Robert J. Twiss

Theory and Applicability of a Recrystallized Grain Size Paleopiezometer

An approximate theoretical relation is derived which relates stress during steady state creep to both subgrain size and dynamically recrystallized grain size. The relation results from equating the dislocation strain energy in the grain boundary to that in the enclosed volume. Available data on metals and silicates are in excellent agreement with the theory. For paleopiezometry, the recrystallized grain size must be preserved by quenching, by cooling under stress, or by inhibition of grain growth by intimate mixture of two or more phases. In general, stress may be underestimated using rocks in which grain size has been reduced by dynamic recrystallization, especially if the grain size is very small. Stress may be overestimated using coarse grained rocks in which the grain size has increased toward the steady state value. Quantitative limits remain to be established. The theoretical relation can in principle be applied to any metal or mineral if only the effective isotropic elastic moduli and the Burgers vector are known. When used as a paleopiezometer, the technique indicates that high stresses on the order of 100 MPa are not infrequently associated with mantle diapirism and with large scale thrust faulting. Consideration of the Mt. Albert ultramafic body suggests that texturally inferred stresses from peridotite massifs and from ultramafic xenoliths in alkali olivine basalts might reflect either horizontal variations in stress across a rising diapir or else a vertical variation in stress as defined by the pyroxene geobarometer (Mercieret al. 1977). In either case the stresses are probably characteristic of local diapirism. Stresses characteristic of global upper mantle flow might be inferred from xenoliths originating from above kimberlite-producing diapirs.

Analysis of fault slip inversions: Do they constrain stress or strain rate?

Fault slip data commonly are used to infer the orientations and relative magnitudes of either the principal stresses or the principal strain rates, which are not necessarily parallel or equal. At the local scale of an individual fault, the shear plane and slip direction define the orientations of the local principal strain rate axes but not, in general, the local principal stress axes. At a large scale, the orientations of P and T axes maxima for sets of fault slip data do not provide accurate inversion solutions for either strain rate or stress. The quantitative inversion of such fault slip data, however, provides direct constraints on the orientations and relative magnitudes of the global principal strain rates. To interpret the inversion solution as constraining the global principal stresses requires that (1) the fault slip pattern must have a characteristic symmetry no lower than orthorhombic; (2) the material must be mechanically isotropic; and (3) there must be a linear constitutive relationship between the global stress and the global strain rate. Isotropic linear elastic constitutive equations are appropriate to describe the local deformation surrounding an individual slip discontinuity. Fault slip inversions, however, constrain the characteristics of a large-scale cataclastic flow, which is described by constitutive equations that are probably, but to an unknown degree, anisotropic and nonlinear. Such material behavior would not strictly satisfy the requirements for the stress interpretation. Thus, at the present state of knowledge, fault slip inversion solutions are most reliably interpreted as constraining the principal strain rates.

The effect of block rotations on the global seismic moment tensor and the patterns of seismic P and T axes

Distributed brittle deformation of the Earths crust involving block rotations is comparable to the deformation of a granular material, with fault blocks acting like the grains. The deformation of a granular material is not adequately described using classical continuum mechanics because the individual grains within the material rotate in a manner that is not uniquely determined by the large-scale average deformation. Thus a theoretical link has not existed between the kinematics of deformation involving block rotation and the associated effects on the seismic moment tensor and focal mechanism solutions. We establish this link using micropolar continuum theory (Eringen, 1964, 1966 a, b; Eringen and Suhubi, 1964) and the analysis of the effect of block rotations on fault slickenline patterns by Twiss et al. (1991). This theory takes into account two separate scales of motion: a large-scale average motion of the material, the macromotion, composed of a macrodeformation rate (i.e., a macrostrain rate) and a macrospin, and a local motion, the microspin, that describes the average rotation rate of grains in the material. The micropolar kinematic theory allows us to predict the orientations of coseismic slip directions V on local shear planes of any orientation in a large-scale shear zone. We define a local and a global asymmetric micropolar seismic moment tensor in terms of these slip directions. For a restricted kinematic model, the theory shows that two scalar parameters, D and W, determine the symmetry of the global micropolar seismic moment tensor and the pattern of seismic P (shortening) and T (lengthening) axes. The deformation rate parameter D is defined in terms of the principal values of the deformation rate tensor . The deformation is transtensional (constrictional) if 0 ≤ D ≤ 0.5, plane strain if D = 0.5, and transpressional (flattening) if 0.5 < D ≤ 1. The net vorticity parameter W is a normalized value of the difference between microspin and macrospin . It is an objective variable. W = 0 implies that the global micropolar seismic moment tensor is symmetric and that P and T axis patterns have orthorhombic or higher symmetry. W ≠ implies that the global micropolar seismic moment tensor is asymmetric and that P and T axis patterns have monoclinic symmetry. The antisymmetric part of the global micropolar seismic moment tensor is associated with the net vorticity that characterizes the deformation. W has different values for different models of rigid block rotation and thus could serve to identify the rotation mechanism.

