Roger Bilham

On the mechanics of earthquake afterslip

We propose a model for earthquake afterslip based on rate and state variable friction laws. In the model, afterslip is attributed to the interaction of a velocity-weakening region at depth (within which earthquakes nucleate) with an upper region of velocity-strengthening frictional behavior. The existence of this upper region is supported by independent seismologic observations and the results of laboratory friction experiments. In our model, afterslip is the result of relaxation of a stress perturbation within the velocity-strengthening region, which arises when an earthquake propagates into that region from below. We derive the stress perturbation and its decay from the friction constitutive law using a simple, 1 degree-of-freedom approximation for the elastic interaction between the fault and its surroundings. This approximation is based on thickness-averaged displacements and slip velocities within the velocity-strengthening region, which is assumed to slip as a rigid block. Coseismic and postseismic slip are coupled through the thickness-averaged stiffness k of the velocity-strengthening region. We assume k to be inversely proportional to the thickness of this region, which means that thicker velocity strengthening regions have a greater tendency to arrest coseismic slip. We model the afterslip-time histories of the 1966 Parkfield and 1987 Superstition Hills earthquakes and relate the model parameters to physical parameters which may govern the rheologic behavior of the faults. In accord with field observations, our model predicts (1) that afterslip on some faults scales with the thickness of the (unconsolidated) sedimentary cover and (2) that proportionally more afterslip occurs for earthquakes in which coseismic surface slip is small compared with coseismic slip at depth. Velocity-strengthening frictional behavior is to be expected for faults within poorly consolidated sediments and for those that contain significant gouge zones (about >500 m) within their shallow regions (<3–5 km). Combining our results with those of recent laboratory friction studies indicates that relatively young faults with little accumulated fault gouge should exhibit little afterslip.

Imaging the Indian subcontinent beneath the Himalaya

The rocks of the Indian subcontinent are last seen south of the Ganges before they plunge beneath the Himalaya and the Tibetan plateau. They are next glimpsed in seismic reflection profiles deep beneath southern Tibet, yet the surface seen there has been modified by processes within the Himalaya that have consumed parts of the upper Indian crust and converted them into Himalayan rocks. The geometry of the partly dismantled Indian plate as it passes through the Himalayan process zone has hitherto eluded imaging. Here we report seismic images both of the decollement at the base of the Himalaya and of the Moho (the boundary between crust and mantle) at the base of the Indian crust. A significant finding is that strong seismic anisotropy develops above the decollement in response to shear processes that are taken up as slip in great earthquakes at shallower depths. North of the Himalaya, the lower Indian crust is characterized by a high-velocity region consistent with the formation of eclogite, a high-density material whose presence affects the dynamics of the Tibetan plateau.

Kinematics of the India‐Eurasia collision zone from GPS measurements

We use geodetic techniques to study the India-Eurasia collision zone. Six years of GPS data constrain maximum surface contraction rates across the Nepal Himalaya to 18 ± 2 mm/yr at 12°N ±13° (1σ). These surface rates across the 150-km-wide deforming zone are well fitted with a dislocation model of a buried north dipping detachment fault striking 105°, which aseismically slips at a rate of 20 ± 1 mm/yr, our preferred estimate for the India-to-southern-Tibet convergence rate. This is in good agreement with various geologic predictions of 18 ± 7 mm/yr for the Himalaya. A better fit can be achieved with a two-fault model, where the western and eastern faults strike 112° and 101°, respectively, in approximate parallelism with the Himalayan arc and a seismicity lineament. We find eastward directed extension of 11 ± 3 mm/yr between northwestern Nepal Lhasa, also in good agreement with geologic and seismic studies across the southern Tibetan plateau. Continuous GPS sites are used to further constrain the style and rates of deformation throughout the collision zone. Sites in India, Uzbekistan, and Russia agree within error with plate model prediction.

Plateau pop-up' in the great 1897 Assam earthquake

The great Assam earthquake of 12 June 1897 reduced to rubble all masonry buildings within a region of northeastern India roughly the size of England, and was felt over an area exceeding that of the great 1755 Lisbon earthquake. Hitherto it was believed that rupture occurred on a north-dipping Himalayan thrust fault propagating south of Bhutan. But here we show that the northern edge of the Shillong plateau rose violently by at least 11 m during the Assam earthquake, and that this was due to the rupture of a buried reverse fault approximately 110 km in length and dipping steeply away from the Himalaya. The stress drop implied by the rupture geometry and the prodigious fault slip of 18 ± 7 m explains epicentral accelerations observed to exceed 1g vertically and surface velocities exceeding 3 m s-1 (ref. 1). This quantitative observation of active deformation of a ‘pop-up’ structure confirms that faults bounding such structures can penetrate the whole crust. Plateau uplift in the past 2–5 million years has caused the Indian plate to contract locally by 4 ± 2 mm yr-1, reducing seismic risk in Bhutan but increasing the risk in northern Bangladesh.

GPS geodetic constraints on Caribbean-North America plate motion

We describe a model for Caribbean plate motion based on GPS velocities of four sites in the plate interior and two azimuths of the Swan Islands transform fault. The data are well fit by a single angular velocity, with average misfits approximately equal to the 1.5–3.0 mm yr−1 velocity uncertainties. The new model predicts Caribbean-North America motion ∼65% faster than predicted by NUVEL-1A, averaging 18–20±3 mm yr−1 (2σ) at various locations along the plate boundary. The data are best fit by a rotation pole that predicts obliquely convergent motion along the plate boundary east of Cuba, but are fit poorly by a suite of previously published models that predict strike-slip motion in this region. The data suggest an approximate upper bound of 4–6 mm yr−1 for internal deformation of the Caribbean plate, although rigorous estimates await more precise and additional velocities from sites in the plate interior.

