A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

/pdf/surface-deformation-due-to-shear-and-tensile-faults-in-a-2vckanzx6g.pdf

Surface deformation due to shear and tensile faults in a half-space

This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

SUMMARY
We describe best-fitting angular velocities and MORVEL, a new closure-enforced set of angular velocities for the geologically current motions of 25 tectonic plates that collectively occupy 97 per cent of Earth's surface. Seafloor spreading rates and fault azimuths are used to determine the motions of 19 plates bordered by mid-ocean ridges, including all the major plates. Six smaller plates with little or no connection to the mid-ocean ridges are linked to MORVEL with GPS station velocities and azimuthal data. By design, almost no kinematic information is exchanged between the geologically determined and geodetically constrained subsets of the global circuit—MORVEL thus averages motion over geological intervals for all the major plates. Plate geometry changes relative to NUVEL-1A include the incorporation of Nubia, Lwandle and Somalia plates for the former Africa plate, Capricorn, Australia and Macquarie plates for the former Australia plate, and Sur and South America plates for the former South America plate. MORVEL also includes Amur, Philippine Sea, Sundaland and Yangtze plates, making it more useful than NUVEL-1A for studies of deformation in Asia and the western Pacific. Seafloor spreading rates are estimated over the past 0.78 Myr for intermediate and fast spreading centres and since 3.16 Ma for slow and ultraslow spreading centres. Rates are adjusted downward by 0.6–2.6 mm yr−1 to compensate for the several kilometre width of magnetic reversal zones. Nearly all the NUVEL-1A angular velocities differ significantly from the MORVEL angular velocities. The many new data, revised plate geometries, and correction for outward displacement thus significantly modify our knowledge of geologically current plate motions. MORVEL indicates significantly slower 0.78-Myr-average motion across the Nazca–Antarctic and Nazca–Pacific boundaries than does NUVEL-1A, consistent with a progressive slowdown in the eastward component of Nazca plate motion since 3.16 Ma. It also indicates that motions across the Caribbean–North America and Caribbean–South America plate boundaries are twice as fast as given by NUVEL-1A. Summed, least-squares differences between angular velocities estimated from GPS and those for MORVEL, NUVEL-1 and NUVEL-1A are, respectively, 260 per cent larger for NUVEL-1 and 50 per cent larger for NUVEL-1A than for MORVEL, suggesting that MORVEL more accurately describes historically current plate motions. Significant differences between geological and GPS estimates of Nazca plate motion and Arabia–Eurasia and India–Eurasia motion are reduced but not eliminated when using MORVEL instead of NUVEL-1A, possibly indicating that changes have occurred in those plate motions since 3.16 Ma. The MORVEL and GPS estimates of Pacific–North America plate motion in western North America differ by only 2.6 ± 1.7 mm yr−1, ≈25 per cent smaller than for NUVEL-1A. The remaining difference for this plate pair, assuming there are no unrecognized systematic errors and no measurable change in Pacific–North America motion over the past 1–3 Myr, indicates deformation of one or more plates in the global circuit. Tests for closure of six three-plate circuits indicate that two, Pacific–Cocos–Nazca and Sur–Nubia–Antarctic, fail closure, with respective linear velocities of non-closure of 14 ± 5 and 3 ± 1 mm yr−1 (95 per cent confidence limits) at their triple junctions. We conclude that the rigid plate approximation continues to be tremendously useful, but—absent any unrecognized systematic errors—the plates deform measurably, possibly by thermal contraction and wide plate boundaries with deformation rates near or beneath the level of noise in plate kinematic data.

