Peter Bird

Lateral extrusion of lower crust from under high topography in the isostatic limit

Where there is isostasy, the rocks of the lower continental crust are subject to an effective lateral pressure gradient equal to the gradient of topographic load, whether compensation is in crustal roots or in the mantle. The result is a Poiseuille flow (planar channel flow) in the weak lower crust, which removes crust from under mountains and smooths and levels the topography. Assuming cubic power law creep, the flux of crust is proportional to the third power of the topographic gradient, to the usual Arrhenius term, to the tenth power of the absolute temperature of the lower crust, and to the negative fifth power of the geothermal gradient. The result is that any initial condition with an isolated high tends eventually toward a state where the topography is pancake shaped, with a flat central plateau and steeper flanks spreading outward. When adjacent “pancakes” merge, most of the relief is eliminated. Flow may either roughen or smooth the Moho, depending on whether there are lateral density contrasts in the mantle lithosphere or not. Although it is difficult to find analytic solutions for this evolution, it is easily simulated numerically. Using various published flow laws for plausible lower crustal rocks, lateral extrusion is shown to be insignificant under the oceans, marginally significant under shields and platforms, important under elevated plains, and dominant beneath high plateaus and/or hot, delaminated regions. In particular, the Basin and Range province of the western United States cannot maintain short-wavelength (100 km) Moho relief of more than 1 km for times greater than 10–20 m.y. at most. If the Tibetan Plateau of China has been delaminated, as recently suggested, then it may flatten even faster, reducing 100-km-wavelength topographic features to 200 m relief in no more than 0.03–0.13 m.y., and leaving only features with wavelengths over 400 km at the present. Therefore the lower crust of Tibet may resemble a hydraulic reservoir, as previously suggested. Because the flatness of the Moho is self-maintained in these regions, information on past tectonics is continually lost, and the present Moho shape cannot be used to balance cross sections for times in the past. The flatness of the Moho today is not a constraint on the mechanisms of extension or shortening in these regions, nor is it evidence for underplating by intrusions. It also follows that very intense and inhomogeneous dilational strains may have occurred locally, as in the metamorphic core complexes of the Basin and Range province.

Formation of the Rocky Mountains, Western United States: A Continuum Computer Model

One hypothesis for the information of the Rocky Mountain structures in late Cretaceous through Eocene time is that plate of oceanic lithosphere was underthrust horizontally along the base of the North American lithosphere. The horizontal components of the motion of this plate are known from paleomagnetism, and the edge of the region of flat slab can estimated from reconstructed patterns of volcanism. New techniques of finite-element modeling allow prediction of the thermal and mechanical effects of horizontal subduction on the North American plate. A model that has a realistic temperature-dependent rheology and a simple plane-layered initial condition is used to compute the consequences of horizontal underthrusting in the time interval 75 million to 30 million years before present. Successful prediction of this model include (i) the location, amount, and direction of horizontal shortening that has been inferred from Laramide structures; (ii) massive transport of lower crust from southwest to northeast; (iii) the location and timing of the subsequent extension in metamorphic core complexes and the Rio Grande rift; and (iv) the total area eventually involved in Basin-and-Range style extension. In a broad sense, this model has predicted the belt of Laramide structures, the transport of crust from the coastal region to the continental interior, the subsequent extension in metamorphic core complexes and the Rio Grande rift, and the geographic region of late Tertiary Basin-and-Range extension. Its principal defects are that (i) many events are predicted about 5 million to 10 million years too late and (ii) the wave of crustal thickening does not travel far enough to the east. Reasonable modifications to the oceanic plate kinematics and rheologies that were assumed may correct these defects. The correspondence of model predictions to actual geology is already sufficiently close to show that the hypothesis that horizontal subduction caused the Laramide orogeny is probably correct. The Rocky Mountain thrust and reverse faults formed in an environment of east-west to northeast-southwest compressive stress that was caused by the viscous coupling between the oceanic plate and the base of the North American crust. Nonuniform crustal thickening by simple-shear transport also caused relative uplifts; therefore, this model is consistent with both of the range-forming mechanisms that have been inferred (1). A new proposal that arises from this simulation is that horizontal subduction also caused the subsequent extensional Basin-and-Range taphrogeny by stripping away the mantle lithosphere so that the crust was exposed to hot asthenosphere after the oceanic slab dropped away.

