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

T his paper investigates the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation. General conditions for a bifurcation, corresponding to the localization of deformation into a planar band, are derived. Although the analysis is general and applications to other localization phenomena are noted, the constitutive relations which are examined in application of the criterion for localization are intended to model the behavior of brittle rock masses under compressive principal stresses. These relations are strongly pressure-sensitive since inelasticity results from frictional sliding on an array of fissures; the resulting inelastic response is dilatant, owing to uplift in sliding at asperities and to local tensile cracking from fissure tips. The appropriate constitutive descriptions involve non-normality of plastic strain increments to the yield hyper-surface. Also, it is argued that the subsequent yield surfaces will develop a vertex-like structure. Both of these features are shown to be destabilizing and to strongly influence the resulting predictions for localization by comparison to predictions based on classical plasticity idealizations, involving normality and smooth yield surfaces. These results seem widely applicable to discussions of the inception of rupture as a constitutive instability.

http://esag.harvard.edu/rice/057_RudnickiRi_localization_JMPS75.pdf

Conditions for the localization of deformation in pressure-sensitive dilatant materials

To date, more than 7300 in situ stress orientations have been compiled as part of the World Stress Map project. Of these, over 4400 are considered reliable tectonic stress indicators, recording horizontal stress orientations to within <±25°. Remarkably good correlation is observed between stress orientations deduced from in situ stress measurements and geologic observations made in the upper 1–2 km, well bore breakouts extending to 4–5 km depth and earthquake focal mechanisms to depths of ∼20 km. Regionally uniform stress orientations and relative magnitudes permit definition of broad-scale regional stress patterns often extending 20–200 times the approximately 20–25 km thickness of the upper brittle lithosphere. The “first-order” midplate stress fields are believed to be largely the result of compressional forces applied at plate boundaries, primarily ridge push and continental collision. The orientation of the intraplate stress field is thus largely controlled by the geometry of the plate boundaries. There is no evidence of large lateral stress gradients (as evidenced by lateral variations in stress regime) which would be expected across large plates if simple resistive or driving basal drag tractions (parallel or antiparallel to absolute motion) controlled the intraplate stress field. Intraplate areas of active extension are generally associated with regions of high topography: western U.S. Cordillera, high Andes, Tibetan plateau, western Indian Ocean plateau. Buoyancy stresses related to crustal thickening and/or lithospheric thinning in these regions dominate the intraplate compressional stress field due to plate-driving forces. These buoyancy forces are just one of several categories of “second-order” stresses, or local perturbations, that can be identified once the first-order stress patterns are recognized. These second-order stress fields can often be associated with specific geologic or tectonic features, for example, lithospheric flexure, lateral strength contrasts, as well as the lateral density contrasts which give rise to buoyancy forces. These second-order stress patterns typically have wavelengths ranging from 5 to 10+ times the thickness of the brittle upper lithosphere. A two-dimensional analysis of the amount of rotation of regional horizontal stress orientations due to a superimposed local stress constrains the ratio of the magnitude of the horizontal regional stress differences to the local uniaxial stress. For a detectable rotation of 15°, the local horizontal uniaxial stress must be at least twice the magnitude of the regional horizontal stress differences. Examples of local rotations of SHmax orientations include a 75°–85° rotation on the northeastern Canadian continental shelf possibly related to margin-normal extension derived from sediment-loading flexural stresses, a 50°–60° rotation within the East African rift relative to western Africa due to extensional buoyancy forces caused by lithospheric thinning, and an approximately 90° rotation along the northern margin of the Paleozoic Amazonas rift in central Brazil. In this final example, this rotation is hypothesized as being due to deviatoric compression oriented normal to the rift axis resulting from local lithospheric support of a dense mass in the lower crust beneath the rift (“rift pillow”). Estimates of the magnitudes of first-order (plate boundary force-derived) regional stress differences computed from modeling the source of observed local stress rotations magnitudes can be compared with regional stress differences based on the frictional strength of the crust (i.e., “Byerlee's law”) assuming hydrostatic pore pressure. The examples given here are too few to provide a definitive evaluation of the direct applicability of Byerlee's law to the upper brittle part of the lithosphere, particularly in view of uncertainties such as pore pressure and relative magnitude of the intermediate principal stresses. Nonetheless, the observed rotations all indicate that the magnitude of the local horizontal uniaxial stresses must be 1–2.5+ times the magnitude of the regional first-order horizontal stress differences and suggest that careful evaluation of such local rotations may be a powerful technique for constraining the in situ magnitude stress differences in the upper, brittle part of the lithosphere.