The motion and active deformation of India

Measurements of surface displacements using GPS constrain the motion and deformation of India and India-Eurasia plate boundary deformation along the Himalaya. The GPS velocities of plate-interior sites constrain the pole of the angular velocity vector of India with respect to Eurasia to lie at 25.6±1.0°N 11.1±9.0°E, approximately 6° west of the NUVEL-1A pole of <3 Ma plate motion. The angular rotation rate of 0.44 ±0.03°Myr−1 is 14% slower than the long-term rate of 0.51° Myr−1. Insignificant velocities between plate interior sites indicate that the exposed Indian plate is stable to within 7 · 10−9 yr−1. The observed contraction vector across the Himalaya (≤20 mm/yr) veers from ∼N20°E in the northwest Himalaya to ∼N25°W in east Nepal, consistent with east-west extension of southern Tibet.

Geodetic evidence for a low slip rate in the Altyn Tagh fault system

The collision between India and Asia has been simulated with a variety of computational models that describe or predict the motions of the main faults of east Asia. Geological slip-rate estimates of 20–30 mm yr -1 suggest that the largest of these faults, the 2,000-km-long Altyn Tagh fault system on the northern edge of the Tibetan plateau, absorbs as much of the Indo-Asian convergence signal as do the Himalayas—partly by oblique slip and partly by contraction and mountain growth. However, the predictions of dynamic models for Asian deformation and the lower bounds of some geological slip-rates estimates (3–9 mm yr -1; refs 7, 8) suggest that the Altyn Tagh system is less active. Here, we report geodetic data from 89–91° E that indicate left-lateral shear of 9 ± 5 mm yr-1 and contraction of 3 ± 1 mm yr-1 across the Altyn Tagh system. This result—combined with our finding that, at 90° E, Tibet contracts north–south at 9 ± 1 mm yr-1—supports the predictions of dynamic models of Asian deformation.

Transient fault slip in Guerrero, southern Mexico

The Guerrero region of southern Mexico has ac- cumulated more than 5 m of relative plate motion since the last major earthquake. In early 1998, a continuous GPS site in Guerrero recorded a transient displacement. Modeling indicates that anomalous fault slip propagated from east to west along-strike of the subduction megathrust. Campaign GPS and leveling data corroborate the model. The moment release was equivalent to an Mw≥6.5 earthquake. No M> 5 earthquakes accompanied the event, indicating the frictional regime is velocity-strengthening at the location of slip.

GPS estimate of relative motion between the Caribbean and South American plates, and geologic implications for Trinidad and Venezuela

Global Positioning System (GPS) data from eight sites on the Caribbean plate and five sites on the South American plate were inverted to derive an angular velocity vector describing present-day relative plate motion. Both the Caribbean and South American velocity data fit rigid-plate models to within ±1–2 mm/yr, the GPS velocity uncertainty. The Caribbean plate moves approximately due east relative to South America at a rate of ∼20 mm/yr along most of the plate boundary, significantly faster than the NUVEL-1A model prediction, but with similar azimuth. Pure wrenching is concentrated along the approximately east-striking, seismic, El Pilar fault in Venezuela. In contrast, transpression occurs along the 068°-trending Central Range (Warm Springs) fault in Trinidad, which is aseismic, possibly locked, and oblique to local plate motion.

Constraints on Himalayan deformation inferred from vertical velocity fields in Nepal and Tibet

Spirit leveling data from the Nepal Himalaya between 1977 and 1990 indicate localized uplift at 2–3 mm/yr in the Lesser Himalaya with spatial wavelengths of 25–35 km and at 4–6 mm/yr in the Greater Himalaya with a wavelength of ≈40 km. Leveling data with significantly sparser spatial sampling in southern Tibet between 1959 and 1981 suggest that the Himalayan divide may be rising at a rate of 7.5±5.6 mm/yr relative to central Tibet. We use two-dimensional dislocation modeling methods to examine a number of structural models that yield vertical velocity fields similar to those observed. Although these models are structurally nonunique, dislocation models that satisfy the data require aseismic slip rates of 2–7 mm/yr on shallow dipping faults beneath the Lesser Himalaya and rates of 9–18 mm/yr on deep thrust faults dipping at ≈25°N near the Greater Himalaya. Unfortunately, the leveling data cannot constrain long-wavelength uplift (>100 km) across the Himalaya, and unequivocal estimates of aseismic slip in central Nepal are therefore not possible. In turn, the poor spatial density of leveling data in southern Tibet may inadequately sample the processes responsible for the uplift of the Greater Himalaya. Despite these shortcomings in the leveling data, the pattern of uplift is consistent with a crustal scale ramp near the Greater Himalaya linking shallow northward dipping thrust planes (3–6°) beneath the Lesser Himalaya and southern Tibet. Aseismic slip on the potential rupture surface of future great earthquakes beneath the Nepal Himalaya south of this ramp appears not to exceed 30% of the total convergence rate between India and southern Tibet resulting in an accumulating slip deficit of 13±8 mm/yr.