Plate-Tectonic Analysis of Shallow Seismicity: Apparent Boundary Width, Beta, Corner Magnitude, Coupled Lithosphere Thickness, and Coupling in Seven Tectonic Settings

A new plate model is used to analyze the mean seismicities of seven types of plate boundary (crb, continental rift boundary; ctf, continental transform fault; ccb, continental convergent boundary; osr, oceanic spreading ridge; otf, oceanic transform fault; ocb, oceanic convergent boundary; sub, subduction zone). We compare the platelike (nonorogen) regions of model PB2002 (Bird, 2003) with the centroid moment tensor (cmt) catalog to select apparent boundary half-widths and then assign 95% of shallow earthquakes to one of these settings. A tapered Gutenberg-Richter model of the frequency/moment relation is fit to the subcatalog for each setting by maximum likelihood. Best-fitting β values range from 0.53 to 0.92, but all 95% confidence ranges are consistent with a common value of 0.61–0.66. To better determine some corner magnitudes we expand the subcatalogs by (1) inclusion of orogens and (2) inclusion of years 1900–1975 from the catalog of Pacheco and Sykes (1992). Combining both earthquake statistics and the plate-tectonic constraint on moment rate, corner magnitudes include the following: crb, ![Graphic][1] ; ctf, ![Graphic][2] ; ccb, ![Graphic][3] ; ocb, ![Graphic][4] ; and sub, ![Graphic][5] . Coupled lithosphere thicknesses are found to be the following: crb, ![Graphic][6] ; ctf, ![Graphic][7] ; ccb, ![Graphic][8] ; osr, ![Graphic][9] for normal faulting and ![Graphic][10] for strike slip; otf, ![Graphic][11] , and ![Graphic][12] at low, medium, and high velocities; ocb, ![Graphic][13] ; and sub, ![Graphic][14] . In general, high coupling of subduction and continental plate boundaries suggests that here all seismic gaps are dangerous unless proven to be creeping. In general, low coupling within oceanic lithosphere suggests a different model of isolated seismic fault patches surrounded by large seismic gaps that may be permanent. Online Material : Global seismic subcatalogs of shallow earthquakes. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif [4]: /embed/inline-graphic-4.gif [5]: /embed/inline-graphic-5.gif [6]: /embed/inline-graphic-6.gif [7]: /embed/inline-graphic-7.gif [8]: /embed/inline-graphic-8.gif [9]: /embed/inline-graphic-9.gif [10]: /embed/inline-graphic-10.gif [11]: /embed/inline-graphic-11.gif [12]: /embed/inline-graphic-12.gif [13]: /embed/inline-graphic-13.gif [14]: /embed/inline-graphic-14.gif

Computer simulations of California tectonics confirm very low strength of major faults

Recent improvements in the technique of modeling fault networks with thin-plate finite elements yield full convergence of the solutions, without any compromise in the representation of the frictional rheology of the upper crust or the transition to dislocation creep in the lower crust. We apply these techniques to model the California region, incorporating all faults with estimated slip rate over 1 mm/yr, as well as variations in elevation, heat flow, and crustal thickness. Velocity boundary conditions on the model sides are based on the NUVEL-1 plate model and an approximation of deformation in the Great Basin. The frictional and dislocation-creep rheologic constants of the crust are calibrated to reproduce the observed variations in the maximum depth of seismicity, which occurs at model temperatures of 350-410 °C. This leaves two free parameters: the (time-averaged) coefficient of friction on faults, and the apparent activation energy for creep in the lower crust. These parameters are systematically varied in three sets of 10, 81, and 64 experiments, respectively. The predictions of each model are tested against three published data sets: a set of 79 geologic limits on average slip rate on faults, a set of 221 principal stress directions, and a set of 841 secular rates of geodetic baselines (both trilateration and VLBI [very long baseline interferometry]). The patterns of model scores indicate that the time-averaged friction coefficient of major faults is only 0.17-0.25, or only 20%-30% of the value (0.85) that is assumed for the friction in the intervening blocks. (The laser trilateration data taken alone would indicate a preference for a high-stress model, but this model is one with very little fault slip and seismicity, which can be rejected on other grounds.) In the final three-parameter set of 64 models, we test whether the anomalous weakness of faults is uniform or proportional to net slip. With slip-dependent weakening, there is a general reduction in prediction errors, which supports the hypothesis. The geologic data and geodetic data agree in implying that fault weakness (that is, friction of 0.17) is general, with an additional 30% slip-dependent weakening of the San Andreas (to friction of 0.12, or 14% of normal). The stress data, however, are fit best if all weakness is slip dependent (effectively, only the San Andreas is weak). Thus, the hypothesis that all weakening is slip dependent should not be rejected. The best models predict all available data with RMS (root mean square) mismatch of as little as 3 mm/yr (6% of the relative plate velocity), so their predictions may be useful for seismic hazard estimation, at least along faults where no data are available. This study extends the finding of very low friction from subduction zones, where it was previously documented, to a dominantly strike-slip system in which underthrusting of wet sediment is not widespread. Return of previously subducted water from the mantle and its chemical or physical binding in fine-grained gouge are possible explanations for the very low friction.

