Principal Strain Rate Research Articles

Present crustal deformation pattern in the Pancardi Region: Constraints from Space Geodesy

It was almost a decade ago when the first space geodetic project was commenced in the Pannonian- Carpathian-Dinaric (PANCARDI) region with the aim of di- rect measurement of present crustal movements and strain. The most effective space geodetic technique for this purpose turned out to be the Global Positioning System (GPS). Sev- eral countries established their own national GPS network for monitoring crustal deformation. Nowadays stations of global, continental, regional, national and many local net- works operate in the territory of the study area. An overview of these GPS geodynamic programs is given in the first sec- tion, then we analyse the data of the regional and the Hun- garian national program and give short reports from other projects in the PANCARDI region. In our analysis we com- pare the velocities derived from space geodesy with those predicted by the NNR-NUVEL1A model based on geolog- ical and geophysical records. Looking into the intraplate crustal velocities the data show a fairly stable Bohemian Massive (BM) with relative crustal velocities smaller than 1 mm/yr. With reference to the BM in the north, the western part of the Alpine-North Pannonian (ANP) unit is moving to the East (E) with generally 1 mm/yr velocity that increases to more than twice this value towards its westernmost parts. The largest principal strain rate between these tectonic do- mains is a NE-SW oriented contraction ( 8.6±2.5◊10 9 /yr (ppb/yr)) over an approximately 300◊300-km area. Here we observe left-lateral shear rate (97 ±7 ; 10±2 ppb/yr) be- tween the Alpine-North Pannonian unit and the Bohemian Massif. South of the Alpine-North Pannonian unit the com- plex structure of junction of several tectonic domains can be described by northward trending velocities with 1-2 mm/yr north component relative to the ANP unit or the BM. The direction of contraction near the boundary of the Adriatic microplate is NW-SE oriented with magnitude of 8.0±5.3 ppb/yr over an area of 300◊120-km. Here we observe E- W oriented (93 ±13 ) right-lateral shear (12±5 ppb/yr) be- tween the ANP unit and the southernmost sites in the Di- narides and Southern Alps. These imply that the northward moving Adriatic region is presently squeezes out the ANP unit to the East from between the BM and the Adriatic mi- croplate. Except for a couple of sites the eastern section shows no significant velocities yet. It seems likely that the eastward escape is absorbed in the central section of the ANP in the Pannonian basin since no detectable eastward compo- nent found for the site velocities in the eastern, north-eastern part of the ANP unit.

Tectonic stress state in NE Japan as part of the Okhotsk plate

An existing geodetic flow velocity model, obtained by using an internal free network adjustment technique, is used to derive estimates for various strain rates parameters in NE Japan. The greatest shortening rates of the principal strains, trending ∼E–W, are located in regions where much steady, internal, frame-invariant plastic flow deformation is observed to be taking place. The internal geodetic adjustment technique yielded the internal deformation in the Tohoku arc; most of the intraplate deformations, including the much folding deformations observed in the inner zone, are produced from within. An interseismic transient elastic loading at a strongly coupled/locked Japan trench would not be needed. The observed ongoing extensive ductile folding deformation in the inner zone of Tohoku may mean that the geodetic strain rates, causing shortening at ∼2–3 cm/yr, probably reflect the more correct level of the deformation, which is steady/permanent, in NE Japan as compared with seismic/faulting data, which indicate ∼0.5 cm/yr shortening. The calculated principal strain rates are used to make an interpretation for the origin of the deviatoric principal stresses within the greater regional plate tectonic framework. The tectonic stress state in NE Japan, as part of the Okhotsk plate, could mostly be influenced by the Okhotsk plate, which is extruding southward to lessen the significant accumulated contractional deformation in NE Asia in the Verkhoyansk–Cherskii mountains. The principal strain rates are ∼N–S extensional essentially everywhere in NE Japan, as a result of the southerly extrusion, except in its southernmost leading edge, in the Uetsu/Fossa Magna province, where the Japan Alps rampart rises in front of the extrusion. Here an ∼E–W compressional stress state prevails. A second ∼E–W contractional zone is found in north-central Tohoku, extending from the Sanriku province in the outer zone to the inner zone in the Japan Sea side, being more prevalent in the latter zone. The calculated rotation rates from the geodetic flow model are clockwise (CW) in both of the ∼E–W contractional regions. NE Japan, extruding southward, faces buttresses in (1) the Oga–Ojika Line (OOL), and/or a crustal weakness zone between the northern and the southern halves of Tohoku approx. at ∼38.5°N latitude, and, especially, (2) the Japanese Alps rampart; these obstacles cause the northern and southernmost Tohoku to veer to its right and rotate CW, thereby setting up the ∼E–W-trending compressional deformation in their respective inner zones. Between the OOL (or the 38.5°N boundary) and the Kanto Tectonic Line (KTL), the sense of the differential rotations is counterclockwise (CCW), towards the ocean to the SE. The northern Tohoku (north of the OOL) and the southernmost Tohoku (south of the KTL) cannot rotate CCW towards the ocean because of the Izu block's collision in the south and the relatively strong coupling along the subduction interface beneath the Japan trench in the north off-Sanriku. The relatively stronger long-term coupling between the northern Tohoku and the Pacific plate at the Sanriku coast, with respect to that in off-Fukushima, is due to a flatter subduction of the Pacific slab there, increasing the plates’ interface contact area; the flattening of the subduction dip angle was caused by CCW rotation and shifting of the northern Tohoku along the dextral Honjo–Matsushima Line, roughly corresponding to the OOL, towards the Pacific and overriding of the subduction zone during the formation of the Japan Sea.

