Brendan J. Meade

Present-day kinematics at the India-Asia collision zone

The collision of the Indian subcontinent with Asia drives the growth and evolution of the greater Tibetan Plateau region. Fault slip rates resulting from the relative motion between crustal blocks can provide a kinematic description of the distribution of presentday deformation. I construct a three-dimensional, regional-scale elastic block model of the India-Asia collision zone that is consistent with geodetic observations of interseismic deforma tion, mapped fault system geometry, historical seismicity, and the mechanics of the earthquake cycle. This mechanical model of the elastic upper crust yields a set of kinematically consistent fault slip rates and block motions that may serve to constrain dynamic models of continental crustal dynamics.

Estimates of Seismic Potential in the Marmara Sea Region from Block Models of Secular Deformation Constrained by Global Positioning System Measurements

We model the geodetically observed secular velocity field in north- western Turkey with a block model that accounts for recoverable elastic-strain ac- cumulation. The block model allows us to estimate internally consistent fault slip rates and locking depths. The northern strand of the North Anatolian fault zone (NAFZ) carries approximately four times as much right-lateral motion (24 mm/yr) as does the southern strand. In the Marmara Sea region, the data show strain accu- mulation to be highly localized. We find that a straight fault geometry with a shallow locking depth of 6-7 km fits the observed Global Positioning System velocities better than does a stepped fault geometry that follows the northern and eastern edges of the sea. This shallow locking depth suggests that the moment release associated with an earthquake on these faults should be smaller, by a factor of 2.3, than previously inferred assuming a locking depth of 15 km. Online material: an updated version of velocity-field data.

Algorithms for the calculation of exact displacements, strains, and stresses for triangular dislocation elements in a uniform elastic half space

We present algorithms for analytically calculating the displacements, strains, and stresses associated with slip on a triangular dislocation element (TDE) in a homogeneous elastic half space. Following previous efforts, the solution is constructed as a dislocation loop where the deformation fields for each of the three triangle legs are calculated by the superposition of two angular dislocations. In addition to the displacements at the surface we derive the displacements and strains at arbitrary depth. We give explicit formulas for the strains due to slip on an angular dislocation, the calculation of angular dislocation slip components, a method for identifying observation coordinates affected by a solid body translation, and rules for internally consistent vertex ordering allowing for the superposition of multiple TDEs. Examples of surface displacements and internal stresses are given and compared with rectangular representations of geometrically complex fault surfaces.

Stress modulation on the San Andreas fault by interseismic fault system interactions

During the interseismic phase of the earthquake cycle, between large earthquakes, stress on faults evolves in response to elastic strain accumulation driven by tectonic plate motions. Because earthquake cycle processes induce non-local stress changes, the interseismic stress accumulation rate on one fault is influenced by the behavior of all nearby faults. Using a geodetically constrained block model, we show that the total interseismic elastic strain field generated by fault interactions within Southern California may increase stressing rates on the Mojave and San Bernardino sections of the San Andreas fault within the Big Bend region by as much as 38% relative to estimates from isolated San Andreas models. Assuming steady fault system behavior since the C.E. 1857 Fort Tejon earthquake, shear stress accumulated on these sections due only to interaction with faults other than the San Andreas reaches 1 MPa, ∼3 times larger than the coseismic and postseismic stress changes induced by recent Southern California earthquakes. Stress increases along Big Bend sections coincide with the greatest earthquake frequency inferred from a 1500-yr-long paleoseismic record and may affect earthquake recurrence intervals within geometrically complex fault systems, including the sections of the San Andreas fault closest to metropolitan Los Angeles.