Kinematics of present crust and mantle flow in southern California

In the southern California region, published geologic studies of prehistoric fault offsets yield at least 81 rates of slip covering various periods of time, chiefly since the opening of the Gulf of California. These rates, together with the known geometries of active faults, are used to constrain a hand-fit block model for present horizontal velocity of the crust. The assumptions employed are that these rates apply to the present, that the blocks are internally rigid down to the greatest depth of earthquakes, and that the over-all Pacific–North American plate motion is correctly given by global models. The resulting model fits 67 data within their uncertainties, 10 more with a small discrepancy (≤ 1 mm/yr), and fails to accommodate only 4 data (2 of which are inconsistent with other data). Nominal precision is good (∼3 mm/yr), but accuracy and uniqueness are both suspect, because many block boundaries are questionable. Despite its many local defects, this model suggests four reliable regional conclusions. First, the rate of shortening on the south side of the Transverse Ranges varies from 6 to 14 mm/yr, increasing eastward, which implies an unrecognized seismic hazard, unless the motion is taken up by folding or fault creep. Second, the pattern of block rotation rates is quite different from the pattern of rotations shown by Tertiary paleomagnetic declinations, which implies some major Pliocene(?) reorganization of blocks. Third, the “great bend” (left step) of the plate boundary fault system in the Transverse Ranges appears to be straightening gradually, by a 3°/m.y. clockwise rotation relative to both plates. Finally, if it is assumed that plate shortening has been occurring at this bend since the early Pliocene and that crust and upper-mantle velocities are similar, then this model predicts mantle-lithosphere downwelling to at least 250-km depth beneath the Transverse Ranges. This prediction is consistent with upper-mantle seismic-velocity structure.

Plane-stress finite-element models of tectonic flow in southern California

Abstract The continuing, distributed crustal deformation in southern California was modelled as creeping flow in a nonlinear continuum. The crust was assumed to be in a membrane state of stress, except for the weight of topography, and subjected to plate-tectonic velocity boundary conditions. The flow law of this membrane contained a rigid-plastic term to represent the frictional faulting in the upper crust and a power-law term to represent dislocation creep in the lower crust. In addition to regional strength variations based on heat flow, some models had a weak belt representing the San Andreas fault. When calculated strain-rates were tested by cross-correlation with actual seismic moment rates, directions of shortening, and rates of vertical movement, the best model was found to be one in which the San Andreas fault is eight times weaker than the surrounding crust, perhaps because of clay gouges or fine-grained mylonites within it. This model is consistent with the absence of a detectable heat-flow anomaly at the San Andreas, and also with the difference between geologic and paleomagnetic plate velocities. The rest of the crust must be at least half as strong as is indicated by laboratory deformation, or the crust would slump southwest toward the continental shelf. However, the failure of all the models to match many details of local tectonics suggests that other faults share the anomalous weakness of the San Andreas. This is expected to limit the success of any future continuum models of the region.

Finite element modeling of lithosphere deformation: The Zagros collision orogeny

Abstract In the Zagros Mountains a formerly stable continental margin is being suddenly deformed. Finite element models of this tectonic flow are used to relate known surface deformations, earthquake locations, and fault plane solutions to unknown rock flow parameters and driving forces, in order to determine the latter. These two-dimensional plane-strain flow models incorporate the effects of nonlinear dislocation creep, frictional faulting, geological inhomogeneity, density anomalies, and varying temperature. All models driven by a subducting slab are unsuccessful because they require subduction of continental crust, which does not match present seismicity. Therefore the former oceanic slab must be detached, and the orogeny must be driven by horizontal compression in the lithosphere. Models also show that the subcrustal lithosphere is not shortened but acts as a stabilizing foundation. These results imply a simple geometry of crustal deformation which can be analytically modeled. The creep strength of the lower crust (75–100 bars) determines the topographic slope of the Zagros. The fact that subduction is not occurring on the old plate boundary places a limit on the shear stress deforming the cold upper crust. This limit is 300 bars if there is limestone at depth in the Crush Zone; otherwise 800 bars. These results are confirmed by a final finite element model. The total driving force of the orogeny associated with these limits is 2.8–5.5 · 10 15 dyne/cm, and the smaller amount could be provided by the gravitational spreading of the Red Sea rift. Shear-strain heating caused by the orogeny to date is less than 20°C. These results imply that even unheated continental crust is considerably weaker than laboratory friction measurements imply, and that it is mechanically decoupled at the Moho from the stronger mantle lithosphere.