Strain accumulation near Yucca Mountain, Nevada, 1993–1998

A 50‐km aperture geodetic network centered on the proposed high‐level radioactive waste disposal site at Yucca Mountain, Nevada, was surveyed with GPS in 1993 and 1998. The average deformation rate across the area is described by the principal strain rates 22.8±8.8 nstrain yr−1 N77.6°W±13.5° and −8.8±11.9 nstrain yr−1 N12.5°E±13.5° (extension reckoned positive) and a clockwise rotation rate about a vertical axis of 9.6±7.4 nrad yr−1 relative to fixed North America. Quoted uncertainties are standard deviations. Those strain rates are consistent with the geodetic strain rates (2±12 nstrain yr−1 N87°±12°W and −22±12 nstrain yr−1 N03°±12°E) previously reported by Savage et al. [1999] for the 1983–1998 interval and with the low extension rate (5–20 nstrain yr−1) [Marrett et al., 1998] inferred from the geologic record. None of those strain rates is consistent with the 50±9 nstrain yr−1 N65°W extension rate for the area reported by Wernicke et al. [1998].

A home exercise program for tibial bone strengthening based on in vivo strain measurements.

To compare the strain and strain rates generated during lower limb calisthenics with walking, an exercise that has been found to have only minimal effect on bone mass. Strengthening of bone, while it still has adaptive ability, can be achieved by exercise. Mechanical loading during physical activity produces strains and strain rates within the bones. It is thought that strain and strain rates higher than the usual provide the stimulus for the bones' adaptation. Three strain-gauged bone staples were inserted percutaneously in a 30 degrees rosette pattern in the medial aspect of the midtibial diaphysis of two volunteers. The principal compression, tension, shear strains, and strain rates were measured during various lower limb calisthenics and compared with those of jogging and walking. Zig-zag hopping was in the grouping of exercises with the highest principal compression, tension, and shear strains and compression strain rates, whereas walking was in the lowest or next-to-the-lowest grouping for all principal strain or strain rates. Zig-zag hopping, based on the high strain and strain rates that it produces, may be an optimal tibial bone-strengthening exercise.

Strain partitioning during oblique plate convergence in northern Sumatra: Geodetic and seismologic constraints and numerical modeling

