Description: Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space $\mathbb {R}^{3}$ is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Description: Using dynamic rupture models of a right-lateral fault embedded in an elastic or elastoplastic 3-D medium, we investigate elastic and inelastic responses of compliant fault zones to nearby earthquake ruptures. We particularly examine effects of fault zone depth, width, shape and rigidity reduction on the surface displacement field. Our results from elastic models show that deeper and wider fault zones generally result in larger residual displacements. However, for shallow fault zones, the vertical residual displacement is insensitive to or even decreases with fault zone width. The width of horizontal displacement anomalies across a fault zone is only indicative of the fault zone width near the Earth's surface. There are trade-off effects among fault zone depth, width, shape and rigidity reduction on the amplitude of surface residual displacements. Our elastoplastic models show that plastic strain can occur along the entire fault zone near the Earth's surface and in the extensional quadrant at depth, if fault zone rocks are close to failure before a nearby earthquake happens. Compared with results from elastic models, plastic strain near the Earth's surface generally enhances surface displacements of a fault zone and does not change the trend of effects of fault zone depth and width, while plastic strain at depth can result in reduced retrograde motion or sympathetic motion across the fault zone, and introduce complexities in effects of fault zone depth and width. Sympathetic horizontal motion more likely occurs across a narrow fault zone with inelastic response at depth. Vertical motion in the extensional quadrant may actually decrease with fault zone width in elastoplastic models. Sympathetic horizontal motion, or small retrograde horizontal motion in conjunction with large vertical motion above a fault zone is indicative of inelastic response of a fault zone at depth.

Description: On 1580 April 6 one of the most destructive earthquakes of northwestern Europe took place in the Dover Strait ( Pas de Calais ). The epicentre of this seismic event, the magnitude of which is estimated to have been about 6.0, has been located in the offshore continuation of the North Artois shear zone, a major Variscan tectonic structure that traverses the Dover Strait. The location of this and two other moderate magnitude historical earthquakes in the Dover Strait suggests that the North Artois shear zone or some of its fault segments may be presently active. In order to investigate the possible fault activity in the epicentral area of the AD 1580 earthquake, we have gathered a large set of bathymetric and seismic-reflection data covering the almost-entire width of the Dover Strait. These data have revealed a broad structural zone comprising several subparallel WNW–ESE trending faults and folds, some of them significantly offsetting the Cretaceous bedrock. The geophysical investigation has also shown some indication of possible Quaternary fault activity. However, this activity only appears to have affected the lowermost layers of the sediment infilling Middle Pleistocene palaeobasins. This indicates that, if these faults have been active since Middle Pleistocene, their slip rates must have been very low. Hence, the AD 1580 earthquake appears to be a very infrequent event in the Dover Strait, representing a good example of the moderate magnitude earthquakes that sometimes occur in plate interiors on faults with unknown historical seismicity.

Description: New Zealand straddles the boundary between the Australian and Pacific Plate. Cenozoic relative plate motion has resulted in a complex pattern of faulting and block rotation in a zone of continental lithosphere up to 250 km wide. I investigate the implications of the short-term kinematics for the strength of the deforming lithosphere. I use a compilation of seismic reflection/refraction studies and high quality receiver function analyses to determine both the regional structure of the crust, which ranges from 20 to 50 km thick, and fields of buoyancy stress (or GPE per unit volume). Deformation over thousands of years is quantified in terms of velocity and strain rate fields, based on an inversion of neotectonic fault slip and palaeomagnetic data, in the context of the short-term relative plate motions. Forces on the subduction megathrust, as well as deviatoric stresses in the behind subduction region, are calculated from simple 2-D force balances across the Hikurangi Margin, given negligible deviatoric stresses at the along-strike transition between backarc extension and compression. Average megathrust shear stresses are in the range 6–15 MPa, and average lithospheric stresses 〈20 MPa in the overriding plate. The regional lithospheric strength of the plate boundary zone, assuming a viscous rheology (Newtonian or power law), is determined from an inversion of the field of gradients of buoyancy stress (averaged over either the top 25 km of the crust, or 100-km-thick lithosphere) and strain rate, using the thin sheet stress balance equations, calibrated with the subduction force balance analysis. Effective viscosities for the deforming lithosphere and/or crust are in the range 0.1–5 x 10 21 Pa s, with marked weakening in zones of high strain rate, and an abrupt transition to viscosities 〉10 22 Pa s at the margins of the rigid plates. If lateral variations in effective viscosity are only due to non-Newtonian behaviour, these data indicate a bulk power law rheology, with exponent n in the range 2–6. Average lithospheric or crustal deviatoric stresses 〈30 MPa. Such low driving stresses for the deforming crust are likely to be the result of a combination of pore fluid pressures much greater than hydrostatic (〉〉40 per cent lithostatic) and low coefficients of friction (〈〈0.6) on crustal faults.