/pdf/first-and-second-order-patterns-of-stress-in-the-lithosphere-595hs86ljh.pdf

First‐ and second‐order patterns of stress in the lithosphere: The World Stress Map Project

The elastic moduli of a solid permeated with an isotropic distribution of flat cracks have been calculated from the energy of a single crack by use of a self-consistent approximation. The results are applicable for a dense network of cracks and give physically reasonable results up to the point that the shear modulus vanishes. Results for both circular and elliptical cracks are essentially the same if the crack density is characterized by 2N〈A2/P〉/π, where N is the number of cracks per unit volume, A is the area of crack, and P is the perimeter of cracks; for circular cracks of radius a this becomes N〈a3〉. This crack density parameter can be related quantitatively to crack traces observed in thin section. Results for completely dry or saturated cracks, for mixtures of dry and saturated cracks, and for cracks saturated with a compressible fluid are presented. For all cases, both seismic wave velocities decrease with increasing crack density. The velocity ratio VP/VS decreases for dry cracks and increases for saturated cracks. For the analysis of data a plot of VP/VS versus VS uniquely specifies the crack density. Comparison of the theory with wave velocities measured in laboratory rock samples demonstrates its validity for large crack densities. Interpretation of velocity changes before the San Fernando earthquake indicates that the region contained a substantial density of cracks at all times, that the anomalous decrease in VP/VS was due to the vaporization of pore fluid in nearly all of the previously saturated cracks without the introduction of new dry cracks, and that during the period of the recovery of the velocities to previous values the number of cracks in the region away from the epicentral zone decreased as they were resaturated, whereas the crack density increased following resaturation in the epicentral zone. Such use of the theoretical results may be useful in further investigations of preseismic phenomena.

Seismic velocities in dry and saturated cracked solids

We investigate the distribution of focal depths for earthquakes that do not appear to be associated with zones of recent subduction, using both new results from analyses of individual events recorded at teleseismic distances and published data for both microearthquakes and larger events. The deepest events in oceanic regions occur in old lithosphere (≥100 Ma), and excluding earthquakes in active mountain belts, the deepest crustal events occur in old cratons (tectonic age ≥800 Ma). Therefore, the temperature at the source region is likely to be an important factor determining whether deformation occurs seismically or not. From estimates of the temperatures at depths of the deepest events, we conclude that those limiting temperatures are about 250°–450°C and 600°–800°C for crustal and mantle materials, respectively. In several regions of recent continental convergence, in addition to shallow crustal seismicity, there is seismic activity in the uppermost mantle. The lower crust, however, is essentially aseismic. We infer that both the upper crustal and the mantle seismic regions correspond to zones of relatively high strength and that they are separated by a zone of lower strength in the lower crust where aseismic, ductile deformation predominates. This simple interpretation is qualitatively in agreement with extrapolated values of brittle and ductile strengths of geologic materials studied under appropriate pressure and temperature conditions in the laboratory. A low-strength zone in the lower crust might allow detachment of crystalline nappes from the underlying mantle (and lower crustal) lithosphere. The apparently greater strength of mantle materials than crustal materials at the same temperature implies that oceanic lithosphere is much stronger than continental lithosphere, and this difference may account for why plate tectonics works well in oceanic regions but not in continents.

