Basil Tikoff

Strain modeling of displacement-field partitioning in transpressional orogens

In regions of oblique plate convergence, deformation is generally partitioned into strike-slip and contractional components. We use a strain model of transpression, based upon a three-dimensional velocity gradient tensor, to address the question of why such partitioning occurs. An exact relationship between angle of plate convergence, instantaneous strain, and finite strain is calculated, providing a predictive tool to interpret the type and orientation of geological structures in zones of oblique convergence. The instantaneous and finite strain axes are not coincident, and thus there is no simple relationship between instantaneous strain (or stress) and structures that developed over a protracted deformation, such as crustal-scale faults. In order to simulate more realistic geological settings, we use a partitioning model of transpression which quantifies the effect of fault efficiency on the displacement field. This model is applied to two transpressional settings: Sumatra and central California. Sumatra shows a very low degree of partitioning of the displacement field and a relatively small offset on the Great Sumatran fault. In contrast, central California displays a large degree of displacement partitioning, and efficient slip on the San Andreas fault system. Since both systems show partitioning of deformation into strike-slip and thrust motion, it is unlikely that the San Andreas fault is rheologically ‘weaker’ than the Great Sumatran fault. We propose that the difference in fault efficiency results from kinematic partitioning of the displacement field controlled by relative plate motion, rather than mechanical decoupling generated by fault weakness.

The deformation matrix for simultaneous simple shearing, pure shearing and volume change, and its application to transpression-transtension tectonics

Simultaneous simple shearing and pure shearing, with or without additional volume change, can be combined into a single, upper triangular deformation matrix. The off-diagonal term, Γ, is named the effective shear strain, and is a simple function of the pure shearing and simple shearing components. A three-dimensional deformation matrix for the simultaneous combination of coaxial deformation, with or without additional volume change, and up to three simple shearing systems with mutually orthogonal shear planes is also presented. By using this matrix, one can easily extract the various properties of incremental as well as finite strain, and the progressive as well as finite rotation of passive markers during deformation. The case of transpression-transtension is revised, using the unified deformation matrix. The orientation of the major axis of the strain ellipsoid (λ1) is always horizontal if the deformation is transtensional, switches from horizontal to vertical during transpressional wrenching (1 >Wk > 0.81 for constant vorticity deformations), and is always vertical for highly transpressional deformations (Wk ⩽ 0.81). For transpression, material lines initially rotate towards the horizontal shearing direction, but generally turn to rotate towards the vertical axis after a certain strain. For transtension, all material lines rotate towards a direction in the horizontal plane which is oblique to the shearing direction.

Oblique plate motion and continental tectonics

Three-dimensional deformation is necessarily associated with oblique plate convergence and commonly results in partitioning of deformation between contractional and transcurrent components along plate margins. Kinematic models of strike-slip partitioning for transpression and transtension allow the exact relation among three critical parameters—plate motion, instantaneous strain axes, and degree of strike-slip partitioning—to be calculated. Application to two end-member tectonic environments characterized by a low (South Island, New Zealand) and high (central California) degree of strike-slip partitioning demonstrates a remarkable consistency among the three parameters, suggesting that strike-slip partitioned transpression is a valid model for deformation in these regions. The extreme degree of strike-slip partitioning in wrench-dominated systems, such as central California, is tentatively associated with a fundamental misorientation of finite and instantaneous strain axes.

Stretching lineations in transpressional shear zones: an example from the Sierra Nevada Batholith, California

A rotary multi-pass horizontal cooker of the type having inner and outer shell spirals with a reel between the spirals admits containers near one end of the outer shell, passes them a short distance along the outer shell spiral, transfers them to the inner shell spiral for one major inner pass, transfers them back to the outer shell spiral for a major outer pass, and discharges them directly from the outer shell.

