavage. Superimposed folds distort the slatey cleavage and a fracture cleavage parallels the hinge surfaces of some of these folds. Striated fractures occur in all formations. The striations, which are interpreted as displacement directions, statistically lie in the northwest-southeast plane which is perpendicular to hinge lines of the bedding folds. Major reverse faults, high-angle longitudinal faults, high-angle transverse faults, and zones of en echelon tension fractures occur with displacements in the same northwest-southeast plane defined by the slatey cleavage, mineral lineation, and striations on fractures. Bedding folds, slatey cleavage and lineation, fracture cleavage, superimposed folds, striated fractures, reverse faults, high-angle longitudinal faults, transverse faults, and zones of en echelon tension fractures are a chronological sequence of structures related to each other by displacement directions statistically oriented in a northwest-southeast plane approximately perpendicular to fold hinges. The sequence indicates that the rocks were first ductile but became more brittle and fractured as deformation proceeded. Principal stress directions were constant enough throughout deformation to keep displacement directions of the various tectonic structures statistically oriented in the same plane. This kinematic uniformity implies, but does not prove, only one Paleozoic diastrophic event in the Blue Ridge of northern Virginia.

Relationships of rock cleavage fabrics to incremental and accumulated strain in the conococheague formation, U.S.A.

Abstract Pressure solution coupled with twin gliding, and recrystallization acted to form two geometrically distinct cleavages in the Conococheague Formation, northwest Virginia and West Virginia. Limestone layers contain a penetrative cleavage ( S p ) formed by pervasive pressure solution (Coble creep), with twin gliding in more highly deformed zones. Dolomite layers contain a spaced solution cleavage ( S s ) formed by pressure solution, also with twin gliding in highly deformed zones. Recrystallization textures occur in highly deformed zones of limestones and dolomites. Incremental strain shows that layering was initially inclined as much as 30° to shortening, and that the deformation was locally non-coaxial, as viewed by the deforming material on the fold limbs. Spaced cleavage zones are curved, and closely match the initial and final orientations of incremental elongation. Penetrative cleavage parallels the elongation axis of accumulated strain (measured using deformed ooids). Pressure solution surfaces in dolomites concentrate insoluble materials. Deformation, together with twin gliding, and recrystallization are greatest in the hinge zones of folds and least on shallowly dipping limbs of asymmetric folds. The deformation mechanism path of calcite and dolomite are similar; changing from pressure solution to twin gliding with recrystallization as strain rate (strain energy density) increases.

Viscosity-based numerical model for fault-zone development in drape folding

Abstract The propagation of a fault zone through homogeneous and layered sedimentary materials above a basement deflection was simulated using a finite-element solution for slow, incompressible viscous flow. The layered models represented a generalized stratigraphic section of the Paleozoic and Mesozoic strata of the Wyoming Province, U.S.A. Fractured elements within the models were determined for each increment of deformation using the Mohr-Coulomb fracture criterion and the viscosity of those elements was decreased prior to subsequent increments. In this manner the effects of local fracturing on subsequent deformation were included. In homogeneous models, failure begins near the basement deflection and propagates discontinuously upward. The length of the fault zone depends on the vertical velocity imposed on the bottom boundary and the width of the deflection. The resulting fault zone is a high-angle, rather straight, reverse fault which is in contrast to the curved, concave downward faults predicted by previous elastic analytical solutions. However, the analytical solutions were based on the initial stress field and do not take into consideration any changes that occur within the body during deformation. In contrast to this, the finite-element models can be used to study the changes in the state of a body that occur during deformation. Deformation rates determine the style of deformation and the location and intensity of fracturing. High gradients of mean pressure occur near the basement deflection and the fault zone is initiated in a region of anomalously low pressure produced by deformation. Faults develop as a consequence of the coalescense of fractured elements that occur during deformation. The width of the fault zone varied from layer to layer depending on its stiffness. Narrow fault zones develop in weak layers and wide zones in stiffer layers. In both homogeneous and layered models, extensional fractures occur near the surface on the upper block.

Evolution of Folds around Broken Bow Uplift, Ouachita Mountains, Southeastern Oklahoma

Folds in the studied area range from a few centimeters to 3 km in wavelength and are asymmetric with sharp angular hinge zones. Anticlines are overturned southward away from the continental interior. Fold hinges trend east-west and are arched over the Broken Bow uplift which trends northeast across the fold hinges. Asymmetric minor folds are present on the limbs of larger structures, but many minor folds do not exhibit a change in symmetry from one limb of the larger fold to the other. Slaty cleavage is common in the southern part of the Broken Bow uplift and rare in the north. Cleavage is distributed symmetrically about axial planes in many folds. However, in the southern part of the uplift, slaty cleavage cuts across axial planes of folds at angles up to 30°. This cross-cutting relation is present in both outcrop-size folds and folds with wavelengths of a kilometer or more. The Broken Bow uplift has at least three recognizable phases of deformation. The first phase produced buckle folds that probably were generated by gravitational body forces during the rapid deepening of the basin axis in the north associated with flysch sedimentation during the Carboniferous. The second phase was associated with the principal Ouachita diastrophism in the Late Pennsylvanian or Early Permian. The northward dipping slaty cleavage was superimposed on the earlier folds and cut across their hinge surfaces. Original fold shapes were modified greatly and anticlines were overturned producing north-dipping fold axial planes. These north-dipping axial planes are inconsistent with previous suggestions that a mobile core or infrastructure is buried beneath the Mesozoic coastal pla n sediments in the south. Additional small-scale folds probably were generated during this second phase. The second phase may have contained a large regional shear-strain component produced by underthrusting the basement toward the continental interior. The last deformation phase produced the Broken Bow uplift by arching east-west-trending folds and slaty cleavage about a northeast-southwest axis. Movements were essentially vertical with little internal deformation of the rocks.