Focal depths of intracontinental and intraplate earthquakes and their implications for the thermal and mechanical properties of the lithosphere

http://science.sciencemag.org/content/sci/181/4102/803.full.pdf

Earthquake Prediction: A Physical Basis

Large premonitory changes in ratio of seismic P and S velocities correlate with time of occurrence and size of earthquakes at Blue Mountain Lake, New York. These changes may be related to the opening of cracks or to changes in pore pressure.

Premonitory Changes in Seismic Velocities and Prediction of Earthquakes

Four telemetered seismic arrays were operated in northeastern Venezuela during the summer of 1979. An analysis of the data collected has resulted in accurate locations for about 100 microearthquakes and four new focal mechanism solutions. On the basis of these new data, an in-depth analysis of teleseismic data, and geologic evidence, we propose a new plate tectonic framework for the southeastern Caribbean. In this model, underthrusting of the Atlantic seafloor along the Lesser Antilles is extended to the southeast of Trinidad. The subducted slab is shown to dip northwesterly beneath Trinidad and the Caribbean Sea, penetrating depths of at least 150 km. This subduction appears to terminate abruptly in the vicinity of the Los Bajos-El Soldado fault zone, which trends WNW-NW and is located in the Gulf of Paria west of Trinidad. Geologic evidence shows right-lateral strike slip (RLSS) motion in this fault zone, probably initiated in the late Pliocene. This WNW-NW trending fault zone joins up with the E-W trending El Pilar-Casanay fault system in northeastern Venezuela, which also moves right laterally. The El Pilar fault is apparently offset by NNW trending faults that exhibit RLSS motion as well as normal faulting. This complex motion on an en echelon series of faults is interpreted to be the result of WNW motion of South America relative to the Caribbean plate. In our interpretation, the E-W component of relative motion is accommodated by RLSS motion on E-W faults and results in normal faulting on NNW-SSE faults. The smaller component of N-S convergence is reflected by RLSS motion on NNW trending faults and is accommodated by some internal deformation. The timing of the initiation of RLSS motion on the Los Bajos fault zone and the known total amount of displacement on it as well as other geologic indicators lead us to suggest that this complex mode of strike slip motion began only a few m.y. ago, and that the average rate of relative plate motion in this region is probably ≥0.9 ± 0.2 cm/yr.

Present‐day tectonics of the southeastern Caribbean and northeastern Venezuela

Renewed earthquake activity at Blue Mountain Lake (BML), New York, in July 1973 provided an excellent opportunity to monitor the travel time ratio of S to P waves (ts/tp) in real time and to test the ts/tp technique as a predictive tool. From a mean value of 1.73 on July 30, 1973, ts/tp decreased to about 1.5 over the next 2–3 days. On August 1 a prediction was made that an earthquake of magnitude 2.5–3 would occur in a few days. Upper limits of the magnitude and the time of occurrence of the expected earthquake were inferred from the spatial extent of the seismic anomaly. As a result of the prediction an additional strong motion accelerograph (SMA) was installed in the source region. At 2310 UT on August 3,1973, a magnitude 2.6 earthquake occurred at BML and triggered two SMA's. In addition to the seismic activity a number of explosions were recorded from a variety of azimuths. The P wave arrivals from distant quarry blasts, refracted from a high-velocity layer at 4 km beneath BML, showed late arrivals at five stations during the premonitory low in ts/tp. The P wave delays were maximum (0.13 s) in the hypocentral region of the earthquake and decreased away from it along two profiles. These results indicate that changes in ts/tp are caused by changes in the material properties of the earthquake source region. The anomalous zone (region of low P velocity) for the August 3 earthquake (aftershock length 1 km, depth 1±0.1 km) was about 3–5 km in radius and was wholly or largely limited to the layer above the interface at 4-km depth. In contrast to the P delays observed from distant quarry blasts, P and S arrivals from local construction blasts (Δ < 10 km) show no large premonitory changes in either P or S travel times. This observation suggests that either no significant velocity anomalies occurred in the upper 0.5 km of the BML region or that the dilatant cracks were predominantly horizontal, the result being strong velocity anisotropy. This conclusion is supported by data from seismic sources; events located at shallow depths show normal (1.75) to high (1.85) ts/tp values even when values as low as 1.5 are observed from deeper sources. This finding places constraints on the use of artificial sources to monitor changes in velocity, since the effects of anisotropy may have to be taken into account in addition to ensuring that ray paths to the recording stations penetrate the zone of anomalous velocity. A maximum likelihood method was used to invert data from individual small earthquakes to determine P and S velocities in the anomalous zone. The results, which are consistent with the explosion data, indicate that the premonitory decreases in P and S velocities were much more pronounced for sources at depths of 1–2 km than for those near the surface. The inferred low values of P and S velocities were, respectively, about 22 and 12% below normal. This study also shows that ts/tp inferred from a Wadati plot is a function of the distribution of stations relative to the anomalous zone. To optimize the use of ts/tp as a predictive tool, this study suggests that not only temporal but spatial variations of velocity anomalies should be monitored. This emphasizes the need for multistation coverage for reliable earthquake prediction.