Geologically current plate motions

[1] A global set of present plate boundaries on the Earth is presented in digital form. Most come from sources in the literature. A few boundaries are newly interpreted from topography, volcanism, and/or seismicity, taking into account relative plate velocities from magnetic anomalies, moment tensor solutions, and/or geodesy. In addition to the 14 large plates whose motion was described by the NUVEL-1A poles (Africa, Antarctica, Arabia, Australia, Caribbean, Cocos, Eurasia, India, Juan de Fuca, Nazca, North America, Pacific, Philippine Sea, South America), model PB2002 includes 38 small plates (Okhotsk, Amur, Yangtze, Okinawa, Sunda, Burma, Molucca Sea, Banda Sea, Timor, Birds Head, Maoke, Caroline, Mariana, North Bismarck, Manus, South Bismarck, Solomon Sea, Woodlark, New Hebrides, Conway Reef, Balmoral Reef, Futuna, Niuafo'ou, Tonga, Kermadec, Rivera, Galapagos, Easter, Juan Fernandez, Panama, North Andes, Altiplano, Shetland, Scotia, Sandwich, Aegean Sea, Anatolia, Somalia), for a total of 52 plates. No attempt is made to divide the Alps-Persia-Tibet mountain belt, the Philippine Islands, the Peruvian Andes, the Sierras Pampeanas, or the California-Nevada zone of dextral transtension into plates; instead, they are designated as “orogens” in which this plate model is not expected to be accurate. The cumulative-number/area distribution for this model follows a power law for plates with areas between 0.002 and 1 steradian. Departure from this scaling at the small-plate end suggests that future work is very likely to define more very small plates within the orogens. The model is presented in four digital files: a set of plate boundary segments; a set of plate outlines; a set of outlines of the orogens; and a table of characteristics of each digitization step along plate boundaries, including estimated relative velocity vector and classification into one of 7 types (continental convergence zone, continental transform fault, continental rift, oceanic spreading ridge, oceanic transform fault, oceanic convergent boundary, subduction zone). Total length, mean velocity, and total rate of area production/destruction are computed for each class; the global rate of area production and destruction is 0.108 m2/s, which is higher than in previous models because of the incorporation of back-arc spreading.

An updated digital model of plate boundaries

The traditional view of tectonics is that the lithosphere comprises a strong brittle layer overlying a weak ductile layer, which gives rise to two forms of deformation: brittle fracture, accompanied by earth- quakes, in the upper layer, and aseismic ductile flow in the layer beneath Although this view is not incorrect, it is imprecise, and in ways that can lead to serious misunderstandings The term ductility, for example, can apply equally to two common rock deformation mechanisms: crystal plasticity, which occurs in rock above a critical temperature, and cataclastic flow, a type of granular deformation which can occur in poorly consolidated sediments Although both exhibit ductility, these two deformation mechanisms have very different rheologies Earthquakes, in turn, are associated with strength and brittleness—associations that are likewise sufficiently imprecise that, if taken much beyond the generality implied in the opening sentence, they can lead to serious misinterpretations about earthquake mechanics Lately, a newer, much more precise and predictive model for the earthquake mechanism has emerged, which has its roots in the observation that tectonic earthquakes seldom if ever occur by the sudden appearance and propagation of a new shear crack (or 'fault') Instead, they occur by sudden slippage along a pre-existing fault or plate interface They are therefore a frictional, rather than fracture, phenomenon, with brittle fracture playing a secondary role in the lengthening of faults 1 and frictional wear 2  This distinction was noted by several early workers 3 , but it was not until 1966 that Brace and Byerlee 4 pointed out that earthquakes must be the result of a stick-slip frictional instability Thus, the earthquake is the 'slip', and the 'stick' is the interseismic period of elastic strain accumula- tion Subsequently, a complete constitutive law for rock friction has been developed based on laboratory studies A surprising result is that a great many other aspects of earthquake phenomena also now seem to result from the nature of the friction on faults The properties traditionally thought to control these processes— strength, brittleness and ductility—are subsumed within the over- arching concept of frictional stability regimes Constitutive law of rock friction In the standard model of stick-slip friction it is assumed that sliding begins when the ratio of shear to normal stress on the surface reaches a value ms, the static friction coefficient Once sliding initiates, frictional resistance falls to a lower dynamic friction coefficient, md, and this weakening of sliding resistance may,