Theory of slickenline patterns based on the velocity gradient tensor and microrotation

Abstract Brittle fault zones commonly are characterized by a multitude of lineated shear planes having a wide distribution of orientations. In our model, we assume the faulted rock comprises an aggregate of rigid blocks whose surfaces are the shear planes. We define two independent scales of motion to distinguish the local rigid rotation of the blocks with their shear planes (the “micromotion”) from the average deformation of the material on a macroscopic scale (the “macromotion”). The macromotion is defined by the macrovelocity gradient tensor, which is separated into symmetric and antisymmetric parts, the deformation rate and the macrospin tensors respectively; the micromotion is defined by a microspin tensor. On any shear plane, slickenlines form parallel to the direction of the maximum rate of shear, which we assume is determined by the direction of the maximum component of the macrovelocity gradient tensor tangent to the shear plane and by a component of the microspin in the shear plane. For a restricted kinematic model, patterns of slickenline orientations are defined on a uniform distribution of shear plane orientations by the values of D and W . D is a ratio of differences in the principal values of the deformation rate tensor, and W is a ratio of the net spin to the maximum rate of macroshear. We distinguish between instantaneous slickenline patterns and finite-deformation patterns. The two are different if the shear planes rotate relative to the principal deformation rate axes, in which case finite-deformation slickenlines form curved or crossing lineations. If W = 0, the instantaneous slickenline patterns have orthorhombic symmetry (0 D D = 1 or 0). If W ≠ 0, the instantaneous slickenline patterns have monoclinic symmetry. For pure shear in an isotropic body, instantaneous slickenline patterns have orthorhombic symmetry ( W = 0, D = 0.5) whereas for pure shear accommodated by shear on a planar anisotropy ( W = −1 , D = 0.5), the pattern is monoclinic. For simple shear with the rigid rotation of local shear planes defined by the shear-induced spin ( W = 0, D = 0.5), the instantaneous slickenline pattern is orthorhombic but the finite-deformation pattern is monoclinic. For simple shear with no shear plane rotation ( W = −1, D = 0.5), the instantaneous pattern is monoclinic. Special cases of our hypothesis are equivalent to the hypothesis that slickenlines are parallel to the direction of maximum resolved shear stress (e.g. Angelier, 1979, 1984). The slickenline patterns predicted for this case are always of orthorhombic or higher symmetry, and are equivalent to our instantaneous patterns for which W = 0 and to our finite-deformation patterns for which, in addition, there is no microspin.

Structural superplastic creep and linear viscosity in the earth's mantle

Abstract The rheology of dry polycrystalline olivine is examined by adopting a hyperbolic sine flow law (which reduces to a power law below 3 kbars) for high stress behavior, and a model for diffusion accommodated, coherent, grain boundary sliding (structural superplastic creep) for low stress behavior. The model for superplastic creep gives a linear relation between stress and strain rate and is consistent with the behavior of polycrystalline olivine during ductile faulting experiments (Post, 1973). For any given stable grain size, linear superplastic creep is promoted by relatively low stress and temperature. For a 1 -cm grain size and a homologous temperature between 0.6 and 0.8, superplastic creep dominates below transition stresses between 402 and 25 bars, respectively. Transition stresses are higher for smaller grain size and lower temperature. If grain size is stress dependent, superplastic creep is non-linear and dominates above a stress of 300 bars. Below that stress, relatively lower temperatures promote superplastic creep. Grain size may be stabilized by either physical or kinetic inhibition of grain growth, thereby allowing linear superplastic creep in the mantle. Results suggest that superplastic creep can dominate in most of the upper mantle except possibly for the asthenosphere where homologous temperatures are maximal and hyperbolic sine law creep can dominate. Mantle diapirism is at least in part accomplished by superplastic flow above and along the margins of the rising diapir.

Curved slickenfibers: a new brittle shear sense indicator with application to a sheared serpentinite

Abstract Brittle fault zones are commonly characterized by penetrative fracturing of the rock to form an aggregate of blocks, so that the rock becomes, in essence, like a granular material composed of rigid ‘grains’. The surfaces of the blocks, or ‘grains’, have a wide distribution of orientations, and shearing of the blocks past one another on these planes accommodates the large-scale motion, i.e. the macromotion, in the fault zone. During a macromotion that is a non-coaxial deformation, the rigid blocks and their surfaces may undergo a progressive rigid rotation that is distinct from the macromotion and is described by the microspin. If a macroscopic non-coaxial deformation has monoclinic symmetry, this symmetry should be reflected in the sense of rigid rotation of the blocks and their surfaces. On the surfaces of the blocks, which are local shear planes, the history of displacement may be recorded by mineral fibers that grow progessively with displacement. Because of the rigid rotation of the local shear planes, slickenfiber lineations commonly are curved. The sense of curvature from the youngest to the oldest part of the fiber, looking down the normal to the local shear plane, is different for those planes whose normals are on opposite sides of the unique monoclinic symmetry plane for the macroscopic shearing. The intersection of the symmetry plane with the plane of the fault zone defines the macroscopic slip direction, and the sense of rigid rotation of the local shear planes determined from the lineations defines the shear sense. Application of this technique to the disrupted and sheared margins of the Feather River Peridotite in the northern Sierra Nevada of California indicates that late deformation involved dextral-normal oblique slip along the Melones fault zone.