Inference of Multiple Earthquake-Cycle Relaxation Timescales from Irregular Geodetic Sampling of Interseismic Deformation

Abstract Characterizing surface deformation throughout a full earthquake cycle is a challenge due to the lack of high‐resolution geodetic observations of duration comparable to that of characteristic earthquake recurrence intervals (250–10,000 years). Here we approach this problem by comparing long‐term geologic slip rates with geodetically derived fault slip rates by sampling only a short fraction (0.001%–0.1%) of a complete earthquake cycle along 15 continental strike‐slip faults. Geodetic observations provide snapshots of surface deformation from different times through the earthquake cycle. The timing of the last earthquake on many of these faults is poorly known, and may vary greatly from fault to fault. Assuming that the underlying mechanics of the seismic cycle are similar for all faults, geodetic observations from different faults may be interpreted as samples over a significantly larger fraction of the earthquake cycle than could be obtained from the geodetic record along any one fault alone. As an ensemble, we find that geologically and geodetically inferred slip rates agree well with a linear relation of 0.94±0.09. To simultaneously explain both the ensemble agreement between geologic and geodetic slip‐rate estimates with observations of rapid postseismic deformation, we consider the predictions from simple two‐layer earthquake‐cycle models with both Maxwell and Burgers viscoelastic rheologies. We find that a two‐layer Burgers model, with two relaxation timescales, is consistent with observations of deformation throughout the earthquake cycle, whereas the widely used two‐layer Maxwell model with a single relaxation timescale, is not, suggesting that the earthquake cycle is effectively characterized by a largely stress‐recoverable rapid postseismic stage and a much more slowly varying interseismic stage.

Temporal Variation in Climate and Tectonic Coupling in the Central Andes

Analog and numerical models predict a coupling between climate and tectonics whereby erosion infl uences the deformation of orogens. A testable prediction from modeling studies is the decrease in width of mountain ranges as a result of increased precipitation. Here we evaluate the effect of climate on a critically tapered orogen, the central Andes, using sequentially restored, balanced cross sections through wet (15°‐16°S) and dry (21°S) regions of the orogen. In these regions, tectonics, basin geometry, and style of deformation are similar, allowing us to use variations in propagation (or changes in percent shortening) to evaluate whether alongstrike changes in width and morphology are climate driven in the north. Results indicate similar total percent shortening along the northern (40%) and southern (37%) sections, suggesting that a wetter climate has not limited the width (propagation) in the north. However, comparison of early (45‐25 Ma) and recent (ca. 20‐0 Ma) shortening indicates that early deformation produced 45% ± 2% shortening of both sections, while recent deformation produced 41% ± 2% (north) versus 32% ± 2% (south) in the actively deforming Subandes. The latter suggests a coupling between climate and tectonics that began between ca. 19 and 8 Ma, and continues to 0 Ma, potentially limiting the width of the northern Subandes by ~40 km.

Rapid slip‐deficit rates at the eastern margin of the Tibetan Plateau prior to the 2008 Mw 7.9 Wenchuan earthquake

The Longmen Shan is the steepest topographic front at the India-Asia collision zone and the site of the Mw 7.9 Wenchuan earthquake. Here to explain the interseismic GPS velocities across the greater Longmen Shan region, we develop a boundary element model including earthquake cycle effects, topography, the westward dipping Beichuan Fault and a ∼20 km deep, shallowly dipping, detachment, inferred from observed afterslip and from structural considerations. Previous analyses which neglected the detachment and earthquake cycle effects have found shortening rates near zero. In contrast, we find that interseismic GPS data are consistent with a shortening rate of 5.7±1.5mm/yr and maximum surface slip-deficit rate of 9.5±2.5mm/yr. This model unifies the interpretation of geodetic deformation throughout the earthquake cycle and suggests that the Longmen Shan is an active fold-and-thrust belt with of Wenchuan-like recurrence intervals as short as 600 years.