/pdf/earthquakes-and-friction-laws-22mbgrykdx.pdf

Earthquakes and friction laws

[1] The GPS velocity field in the North Island of New Zealand is dominated by the long-term tectonic rotation of the eastern North Island and elastic strain from stress buildup on the subduction zone thrust fault. We simultaneously invert GPS velocities, earthquake slip vectors, and geological fault slip rates in the North Island for the angular velocities of elastic crustal blocks and the spatially variable degree of coupling on faults separating the blocks. This approach allows us to estimate the distribution of interseismic coupling on the subduction zone interface beneath the North Island and the kinematics of the tectonic block rotations. In agreement with previous studies we find that the subduction zone interface beneath the southern North Island has a high slip rate deficit during the interseismic period, and the slip rate deficit decreases northward along the margin. Much of the North Island is rotating as several, distinct tectonic blocks (clockwise at 0.5-3.8 deg Myr -1 ) about nearby axes relative to the Australian Plate. This rotation accommodates much of the margin-parallel component of motion between the Pacific and Australian plates. On the basis of our estimation of the block kinematics we suggest that rotation of the eastern North Island occurs because of the southward increasing thickness of the subducting Hikurangi Plateau. These results have implications for our understanding of convergent margin plate boundary zones around the world, particularly with regard to our knowledge of mechanisms for rapid tectonic block rotations at convergent margins and the role of block rotations in the slip partitioning process.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004JB003241

Subduction zone coupling and tectonic block rotations in the North Island, New Zealand

[1] The installation of a continuous GPS (cGPS) network in New Zealand since 2002 has enabled the discovery of 15 slow slip events at the Hikurangi subduction margin. Our analysis and interpretation of the cGPS data reveal a marked diversity in characteristics of slow slip events (SSEs) in the North Island, with durations varying from 6 days to 1.5 years, equivalent moment release between Mw 6.3–7.2, and recurrence intervals of repeating SSEs on the order of 2 years to more than 5 years. The duration and magnitude characteristics of Hikurangi SSEs appear to be related to the depth where they occur. The deepest, longest duration, and largest SSEs occur at the southern Hikurangi margin, near the downdip limit of deep (down to ∼40 km depth), strong interseismic coupling. The shallowest, shortest duration, smallest, and most frequent SSEs occur at the northern and central Hikurangi margin near the downdip limit of unusually shallow (<10–15 km depth) interseismic coupling. The direction of slip on the interface in the Hikurangi SSEs is consistent with slip partitioning at the Hikurangi subduction margin. We also show that moment accumulation rates on the interface for the time periods between SSEs are ∼40% higher than for the period of more than a decade averaging through the SSEs, indicating that SSEs compose a major portion of the overall moment release budget of the Hikurangi subduction interface.

Diverse slow slip behavior at the Hikurangi subduction margin, New Zealand

[1] Using up to 11 years of data from a global network of Global Positioning System (GPS) stations, including 12 stations well distributed across the Pacific Plate, we derive present-day Euler vectors for the Pacific Plate more precisely than has previously been possible from space geodetic data. After rejecting on statistical grounds the velocity of one station on each of the Pacific and North American plates, we find that the quality of fit of the horizontal velocities of 11 Pacific Plate (PA) stations to the best fitting PA Euler vector is similar to the fit of 11 Australian Plate (AU) velocities to the AU Euler vector and � 20% better than the fit of nine North American Plate (NA) velocities to the NA Euler vector. The velocities of stations on the Pacific and Australian Plates each fit a rigid plate model with an RMS residual of 0.4 mm/yr, while the North American velocities fit a rigid plate model with an RMS velocity of 0.6 mm/yr. Our best fitting PA/AU relative Euler vector is located � 170 km southeast of the NUVEL-1A pole but is not significantly different at the 95% confidence level. It is also close (<70 km in position and <3% in rate) to a pole derived from transform faults identified from satellite altimetry, suggesting that the vector has not changed significantly over the past 3 Myr. Our relative Euler vector is also consistent with all known geological and geodetic evidence concerning the AU/PA plate boundary through New Zealand. The GPS sites offshore of southern California are presently moving 4–5 ± 1 mm/yr relative to predicted Pacific velocity, with their residual velocities in approximately the opposite direction to PA/NA relative motion. Likewise, the easternmost sites in South Island, New Zealand, are moving � 3 ± 1 mm/yr relative to predicted Pacific velocity, with the residuals in approximately the opposite direction to PA/AU relative motion. These velocity residuals are in the same sense as predicted by elastic strain accumulation on known plate boundary faults but are of a significantly higher magnitude in both southern California and New Zealand, implying that the plate boundary zones in both regions are wider than previously believed. INDEX TERMS: 1206 Geodesy and Gravity: Crustal movements—interplate (8155); 1208 Geodesy and Gravity: Crustal movements—intraplate (8110); 1243 Geodesy and Gravity: Space geodetic surveys; 8158 Tectonophysics: Evolution of the Earth: Plate motions—present and recent (3040); 8159 Tectonophysics: Evolution of the Earth: Rheology—crust and lithosphere; KEYWORDS: Pacific plate motion, plate rigidity, plate boundary deformation