Global Positioning System (GPS) measurements along the subduction zone of northern Sumatra (2°S to 3°N) reveal that the strain associated with the oblique convergence of the Australian plate with Eurasia is almost fully partitioned between trench‐normal contraction within the forearc and trench‐parallel shear strain within a few tens of kilometers of the Sumatran fault Kinematic analyses of interplate earthquake slip vectors provide slip rates on the Sumatran fault within a few millimeters per year of GPS and geologic rates, giving us more confidence in the use of slip vectors for inferring slip partitioning elsewhere. The inferred slip rate on the Sumatran fault is ∼1/3 less than the full margin parallel component of plate motion. An across‐forearc rotation in the slip vectors suggests that the missing arc‐parallel shear occurs seaward of the geodetic network, between the forearc islands and the trench. Simple finite element models are used to explore the conditions under which the change in the principal strain rate directions between the forearc and the arc region can occur. Modeling suggests that neither a preexisting strike‐slip fault nor a zone of thermally induced lithospheric weakness in the overriding plate is needed for strain partitioning to occur. In general, forearc slivers form over the region of interplate coupling and are driven along strike by the basal shear. A volcanic arc can help the partitioning process by localizing the margin‐parallel shear strain in the upper plate if its crust and mantle are weaker than its surroundings. Interplate slip vectors and geodetic results from Sumatra together suggest that the highest coupling on the plate boundary occurs beneath and seaward of the forearc islands, consistent with inferences about the rupture zones of great nineteenth century earthquakes there. The Sumatra example suggests that geodetic measurements of interseismic, margin‐parallel shear strain at oblique convergent margins can be used to map the landward extent of the relatively high basal stress beneath the overriding plate if one can correct for strain localization caused by weak upper plate strike‐slip faults.

Nonsteady planar ideal plastic flow: general and special analytical solutions

Ideal plastic flows are those for which all material elements follow minimum work paths. For planar flows this implies that two orthogonal families of material lines, called principal lines, are perpetually tangent to the principal strain rate vectors. The general equations for ideal flows in Tresca solids have been given elsewhere as have specific examples of steady plane strain and axisymmetric flows and nonsteady membrane flows. Here we focus on the case of nonsteady plane strain and show that the representation of such flows can be reduced to the solution of a telegraph equation in two independent spatiotemporal characteristic variables. In obtaining this general result, two special cases are lost: those corresponding to the cases where one and two families of characteristics are straight in both Cartesian and principal line spaces. Results for these cases are given as well. Finally, an application to forming process design problems is discussed and a simple example is illustrated using the general solution.

Simultaneous measurement of velocity and CH layer distribution in turbulent non-premixed flames

The velocity field and the location of the CH layer are measured simultaneously in diluted ethylene flames by applying particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) of CH radicals. CH layer measurements are used to locate the position of the flame front, and accompanying velocity fields provide the instantaneous velocity, strain, and residence time information simultaneously. The location of the CH layer is found to correspond well with the location of the stoichiometric velocity contour and also with high strain rate zones: however, significantly higher values of instantaneous velocity and strain rates, compared to the mean value, are frequently observed. The residence time on the flame surface is estimated by dividing the thickness of the CH layer by the mean value of radial velocity on the CH layer. The flame sheet residence time estimated by this method remains nearly constant with axial distance downstream. The mean value of the maximum principal strain rate on the CH layer is observed to decrease along the axial direction while the change in the value is relatively small except for the region near the nozzle exit. The mean value of the strain rate is found to show a good correlation to a S≈(x/d) −0.7 relation for a wide range of Reynolds number.

Contribution of ductile flow to exhumation of low‐temperature, high‐pressure metamorphic rocks: San Juan‐Cascade nappes, NW Washington State

The San Juan‐Cascade (SJC) nappes were subducted to a depth of ∼18 km, metamorphosed under low‐temperature, high‐pressure conditions, and then exhumed, all within ∼16 m.y. During exhumation, penetrative deformation by solution mass transfer (SMT) resulted in a widespread spaced cleavage. Strain directions were determined for 27 sandstone samples, and absolute strain measurements for a subset of 19 samples. Z directions generally plunge moderately to the NE, and X and Y directions are scattered in the plane perpendicular to Z. SMT deformation is constrictional at the local scale, but the tensor average indicates plane‐strain uniaxial shortening at the regional scale, with Sx, Sy, and Sz equaling 1.01, 0.91, and 0.58, respectively. The average flattening plane (XY) dips 30° to the NE, and the average X direction plunges 20° to the north. The large shortening in Z was compensated by a mass‐loss volume strain of ∼47%. We present a simple one‐dimensional model that illustrates the relationship between finite strain and ductile exhumation for a steady state convergent wedge. Assuming depth‐dependent ductile flow and no reversal of principal strain rates with depth, this model indicates that ductile thinning of the SJC nappes accomplished only 13% of the total exhumation, despite a vertical shortening strain of 36%. There is no evidence that normal faulting contributed significantly to exhumation. We conclude that erosion operating at an average rate of ∼1.1 km m.y.−1 was the dominant exhumation process.