Spatial and temporal variations in ts /tp and in P wave residuals at Blue Mountain Lake, New York: Application to earthquake prediction

Data for local earthquakes recorded by a network of stations in northeastern United States and adjacent Canada were analyzed to study the seismicity, the relationship between earthquakes and known faults, the state of stress, and crustal and upper mantle velocity structure. In addition, portable seismographs were deployed in the field to study aftershocks. As a result, accurate locations for about 364 local earthquakes (2 ≤ mb ≤ 5) and 22 focal mechanism solutions were determined. A comparison of the spatial distribution of these events (1970–1979) with historical earthquakes (1534–1959) reveals that seismic activity in the northeast is relatively stationary in space: those areas that have had little or no seismicity historically are relatively aseismic today, whereas the historically active areas are also active today. The instrumental locations, historical seismicity, and focal mechanism solutions show an internal consistency that help us distinguish two distinct seismogenic provinces. (1) The Adirondack-western Quebec province is a northwesterly trending zone of seismic activity, about 200 km wide and at least 500 km long, extending from the SE Adirondacks into western Quebec, Canada. Thrust faulting on planes striking NNW to NW appears to predominate, and the inferred axis of maximum horizontal compression is largely uniform and trends WSW, nearly parallel to the calculated absolute plate motion of North America. Little or no seismicity is found where anorthosite outcrops at the surface. Correlations between gravity anomalies and earthquake locations suggest that seismic activity in this zone is localized to regions of steep NE or SW gradient in Bouguer anomalies. This zone does not appear to extend southeastward to Boston, as proposed by some workers. (2) The Appalachian province is a northeasterly trending zone of seismic activity extending from northern Virginia to New Brunswick, Canada. Highangle reverse or thrust faulting on N to NE trending planes appears to predominate. The western margin of this province, however, appears to be relatively aseismic. We attribute this relative lack of activity to one or more of the following: the presence of igneous activity postdating rifting of Africa from North America, the occurrence of intense metamorphism during the Acadian orogeny which may have annealed preexisting faults, and the predominance of ductile as opposed to brittle deformation in the geologic past. The inferred axis of maximum horizontal compression along the eastern margin of the Appalachians is rather uniform and trends W-WNW, almost perpendicular to the magnetic lineations offshore. We suggest that this W-WNW compression reflects the gravitational force arising from horizontal density variations in the oceanic lithosphere as it cools and moves away from spreading centers.

Yash P. Aggarwal

Papers

Earthquake Prediction: A Physical Basis

Premonitory Changes in Seismic Velocities and Prediction of Earthquakes

Present‐day tectonics of the southeastern Caribbean and northeastern Venezuela

Spatial and temporal variations in ts /tp and in P wave residuals at Blue Mountain Lake, New York: Application to earthquake prediction

Seismotectonics of northeastern United States and adjacent Canada