The signature of an unbalanced earthquake cycle in Himalayan topography

Fifty percent of the relative motion between the Indian and Asian plates is accommodated by active convergence at the Himalayan Range Front (HRF). Earthquake cycle processes on shallowly dipping HRF thrust faults generate large earthquakes (MW ≥ 7) and contribute to the growth of HRF topography. Interseismic rock uplift rates reach a maximum north of the active Main Frontal Thrust and have been suggested to significantly influence the collocated convex bulge in HRF topography. Using geodetically constrained models of interseismic rock uplift rates and simple channel erosion rate laws, we show that convex channel profiles are predicted when interseismic deformation outpaces coseismic deformation. Applying this model to the observed elevation profiles of 20 HRF-spanning channels in Nepal yields a minimum mean residual elevation (72 m) if interseismic deformation has outpaced coseismic deformation by a factor of four. The long-term earthquake deficit required for the application of this model is consistent with some estimates of historical moment imbalance but requires temporally variable fault system activity. The spatial correlation between nominally interseismic rock uplift and the HRF topographic bulge may be explained by (1) a noncausal geometric coincidence, (2) geodetic observations of significant deformation not directly related to earthquake cycle processes, or (3) an unbalanced earthquake cycle at the HRF.

Kinematically consistent models of viscoelastic stress evolution

Following large earthquakes, coseismic stresses at the base of the seismogenic zone may induce rapid viscoelastic deformation in the lower crust and upper mantle. As stresses diffuse away from the primary slip surface in these lower layers, the magnitudes of stress at distant locations (>1 fault length away) may slowly increase. This stress relaxation process has been used to explain delayed earthquake triggering sequences like the 1992Mw= 7.3 Landers and 1999Mw=7.1 Hector Mine earthquakes in California. However, a conceptual difficulty associated with thesemodels is that themagnitudes of stresses asymptote to constant values over long time scales. This effect introduces persistent perturbations to the total stress field over many earthquake cycles. Here we present a kinematically consistent viscoelastic stress transfer model where the total perturbation to the stress field at the end of the earthquake cycle is zero everywhere. With kinematically consistent models, hypotheses about the potential likelihood of viscoelastically triggered earthquakes may be based on the timing of stress maxima, rather than on any arbitrary or empirically constrained stress thresholds. Based on these models, we infer that earthquakes triggered by viscoelastic earthquake cycle effects may be most likely to occur during the first 50% of the earthquake cycle regardless of the assumed long-term and transient viscosities.

Geodetically constrained models of viscoelastic stress transfer and earthquake triggering along the North Anatolian fault

Over the past 80 years, 8 MW > 6.7 strike-slip earthquakes west of 40° longitude have ruptured the North Anatolian fault (NAF) from east to west. The series began with the 1939 Erzincan earthquake in eastern Turkey, and the most recent 1999 MW = 7.4 Izmit earthquake extended the pattern of ruptures into the Sea of Marmara in western Turkey. The mean time between seismic events in this westward progression is 8.5 ± 11 years (67% confidence interval), much greater than the timescale of seismic wave propagation (seconds to minutes). The delayed triggering of these earthquakes may be explained by the propagation of earthquake-generated diffusive viscoelastic fronts within the upper mantle that slowly increase the Coulomb failure stress change ( ΔCFS) at adjacent hypocenters. Here we develop three-dimensional stress transfer models with an elastic upper crust coupled to a viscoelastic Burgers rheology mantle. Both the Maxwell (ηM = 4 × 1018−1 × 1019 Pa s) and Kelvin (ηK = 1 × 1018−1 × 1019 Pa s) viscosities are constrained by studies of geodetic observations before and after the 1999 Izmit earthquake. We combine this geodetically constrained rheological model with the observed sequence of large earthquakes since 1939 to calculate the time evolution of ΔCFS changes along the North Anatolian fault due to viscoelastic stress transfer. Apparent threshold values of mean ΔCFS at which the earthquakes in the eight decade sequence occur are between ∼0.02 to ∼3.15 MPa and may exceed the magnitude of static ΔCFS values by as much as 177%. By 2023, we infer that the mean time-dependent stress change along the northern NAF strand in the Marmara Sea near Istanbul, which may have previously ruptured in 1766, may reach the mean apparent time-dependent stress thresholds of the previous NAF earthquakes.