Description and classification of folds in single surfaces

Abstract I propose a new three-parameter description of fold style in folded surfaces based on the ratio of the amplitude to the half-wavelength (the aspect ratio P), the maximum angle of relative rotation of opposite limbs of the fold (the folding angle φ), and a measure of the relative curvature at the fold closure (the bluntness b ). For symmetric folds, the first two parameters define a trapezoid that circumscribes the fold and provides the primary criterion for the classification of fold style. Within a given trapezoid, fold style variations are defined by the bluntness. Perfect folds in profile are defined to have a single hinge with perfectly straight limbs tangent to hinge zones that are perfect circular arcs. An analytic description of the variation in perfect fold geometry defines the limits for all natural single-hinged folds. The proposed system includes folds with folding angles both less than and greater than isoclinal folds, it applies to both single-hinged and multiple-hinged folds, and it also can be extended to apply to asymmetric folds. Previously proposed two-parameter classification systems can only describe folds that are restricted to a specific surface through the three-parameter fold style space proposed here.

Theory of mixtures for micromorphic materials-II. Elastic constitutive equations

Abstract In Part I of this work[1], the balance equations were derived for micromorphic and micropolar mixtures. In this part, the general form of the non-linear, anisotropic, elastic, constitutive equations for micromorphic and micropolar mixtures are developed. Such equations should have application in describing the behavior of polyatomic or polymolecular crystal lattices as well as that of such materials as polycrystalline mixtures and granular composites. As an illustration, the general micropolar equations are given explicitly for a linear elastic, isotropic, two constituent mixture. The field equations are developed for the case of restricted coupling, and with these the propagation of a plane wave is studied. The longitudinal and transverse displacement waves of classical theory arise as well as longitudinal and transverse microrotation waves. Dispersion of the two displacement waves arises from the intrinsic structure of the material and is expected to be of importance at high frequencies. The two transverse waves are complexly coupled. Simplification by assuming no microrotation shows that the propagation velocity of the classical transverse displacement wave is dependent on the microrotation material parameter.

Seismogenic deformation field in the Mojave block and implications for tectonics of the eastern California shear zone

From the aftershocks of the 1992 Landers earthquake, we infer the orientation of the principal strain rate axes (d_1 > d_2 > d_3; d_1 lengthening), their relative magnitude, and the relative spin of fault blocks by using a micropolar continuum model to invert the seismic P and T axes. The seismogenic deformation is consistent with the geodetic measurements of the coseismic displacement and with the secular deformation of the central Mojave block. Regionally, the aftershock data define two major domains within the central Mojave block: (1) the western Mojave block, including the San Bernardino Mountains and the epicentral area of the Big Bear earthquake, which is characterized by E-W d_1 (lengthening) and N-S d_3 (shortening); and (2) the central Mojave block, including the Landers surface rupture zone, which is characterized by NW-SE d_1 and NE-SW d_3. Inversion for the principal strain axes of geodetically measured coseismic displacements across the Big Bear and Landers seismogenic zones gives results similar to the aftershock inversions for those areas, indicating that the aftershocks accommodate a deformation similar to the main rupture and do not reflect elastic rebound or residual stresses. The background seismicity for 1981 to 1991 shows the same characteristic d_1 and d_3 orientations for the two domains, indicating that the secular seismogenic strain has the same regional geometry as the 1992 coseismic deformation. The micropolar inversion also provides values of the relative vorticity parameter W, which reflects a difference between the vorticity of a shearing continuum and the vorticity of fault-bounded blocks rotating within tabular seismogenic shear zones. The observed fault geometry along the Kickapoo fault suggests a pinned-block model for the local block rotation that is consistent with the values of W obtained from our inversions. We interpret the regional NW-SE orientation of d_1 in the central Mojave block to be characteristic of the dextral eastern California shear zone, which transfers approximately 22% of the Pacific-North American plate motion from the San Andreas system to the Walker Lane Belt in eastern California. Our results and geodetic determinations of the secular shear strain in the central Mojave block indicate that the locus of NW dextral shear generally lies between the San Bernardino Mountains and the Pisgah fault.

Seismogenic strain and motion of the Oregon coast block

The geometry of brittle strain at the Cascadia convergent margin is inferred from small-magnitude earthquakes in the upper crust. This analysis provides quantitative data on part of the nonrecoverable component of active deformation that is reflected in geodetic observations. Our results are consistent with paleomagnetic and geodetic models that invoke northward translation of the Oregon forearc region (Oregon coast block) relative to stable North America. The latitudinal variation in the kinematics of the seismogenic deformation is best explained by Euler poles for motion between the Oregon coast block and the North America plate that are near the eastern Washington-Oregon border. General correspondence between our principal strain directions and those from recent residual global positioning system (GPS) velocities indicates progress in understanding active crustal strain from complimentary perspectives (i.e., seismicity and geodesy). Systematic differences may reflect the patchiness of seismicity relative to the coarse GPS network, the possibility of nonseismogenic permanent deformation, and/or the relative simplicity of the elastic model used to isolate the nonrecoverable deformation from the raw GPS velocities.