Extended models of transpression and transtension, and application to tectonic settings

Abstract We introduce a spectrum of transpressional and transtensional deformations that potentially result from oblique plate interaction. Five separate types of deformation are designated, in which a simple shear deformation is combined with an orthogonal coaxial deformation. The types vary in the amount of extension v. contraction, both parallel to the margin and vertically. The interaction between the angle of convergence, kinematic vorticity, infinitesimal strain axes, finite strain, and rotation of material lines and planes is investigated. Quantification of the finite strain indicates that the orientation, magnitude, and geometry (flattening, constriction, etc.) change continually during steady-state transpression. These results are then applied to the cases of transpression, particularly resulting from oblique plate convergence of terranes. The obliquity of plate motion and the geometry of the plate margin determine which of the types of transpression or transtension is favoured. A component of margin-parallel stretching also potentially causes terrane motion to locally exceed oblique plate motion, or move opposite to the general direction of movement between the converging plate boundaries. The kinematic models also suggest that the boundaries between converging terranes are likely to exhibit vertical foliation, but either vertical or horizontal lineation. Finally, narrow transpressional zones between colliding blocks may have very high uplift rates, resulting in exhumation of high-grade metamorphic fabrics.

Crustal-scale, en echelon "P-shear" tensional bridges: A possible solution to the batholithic room problem

The apparent paradox of voluminous granitoid emplacement in an overall compressional magmatic are has been somewhat alleviated by the idea of pluton emplacement in tension cracks and dilational jogs within arc-parallel, strike-slip fault systems. As an alternative hypothesis, we propose that an en echelon P-shear array provides a continuous, batholith-scale zone of dilation along the trend of active magmatism and that it is favored by transpressional tectonics. In the Sierra Nevada, California, the Late Cretaceous granitoids of the Cathedral Range intrusive epoch are consistent with emplacement into bridges between P shears because (1) they are elongated oblique to the magmatic trend, consistent with P-shear orientation within a dextral system; (2) they were all emplaced within 5-10 m.y. along a 300 km trend, resulting in a displacement rate of ∼1 cm/yr across the arc; and (3) syn- to late-magmatic, dextral shear zones bound and crosscut the plutons, as in a P-shear tensional bridge.

Upper mantle tectonics: three-dimensional deformation, olivine crystallographic fabrics and seismic properties

Forward numerical models are used to investigate the effect of deformation regime on the development of olivine lattice-preferred orientations (LPO) and associated seismic anisotropy within continental deformation zones. LPO predicted to form by pure shear, simple shear, transpression, or transtension are compared to a database comprising ca. 200 olivine LPO from naturally deformed upper mantle rocks. This comparison suggests that simple shear or plane combinations of simple and pure shear are probably the dominant deformation regimes in the upper mantle. Seismic properties, calculated using the modeled olivine LPO, suggest that seismic anisotropy data may carry information on the deformation regimes active in the lithospheric mantle, although not all deformation regimes are characterized by a distinct seismic anisotropy signal. Transtensional deformation in continental rift systems should result in fast S-wave polarization and P-wave propagation directions oblique to the rift trend within the extended lithospheric mantle. Simple shear (wrench) or transpression in vertical deformation zones and pure shear (horizontal extension) result in similar seismic anisotropy. Simple shear or widening‐thinning shear may, however, induce obliquity between seismic and magnetotelluric electrical conductivity anisotropy data. Similarly, it is not possible to distinguish between simple shear or lengthening‐thinning shear (plane transpression) in horizontal deformation zones (thrusts) and pure shear (vertical contraction=horizontal extension). In all cases, the polarization direction of the fast split S-wave and the fast P-wave direction parallels the flow direction, but the anisotropy for both Pn- and S-waves is lower in horizontal structures than in vertical ones. Finally, several deformations show an isotropic response to SKS and=or Pn waves, suggesting that seismic isotropy does not necessarily imply absence (or heterogeneity) of deformation. There is a good agreement between model predictions and seismic anisotropy data in both transtensional and transpressional zones, suggesting coupled deformation of the crust and mantle. Oblique fast S-wave polarization directions in the East African rift, for instance, may result from an early transtensional deformation in the mantle lithosphere below the rift system. In contrast, most thrust belts display fast S-waves polarized parallel to the trend of the belt. One possible interpretation is that the upper mantle is decoupled from the crust in these areas.