/pdf/motion-and-rigidity-of-the-pacific-plate-and-implications-32hzpcg7qy.pdf

Motion and rigidity of the Pacific Plate and implications for plate boundary deformation

We have inverted velocity solutions from nine geodetic networks distributed across New Zealand to derive present-day continuous horizontal velocity and strain rate fields at the Earth's surface throughout the country. The nine networks contain a total of 362 Global Positioning System (GPS) stations that have been observed at least twice and at least a year apart between 1991 and 1998. The model velocity field is expanded as bicubic spline interpolation functions defined within a curvilinear grid that covers the country and extends into the assumed rigid Australian and Pacific plates to west and east. The inversion jointly minimizes the magnitudes of fitted strain rates and the misfit to the observed velocity data. The spline technique allows high spatial resolution of strain rate variations, especially in regions with spatially dense GPS data. Expansion of the model velocity field on the surface of a sphere allows arbitrarily large areas to be studied. Previously known aspects of New Zealand plate boundary deformation are highlighted with improved resolution, including back-arc extension in the Taupo Volcanic Zone, rotation of the Hikurangi forearc away from this zone in the North Island, and a band of high shear strain rate under the Southern Alps to the southeast of the Alpine fault. Our results reveal several new features, including a region of enhanced shear straining apparently associated with strike-slip faults in the southern North Island and a band of contractional straining subparallel and well east of the Alpine fault that is similar to features found in numerical and sandbox models of continental collision.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900302

Contemporary horizontal velocity and strain rate fields of the Pacific‐Australian plate boundary zone through New Zealand

SUMMARY The landmass of New Zealand exists as a consequence of transpressional collision between the Australian and Pacific plates, providing an excellent opportunity to quantify the kinematics of deformation at this type of tectonic boundary. We interpret GPS, geological and seismological data describing the active deformation in the South Island, New Zealand by using an elastic, rotating block approach that automatically balances the Pacific/Australia relative plate motion budget. The data in New Zealand are fit to within uncertainty when inverted simultaneously for angular velocities of rotating tectonic blocks and the degree of coupling on faults bounding the blocks. We find that most of the plate motion budget has been accounted for in previous geological studies, although we suggest that the Porter’s Pass/Amberley fault zone in North Canterbury, and a zone of faults in the foothills of the Southern Alps may have slip rates about twice that of the geological estimates. Up to 5 mm yr −1 of active deformation on faults distributed within the Southern Alps <100 km to the east of the Alpine Fault is possible. The role of tectonic block rotations in partitioning plate boundary deformation is less pronounced in the South Island compared to the North Island. Vertical axis rotation rates of tectonic blocks in the South Island are similar to that of the Pacific Plate, suggesting that edge forces dominate the block kinematics there. The southward migrating Chatham Rise exerts a major influence on the evolution of the New Zealand plate boundary; we discuss a model for the development of the Marlborough fault system and Hikurangi subduction zone in the context of this migration.

/pdf/balancing-the-plate-motion-budget-in-the-south-island-new-3azad2irjb.pdf

John Beavan

Papers

Subduction zone coupling and tectonic block rotations in the North Island, New Zealand

Diverse slow slip behavior at the Hikurangi subduction margin, New Zealand

Motion and rigidity of the Pacific Plate and implications for plate boundary deformation

Contemporary horizontal velocity and strain rate fields of the Pacific‐Australian plate boundary zone through New Zealand

Balancing the plate motion budget in the South Island, New Zealand using GPS, geological and seismological data