Description: The mechanical damage characteristics of sandstone subjected to cyclic loading is very significant to evaluate the stability and safety of deep excavation damage zones. However to date, there are very few triaxial experimental studies of sandstone under cyclic loading. Moreover, few X-ray micro-computed tomography (micro-CT) observations have been adopted to reveal the damage mechanism of sandstone under triaxial cyclic loading. Therefore, in this research, a series of triaxial cyclic loading tests and X-ray micro-CT observations were conducted to analyse the mechanical damage characteristics of sandstone with respect to different confining pressures. The results indicated that at lower confining pressures, the triaxial strength of sandstone specimens under cyclic loading is higher than that under monotonic loading; whereas at confining pressures above 20 MPa, the triaxial strength of sandstone under cyclic loading is approximately equal to that under monotonic loading. With the increase of cycle number, the crack damage threshold of sandstone first increases, and then significantly decreases and finally remains constant. Based on the damage evolution of irreversible deformation, it appears that the axial damage value of sandstone is all higher than the radial damage value before the peak strength; whereas the radial damage value is higher than the axial damage value after the peak strength. The evolution of Young's modulus and Poisson's ratio of sandstone can be characterized as having four stages: (i) Stage I: material strengthening; (ii) Stage II: material degradation; (iii) Stage III: material failure and (iv) Stage IV: structure slippage. X-ray micro-CT observations demonstrated that the CT scanning surface images of sandstone specimens are consistent with actual surface crack photographs. The analysis of the cross-sections of sandstone supports that the system of crack planes under triaxial cyclic loading is much more complicated than that under triaxial monotonic loading. More axial and lateral tensile cracks were observed in the specimens under cyclic loading than under monotonic loading.

Description: We present observations and models of the Sulaiman Range of western Pakistan that shed new light on the evolution and deformation of fold-thrust belts. Earthquake source inversions show that the seismic deformation in the range is concentrated in the thick pile of sediments overlying the underthrusting lithosphere of the Indian subcontinent. The slip vectors of the earthquakes vary in strike around the margin of the range, in tandem with the shape of the topography, suggesting that gravitational driving forces arising from the topography play an important role in governing the deformation of the region. Numerical models suggest that the active deformation, and the extreme plan-view curvature of the range, are governed by the presence of weak sediments in a pre-existing basin on the underthrusting Indian Plate. These sediments affect the stress-state in the over-riding mountain range and allow for the rapid propagation of the nose of the range and the development of extreme curvature and laterally varying surface gradients.

Description: Numerous regional plate reorganizations and the coeval ages of the Hawaiian Emperor bend (HEB) and Louisville bend of 50–47 Ma have been interpreted as a possible global tectonic plate reorganization at ~chron 21 (47.9 Ma). Yet for a truly global event we would expect a contemporaneous change in Africa absolute plate motion (APM) reflected by physical evidence distributed on the Africa Plate. This evidence has been postulated to take the form of the Réunion-Mascarene bend which exhibits many HEB-like features, such as a large angular change close to ~chron 21. However, the Réunion hotspot trail has recently been interpreted as a sequence of continental fragments with incidental hotspot volcanism. Here we show that the alternative Réunion-Mascarene Plateau trail can also satisfy the age progressions and geometry of other hotspot trails on the Africa Plate. The implied motion, suggesting a pivoting of Africa from 67 to 50 Ma, could explain the apparent bifurcation of the Tristan hotspot chain, the age reversals seen along the Walvis Ridge, the sharp curve of the Canary trail, and the diffuse nature of the St. Helena chain. To test this hypothesis further we made a new Africa APM model that extends back to ~80 Ma using a modified version of the Hybrid Polygonal Finite Rotation Method. This method uses seamount chains and their associated hotspots as geometric constraints for the model, and seamount age dates to determine APM through time. While this model successfully explains many of the volcanic features, it implies an unrealistically fast global lithospheric net rotation, as well as improbable APM trajectories for many other plates, including the Americas, Eurasia and Australia. We contrast this speculative model with a more conventional model in which the Mascarene Plateau is excluded in favour of the Chagos-Laccadive Ridge rotated into the Africa reference frame. This second model implies more realistic net lithospheric rotation and far-field APMs, but fails to explain key details of the Atlantic Ocean volcanic chains. Both models predict a Canary plume influence beneath the Madeiras. Neither model, when projected via the global plate circuit into the Pacific, predicts any significant change in plate motion around chron 21. Consequently, Africa APM models do not appear to provide independent support for a chron 21 global reorganization.