Testing hypotheses on plate‐driving mechanisms with global lithosphere models including topography, thermal structure, and faults

A popular concept of plate tectonics is that the most important density anomalies are in oceanic plates, which descend from rise to trench while subducting slabs act as velocity regulators and the drag on the base of the lithosphere is resistive. This hypothesis has been shown to be consistent with velocities of rigid plates and to approximately predict stress directions in a global elastic shell. Here I test whether the hypothesis leads to correct plate velocities and stress directions in models of laterally heterogeneous plates of nonlinear rheology separated by faults with low friction. All models have bottom boundary conditions based on simple shear in an olivine asthenosphere extending to the transition zone, where various patterns of lower mantle flow are assumed. These models show that topography alone is not sufficient to drive plate motion at actual rates over a static or sluggish transition zone. If the forward component of velocity of each subducting slab is also imposed, then velocities are improved, but errors in stress direction become unacceptable. Better models are found by assuming that at least some parts of the transition zone have velocities greater than surface velocities, leading to active or forward basal drag. In the most plausible model, this forward drag acts only on continents, while oceanic lithosphere experiences negligible basal shear tractions. Probably the dense descending slabs of oceanic lithosphere not only pull the oceanic plates, but also stir the more viscous lower mantle, and this in turn helps to drive the slower drift of continents.

Kinematic history of the Laramide orogeny in latitudes 35°–49°N, western United States

The kinematic history of the Rocky Mountain foreland and adjacent areas is computed back to 85 Ma, using virtually all the structural, paleomagnetic, and stress data in the literature. A continuous velocity field is fit to the data in each time step by weighted least squares, and this velocity is integrated back through time. As proposed by Hamilton [1981], the net movement of the Colorado Plateau was a clockwise rotation about a pole in northern Texas; but the rotation was less (3°) than some have inferred from paleomagnetism. The Laramide orogeny occurred during 75–35 Ma, with peak Colorado Plateau velocities of 1.5 mm yr−1 during 60–55 Ma. The mean azimuth of foreland velocity and mean direction of foreland shortening was stable at 40° for most of the orogeny, increasing to 55° in 50–40 Ma; the counterclockwise rotation of shortening directions proposed by some previous authors is incorrect. Comparing the computed histories of foreland flow speed and direction with the known motions of the Kula and Farallon plates confirms that the Laramide orogeny had a different mechanism from the early Sevier orogeny: it was driven by basal traction during an interval of horizontal subduction, not by edge forces due to coastal subduction or the spreading of the western cordillera or by accretion of terranes to the coast. Tentatively, a minor clockwise rotation of shortening directions at 50 Ma may record the passage of an active Kula-Farallon transform within the subducted slab.

Hydration-phase diagrams and friction of Montmorillonite under laboratory and geologic conditions, with implications for shale compaction, slope stability, and strength of fault gouge

Abstract Absorption of water into the crystal structure of smectite clays causes a reversible volume increase exceeding 80% and a friction decrease by a factor of three. This behavior can be predicted if clay swelling is approximated as the formation of successive hydration phases and the generalized Clapeyron law is applied. In this study, new data on two standard montmorillonites saturated with sodium and calcium (Na-MM and Ca-MM) are combined with published results to define relative humidity boundaries of proposed phases at 20°C and 1 bar. From molar volumes, the effect of confining pressure is predicted; only phases with an integral number of full interlaminar water layers are stable at high pressures. In contact with liquid water, the number of interlaminar layers is governed by the “effective normal stress” on crystals. Next, vapour pressure measurements at 20°–60°C are used to calculate dehydration enthalpies, from which the effect of geologic temperatures is predicted. Under typical crustal conditions, Na-MM does not fully dehydrate until 7 km depth, and Ca-MM retains one water layer to 11 km. Since the zones of hydrocarbon maturation and montmorillonite dehydration overlap, this effect may play a part in petroleum geology, controlling migration and/or reservoir pressurization. For the first time, the friction of individual hydration phases of montmorillonite has been measured without excess water and within their stability fields. Stable-sliding deformation with negligible rate-dependence and definite work-hardening is observed, but the pressure-dependence is less than in classical friction. Na-MM phases are always weaker than their Ca-MM analogues. In both clays, the addition of the first water layer causes the greatest strength decrease, but two- and three-layer phases are successively weaker. The friction coefficient of three-layer Na-MM at low pressure is near 0.27, consistent with most observed bedding plane rockslides in shales. If Ca-MM is abundant in fault gouge, average friction in the top 10 km of strike-slip and normal faults may be as low as 0.34. Such weak faults would permit major deformation of continental crust by regional shear stresses as low as 27 MPa. This model would also explain the frequent reactivation of ancient faults by later stresses of diverse orientations.