Interpretations of a Middle Miocene and late Quaternary steady dextral transpression in SW Japan and the opening tectonics for the Japan Sea

An internal-rotation hypothesis for the deformation of SW Japan for Middle Miocene and Recent times is studied. Rotations are known to have occurred from paleomagnetic data for the earlier case; two geodetic flow field estimates, as well as another tectonic study, suggest that the rotations are also taking place at present. A further examination of the geodetic flow models suggests that the rotations contained in these flow models are intrinsic to the deformation of SW Japan, which occurs in an ∼E–W dextral-transpressive, simultaneous pure- and simple-shear, tectonic regime. Maps of rotation rates (one-half of vorticity) and shear gradients (the N–S variation of the E–W velocity field), constructed from the geodetic flow models, resemble one another in pattern. The estimates of the directions of the principal strain rates from the geodetic models are, on the whole, ∼N–S contractional and/or ∼E–W extensional, which match the geodetic reference coordinate system used in the adjustment of the geodetic data. These observations suggest that the vortical flow contained in the geodetic flow models is a frame-independent, shear-induced vorticity as the material is rotating with respect to the principal directions of the strain rates, and that the oblique motion of the Philippine Sea plate is partitioned between shear and arc-normal convergence components. The rotation rate is ∼10–12°/Ma. Furthermore, the kinematical vorticity number estimates from the geodetic data correlate well with the first-order tectonic fabric patterns in SW Japan. Super-simple-shear deformation for large parts of SW Japan, where the Median Tectonic Line and other large strike-slip faults are found, is also indicated in the (internal) kinematical vorticity number estimates. A new model for the formation of the Japan Sea is proposed: extrusion of Japan due to the Okhotsk–Eurasia collision. This model agrees with the fundamental observations of the Early–Middle Miocene deformation in the region. The application of an indentation–extrusion model to the Okhotsk–Eurasia collision results in a better agreement between the predicted and observed structures, and leads to simpler, more reasonable and coherent interpretations for the origin and development of the structures compared with the achievements of the previous models. The ∼NNE-trending Early–Middle Miocene rifts lying along the continental margin of western Hokkaido formed as pull-apart basins along a sinistral fault, related to the collision of the Okhotsk plate, which segmented, in a left-handed sense, because the collision was oblique. The ∼N–S-trending rifts and the normal faults found in the back-arc domain of the NE Honshu arc formed by eastward extrusion under the influence of the Mariana-type subduction in the Japan Trench. These rift basins were subsequently left-laterally displaced by movement along ∼NW-trending sinistral strike-slip faults. The Shikoku Basin opened from the east toward the west, and dextral shear was imparted to the SW margin from the Nankai Trough, leading to clockwise rotations in the Middle Miocene in SW Japan. The paleomagnetic rotations are accommodated as fully internal-structural rotations in the new model for the origin of the Japan Sea. The current episode of deformation in SW Japan began ∼1–5 million years ago, after a hiatus during a 15–5 Ma interval, and is likely a continuation of the Middle Miocene style of tectonics.

Crustal deformation of the Marlborough Fault Zone in the South Island of New Zealand: Geodetic constraints over the interval 1982–1994

Crustal deformation across the Marlborough fault zone in the South Island of New Zealand has been investigated by resurveying with the Global Positioning System (GPS) a triangulation and trilateration network across part of the zone. The principal strain rates, which mostly have errors between 5% and 10%, vary systematically across the region. The principal axis of horizontal contraction gradually swings from SE‐NW southeast of the Hope fault to almost east‐west in the west. The component of velocity parallel to the strike of the faults can account for 95% of the relative motion between the Australian and Pacific plates. This component exhibits little variation west of the Alpine (Wairau) fault, and shows an almost linear variation from the Wairau fault to the east coast. The horizontal strain rate northwest of the Wairau fault is a small east‐west uniaxial contraction (∼0.1 ppm yr−1). If it is assumed that the crustal blocks bounded by the major faults are primarily driven by basal shear tractions, with stresses on the faults being relatively insignificant, then the slip rates expected on the faults may be derived from the observed velocity variations across the fault zone. These predicted slip rates are in good agreement with geologically observed slip rates. The larger slip rates on the Hope fault are related to the observation that the strain field extends southeast of the fault over a distance large compared with the spacing between the faults. The agreement between predicted and geological slip rates lends support to the idea that the observed pattern of deformation reflects that in the lower lithosphere.