Simultaneous pure and simple shear: the unifying deformation matrix

Abstract Any simultaneous combination of finite simple shear and finite pure shear is a linear transformation which can be expressed as a single transformation matrix. For two dimensions, the matrix is upper triangular with an off-diagonal term, Γ, called the effective shear strain. Γ is a simple function of the pure and simple shear components. For three dimensions, a simultaneous combination of thrusting in the x direction, thrusting in the y direction, and a wrench in the x direction, in addition to 3 orthogonal components of coaxial strain, can also be represented by a 3 × 3, upper triangular matrix. Here, three off-diagonal terms (Γxy, Γx,y, and Γy,z) occur. Γxy is a simple function of the horizontal coaxial strain values and thrusting in the x direction, Γyz depends on the coaxial strain components in the y and z directions and the thrusting in the y direction, while Γxz is related to all six strain components. The matrix also allows for volume change, either homogeneously or preferentially in a single direction. A method of decomposing the deformation matrix into a series of incremental deformation matrices, where each incremental deformation records the same kinematic vorticity number as the finite deformation is shown. The orientation and magnitude of the finite-strain ellipsoid (ellipse) is easily and accurately found at any increment during the deformation.

Transpressional kinematics and magmatic arcs

Abstract Most continental magmatic arcs occur in obliquely convergent settings and display strike-slip movement within, or adjacent to, the magmatic arc, and contractional structures in the forearc and backarc regions. Thus, three-dimensional transpressional kinematics typifies many arc settings, both modern and ancient. Intrusions cause magma-facilitated strike-slip partitioning, even in cases where the relative angle of plate convergence is almost normal to the plate boundary. Transpressional systems are preferentially intruded by magmas because of the steep pressure gradients in vertical strike-slip shear zones and their ability to force magma upward. Both buoyancy and transpressional dynamics cause a component of magma overpressuring, which in turn expels granitic magma upward following the vertical pressure gradient. The tectonic and magmatic processes are linked in a positive feedback loop which facilitates the upward movement of magma. We propose a lithospheric-scale, three-dimensional model of transpressional arc settings. Strike-slip motion is partitioned into the magmatic arc settings because of the linear and margin-parallel trend of the vertical, lithospheric-scale weakness caused by ascending magma. The parallelism of contraction structures in the forearc and backarc regions is caused by mechanical coupling through the lower crust and upper lithospheric mantle. The displacement field of the basal layer of the arc system provides the boundary condition for the upper-crustal, strike-slip partitioned deformation.

Thirty-Five-Year Creep Rates for the Creeping Segment of the San Andreas Fault and the Effects of the 2004 Parkfield Earthquake: Constraints from Alignment Arrays, Continuous Global Positioning System, and Creepmeters

We present results from differential Global Positioning System (gps) surveys of seven alignment arrays and four continuous gps sites along the creeping segment of the San Andreas fault. Surveys of four alignment arrays from the central creeping segment yield 33- to 36-year average minimum slip rates of 21–26 mm/yr. These rates are consistent with previous alignment array surveys spanning a 10-year period and with rates determined by creepmeters, indicating approximate steady- state creep along the central creeping segment for at least 35 years. Motion between continuous gps sites that span the central creeping segment is 28.2 ± 0.5 mm/yr for two sites that are 1 km apart and 33.6 ± 1 mm/yr for two sites that are 70 km apart. Slip rates therefore increase with distance from the creeping segment of the San Andreas fault. All rates reported here are significantly slower than the 39 ± 2 mm/yr rate predicted for motion between the Sierra Nevada–Great Valley block and the Pacific plate. Repeat surveys of three alignment arrays following the 2004 Parkfield earthquake demonstrate that its coseismic and short-term postseismic offsets decrease rapidly with distance from the epicenter, from 150 mm to 15 mm to <5 mm at respective distances of 9, 36, and 54 km to the northwest. Continuous gps data confirm that little coseismic and postseismic slip occurred along the central creeping segment. Geodetic and geologic slip rates are compared and different models for the accommodation of transcurrent deformation across the creeping segment are discussed.