Description: The Algerian margin formed through back-arc opening of the Algerian basin (Mediterranean Sea) resulting from the roll-back of the Tethyan slab. Recent geophysical data acquired along the Algerian margin showed evidence of active or recent compressive deformation in the basin due to the ongoing Africa–Eurasia convergence. Published data from four wide-angle seismic profiles have allowed imaging the deep structure of the Algerian margin and its adjacent basins. In this study, we converted these velocity models into density models, then into isostatic anomalies. This allowed us to image an isostatic disequilibrium (relative to a local isostasy model) reaching a maximum amplitude at the margin toe. Converting isostatic anomalies into Moho depth variations shows that the Moho extracted from wide-angle seismic data is deeper than the one predicted by a local isostasy model in the oceanic domain, and shallower than it in the continental domain. These anomalies can be interpreted by opposite flexures of two plates separated by a plate boundary located close to the margin toe. We use a finite element model to simulate the lithospheric flexure. The amplitude of the equivalent vertical Moho deflection is larger in the central part of the study area (6–7 km) than on the easternmost and westernmost profiles (3 km). The effective elastic thickness used to best match the computed deflection is always extremely low (always less than 10 km) and probably reflects the relatively low strength of the lithosphere close to the plate boundary. Comparison with other wide-angle seismic profiles across an active and a passive margin show that the North Algerian margin displays isostatic anomalies close to that of an active margin. Finally, plate flexure is highest at the southern tip of the ocean-continent transition, possibly indicating that a former passive margin detachment is reactivated as a crustal scale reverse fault pre-dating a future subduction.

Description: In the central Andes, the Nazca plate displays large along strike variations in dip with a near horizontal subduction angle between 28 and 32°S referred to the Pampean flat slab segment. The upper plate above the Pampean flat slab has high rates of crustal seismicity and active basement cored uplifts. The SIEMBRA experiment, a 43-broad-band-seismic-station array was deployed to better characterize the Pampean flat slab region around 31°S. In this study, we explore the lithospheric structure above the flat slab as a whole and its relation to seismicity. We use the SIEMBRA data to perform a joint inversion of teleseismic receiver functions and Rayleigh wave phase velocity dispersion to constrain the shear wave velocity variations in the lithosphere. Our joint inversion results show: (1) the presence of several upper-plate mid-crustal discontinuities and their lateral extent that are probably related to the terrane accretion history; (2) zones of high shear wave velocity in the upper-plate lower crust associated with a weak Moho signal consistent with the hypothesis of partial eclogitization in the lower crust; (3) the presence of low shear-wave velocities at ~100 km depth interpreted as the subducting oceanic crust. Finally, in order to investigate the relation of the lithospheric structure to seismicity, we determine an optimal velocity–depth model based on the joint inversion results and use it to perform regional moment tensor inversions (SMTI) of crustal and slab earthquakes. The SMTI for 18 earthquakes that occurred between 2007 and 2009 in the flat slab region below Argentina, indicates systematically shallower focal depths for slab earthquakes (compared with inversions using previous velocity models). This suggests that the slab seismicity is concentrated mostly between 90 and 110 km depths within the subducting Nazca plate's oceanic crust and likely related to dehydration. In addition, the slab earthquakes exhibit extensional focal mechanisms suggesting new faulting at the edges of the flat portion of the slab. SMTI solutions for upper-plate crustal earthquakes match well the geological observations of reactivated structures and agree with crustal shortening. Our new constraints on flat slab structure can aid earthquake characterization for regional seismic hazard assessment and efforts to help understand the mechanisms for slab flattening in the central Andes.

Description: The resistivity structure of the lithospheric mantle beneath the Proterozoic Grenville Province in southern Ontario, Canada is investigated using 84 magnetotelluric (MT) sites divided into four profiles. Depth-based regional geoelectric dimensionality analyses of the MT responses indicate that the mantle lithosphere north of Lake Ontario can be subdivided into upper (45–150 km) and deeper (〉200 km) lithospheric mantle layers with regional strike azimuths of N85°E (±5°) and N65°E (±5°), respectively. MT responses from the Grenville Front and the northwest part of the Central Gneiss Belt are compatible with the presence of 2-D resistivity structures but farther to the southeast, in the southeast part of the Central Gneiss Belt and Central Metasedimentary Belt, they suggest the presence of localized 3-D structures. 2-D inversion of distortion-free MT responses images a large scale very resistive (〉20 000  m) region that extends 300 km southeast of the Grenville Front and for at least 800 km along-strike in the lithospheric mantle beneath the Grenville Province. This feature is interpreted to be Superior Province lithosphere and the corresponding N85°E geoelectric strike to be associated with the fabric of the Superior Province. The base of the resistor reaches depths of 280 km on two of the three MT profiles north of Lake Ontario and this depth is interpreted to be the base of the lithosphere. A large region of enhanced conductivity in the lower lithosphere, spatially correlated with decreased seismic velocity, is bounded to the northwest by a subvertical resistivity anomaly located near the Kirkland Lake and Cobalt kimberlite fields. The enhanced conductivity in the lower lithosphere is attributed to refertilization by fluids associated with Cretaceous kimberlite magmatism and can be explained by water content in olivine of 50 wt ppm in background areas with higher values in a localized anomaly beneath the kimberlite fields. Farther to the southeast the resistivity models include a lithospheric conductor between 100 and 150 km depth beneath the Central Metasedimentary Belt. The enhanced conductivity is attributed to grain boundary graphite films, associated with the Cretaceous kimberlitic magmatic process, or to water and carbon, introduced into the mantle during the pre-Grenvillian tectonism.