Spatial distribution of horizontal seismic strain in the Apennines from historical earthquakes

Horizontal principal seismic strain rate axes have been calculated within a regular mesh of triangles covering the Italian peninsula in a time interval of 700 years. I have used both the method of Kostrov (1974), that requires knowledge of the seismic moment tensor of earthquakes, and the modified version provided by England and Molnar (1997) that makes use of length and kinematics of the activated faults. Seismic moment tensor of historical earthquakes can be inferred from recent literature, while length of faults has been obtained from the observation that strain drop is almost constant for large Apenninic earthquakes. Spatial strain distribution from historical earthquakes shows that the Apennines can be divided into three homogeneous structural arcs (Northern Apenninic, Southern Apenninic and Calabrian arcs) within which strain is roughly constant. Although NE-SW extension is the main deformation process along the two Apenninic arcs it involves a velocity more than five times greater in the Southern Apennines. Along the Calabrian arc, I tested the effect on the strain field of the contemporaneous ~WNW-ESE and ~NNE-SSW extension due to the longitudinal dilatation of the arc during its still ESE migration.

Seismic deformation at the Alban Hills volcano during the 1989-1990 seismic sequence

We analysed the one-year-long seismic swarm at the Alban Hills volcano which occurred during 1989-1990. We portray spatial distribution of seismic moment release, better delineating the activated volume during the swarm. The seismic structure is imaged as a 7-km long, 3-km wide, and 3-km thick volume, located between 2 and 5 km depth, and NW-SE striking. Fault plane solutions and scalar seismic moments for the largest earthquakes provide the description of the average strain rate tensor. The principal strain rate axes show a dominant extension in NE-SW direction, a SE-NW direction of compression and a negligible thickening rate. P and T axes direction of the smaller earthquakes suggests that the same mode of deformation is distributed all over the activated volume. These results are discussed in terms of seismic deforming processes active at the Alban Hills volcano, in the frame of magmatic inflation recently invoked to explain the rapid vertical uplift affecting part of the volcano. The observed average deformation is consistent with shear failures occurring on faults connecting stress-oriented dykes in response to an increasing fluid pressure.

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 relationship between vorticity/strain and reaction zone structure in turbulent non-premixed jet flames

Simultaneous velocity and OH field measurements were made in unsteady laminar and turbulent nonpremixed planar jet flames to investigate the relationship between vorticity, principal strain rates, and reaction zone structure. Planar laser-induced fluorescence (PLIF) of the OH radical was used as an approximate reaction zone marker, while simultaneous two-component particle image velocimetry (PIV) provided the velocity field information. It is observed that in a turbulent flame, the thinnest reaction zones tend to align at 45° to the flow direction, which is orthogonal to the direction of the maximum principal compressive strain. Furthermore, the maximum compressive strain rates are typically an order of magnitude larger than the outer-scale strain rate, and it is not uncommon for the reaction zone to undergo strain that is significantly larger than the steady-state extinction strain rate. Diffuse OH zones are generally in regions of low compressive strain and low velocity gradients, and in some cases, they are observed to be aligned normal to the principal extensive strain direction. This suggests that the thick reaction zones result from broadening due to diffusion and extensive strain normal to the reaction sheet. Furthermore, some of the OH zones are associated with elongated regions of high vorticity, particularly in the highly laminarized reaction zones at low Reynolds number.

Crevasse patterns and the strain-rate tensor: a high-resolution comparison

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2 reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e. x > 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

Crevasse patterns and the strain-rate tensor: a high-resolution comparison

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e.x> 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

Surface strain accumulation and the seismic moment tensor

Abstract Although the scalar moment accumulation rate within the seismogenic zone beneath a given area is sometimes deduced from the observed average surface strain accumulation rate over that same area (e.g., Working Group on California Earthquake Probabilities, 1995), the correspondence between the two is very uncertain. The equivalence between surface strain accumulation and scalar moment accumulation is based on Kostrov's (1974) relation between the average strain rate over a volume and the moment-rate tensor for that volume. The average strain rate over the volume is replaced by the average strain rate measured at the free surface to deduce an approximate moment-rate tensor. Only in exceptional circumstances will that moment-rate tensor correspond to a double-couple mechanism, a mechanism that can be represented by a scalar moment accumulation rate. More generally, the moment tensor must be resolved into the superposition of two or more double-couple mechanisms, and that resolution can be done in many ways, each with its own scalar moment rate. Thus the resolution is not unique. This is demonstrated by deducing scalar moment accumulation rates for a GPS network that covers most of California south of San Francisco. It is shown that resolutions into different double-couple mechanisms lead to scalar moment accumulation rates differing by factors of ∼2. We suggest that the minimum scalar moment rate equivalent to principal surface strain rates ɛ1 and ɛ2 acting over the area A is M0(min) = 2μHA Max (¦ɛ1¦, ¦ɛ2¦, ¦ɛ1 + ɛ2¦), where μ is the rigidity and H the depth of seismogenic zone, and the function Max is equal to the largest of its arguments. Within the uncertainites of measurement, the scalar moment accumulation rate in southern California based on that approximation is in balance with the average historic seismic moment release rate so that no current earthquake deficit need be accumulating.

Geodetic measurements of horizontal strain near the White Wolf fault, Kern County, California, 1926–1993

The White Wolf fault, located north of the Big Bend segment of the San Andreas fault, is the NE‐SW trending, left lateral‐oblique reverse fault responsible for the Ms=7.8 1952 Kern County earthquake. We combined Global Positioning System (GPS) measurements with historical triangulation and trilateration data to determine changes in the strain rate over 7 decades (1926–1993). We reanalyzed the historical geodetic data and calculated an elevated preseismic (1926–1952) maximum shear strain rate of 0.62±0.16 μstrain/yr across the White Wolf fault. The maximum shear strain rate decreased with distance toward the Garlock fault to 0.09±0.08 μstrain/yr. In the decade following the earthquake (1952–1963), the near fault was high (0.85±0.23μstrain/yr), and decreased to 0.23±0.13 μstrain/yr across the Garlock fault. In 1993, we resurveyed many of the same monuments with GPS receivers to estimate fault‐crossing and off‐fault strain rates for the preceding 30 years. Across the White Wolf fault, the maximum shear strain rate dropped to 0.19±0.07 μstrain/yr. The azimuths of the maximum principal strain rates (ϕ) for the 1963–1993 epoch rotate from a fault normal orientation (−57°±15°) across the White Wolf fault to 11°±3°E across the Garlock fault.

Interseismic horizontal deformation in northern Honshu and its relationship with the subduction of the Pacific Plate in the Japan Trench

We investigate the origin of the geodetically observed interseismic horizontal deformation in northern Honshu by comparing shear strain rates, principal strain rates, and velocity fields determined from geodetic data with those calculated from the elastic dislocation models involving interplate motion at the Japan trench. The agreement between the observed and predicted directions of the principal strain axes indicates that the geodetic strain field in northern Honshu is primarily elastic strain transmitted from the Japan trench. In order to match the strain rate tensors and velocity magnitudes obtained from the geodetic data, the dislocation model requires that 35% to 60% of the NUVEL1‐A Pacific‐North American plate motion is locked at the plate interface along the Japan trench. The down‐dip depth limit of the locked zone is inferred to be 55 km, which is consistent with the seismic data in the Japan trench.

On the mesoscale interaction of lead ice and floes

The plasticity of the Arctic ice pack depends on its granular nature, in particular on the size and distribution of areas of thin ice and open water surrounding multiyear ice floes. The paper begins with construction of a mesoscale (10–100 km) granular model of the central Arctic ice pack. The mesoscale model is based on a dynamic particle simulation in which individual multiyear ice floes and surrounding parcels of first‐year ice are explicitly modeled as discrete, convex polygons in a two‐dimensional domain. Deformation of the domain produces areas of localized failure and areas of open water. The areas of localized failure are modeled as pressure ridging events using the results of numerical experiments performed with a computer simulation of the ridging process. The paper focuses on the results of numerical experiments performed with the mesoscale model. In the experiments the model ice pack is biaxially deformed at constant strain rates. The principal strain rates are varied to create deformation states ranging from pure shear to uniform compression. The results define the shape and magnitude of the plastic yield surface, the strain rate vectors associated with points on the yield surface, the partition of energy dissipation between ridging and in‐plane sliding, and the changes in the ice thickness distribution associated with various deformation states.