Preliminary reference earth model

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

A global plate motion model, named NUVEL-1, which describes current plate motions between 12 rigid plates is described, with special attention given to the method, data, and assumptions used Tectonic implications of the patterns that emerged from the results are discussed It is shown that wide plate boundary zones can form not only within the continental lithosphere but also within the oceanic lithosphere; eg, between the Indian and Australian plates and between the North American and South American plates Results of the model also suggest small but significant diffuse deformation of the oceanic lithosphere, which may be confined to small awkwardly shaped salients of major plates

Current plate motions

SUMMARY 
We determine best-fitting Euler vectors, closure-fitting Euler vectors, and a new global model (NUVEL-1) describing the geologically current motion between 12 assumed-rigid plates by inverting plate motion data we have compiled, critically analysed, and tested for self-consistency. We treat Arabia, India and Australia, and North America and South America as distinct plates, but combine Nubia and Somalia into a single African plate because motion between them could not be reliably resolved. The 1122 data from 22 plate boundaries inverted to obtain NUVEL-1 consist of 277 spreading rates, 121 transform fault azimuths, and 724 earthquake slip vectors. We determined all rates over a uniform time interval of 3.0m.y., corresponding to the centre of the anomaly 2A sequence, by comparing synthetic magnetic anomalies with observed profiles. The model fits the data well. Unlike prior global plate motion models, which systematically misfit some spreading rates in the Indian Ocean by 8–12mm yr−1, the systematic misfits by NUVEL-1 nowhere exceed ∼3 mm yr−1. The model differs significantly from prior global plate motion models. For the 30 pairs of plates sharing a common boundary, 29 of 30 P071, and 25 of 30 RM2 Euler vectors lie outside the 99 per cent confidence limits of NUVEL-1. Differences are large in the Indian Ocean where NUVEL-1 plate motion data and plate geometry differ from those used in prior studies and in the Pacific Ocean where NUVEL-1 rates are systematically 5–20 mm yr−1 slower than those of prior models. The strikes of transform faults mapped with GLORIA and Seabeam along the Mid-Atlantic Ridge greatly improve the accuracy of estimates of the direction of plate motion. These data give Euler vectors differing significantly from those of prior studies, show that motion about the Azores triple junction is consistent with plate circuit closure, and better resolve motion between North America and South America. Motion of the Caribbean plate relative to North or South America is about 7 mm yr−1 slower than in prior global models. Trench slip vectors tend to be systematically misfit wherever convergence is oblique, and best-fitting poles determined only from trench slip vectors differ significantly from their corresponding closure-fitting Euler vectors. The direction of slip in trench earthquakes tends to be between the direction of plate motion and the normal to the trench strike. Part of this bias may be due to the neglect of lateral heterogeneities of seismic velocities caused by cold subducting slabs, but the larger part is likely caused by independent motion of fore-arc crust and lithosphere relative to the overriding plate.

Two models, a simple cooling model and the plate model, have been advanced to account for the variation in depth and heat flow with increasing age of the ocean floor. The simple cooling model predicts a linear relation between depth and t½, and heat flow and 1/t½, where t is the age of the ocean floor. We show that the same t½ dependence is implicit in the solutions for the plate model for sufficiently young ocean floor. For larger ages these relations break down, and depth and heat flow decay exponentially to constant values. The two forms of the solution are developed to provide a simple method of inverting the data to give the model parameters. The empirical depth versus age relation for the North Pacific and North Atlantic has been extended out to 160 m.y. B.P. The depth initially increases as t½, but between 60 and 80 m.y. B.P. the variation of depth with age departs from this simple relation. For older ocean floor the depth decays exponentially with age toward a constant asymptotic value. Such characteristics would be produced by a thermal structure close to that of the plate model. Inverting the data gives a plate thickness of 125±10 km, a bottom boundary temperature of 1350°±275°C, and a thermal expansion coefficient of (3.2±1.1) × 10−5°C−1. Between 0 and 70 m.y. B.P. the depth can be represented by the relation d(t) = 2500 + 350t½ m, with t in m.y. B.P., and for regions older than 20 m.y. B.P. by the relation d(t) = 6400 - 3200 exp (−t/62.8) m. The heat flow data were treated in a similar, but less extensive manner. Although the data are compatible with the same model that accounts for the topography, their scatter prevents their use in the same quantitative fashion. Our analysis shows that the heat flow only responds to the bottom boundary at approximately twice the age at which the depth does. Within the scatter of the data, from 0 to 120 m.y. B.P., the heat flow pan be represented by the relation q(t) = 11.3/t½ μcal cm−2s−1. The previously accepted view that the heat flow observations approach a constant asymptotic value in the old ocean basins needs to be tested more stringently. The above results imply that a mechanism is required to supply heat at the base of the plate.

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An analysis of the variation of ocean floor bathymetry and heat flow with age

Summary A number of possible mechanisms have recently been proposed for driving the motions of the lithospheric plates, such as pushing from mid-ocean ridges, pulling by downgoing slabs, suction toward trenches, and coupling of the plates to flow in the mantle. We advance a new observational method of testing these theories of the driving mechanism. Our basic approach is to solve the inverse problem of determining the relative strength of the plausible driving forces, given the observed motions and geometries of the lithospheric plates. Since the inertia of the plates is negligible, each plate must be in dynamic equilibrium, so that the sum of the torques acting on a plate must be zero. Thus, our problem is to determine the relative sizes of the forces that minimize the components of net torque on each plate. The results indicate that the forces acting on the downgoing slab control the velocity of the oceanic plates and are an order of magnitude stronger than any other force. Namely, all the oceanic plates attached to substantial amounts of downgoing slabs move with a ' terminal velocity ' at which the gravitational body force pulling the slabs downward is nearly balanced with the resistance acting on the slab; regardless of the other features of the trailing horizontal part of the plates. The drag on the bottom of the plates which resist motion is stronger under the continents than under the oceans.

On the Relative Importance of the Driving Forces of Plate Motion

The orientations of fault planes and slip directions indicated by a population of earthquake focal mechanisms can be used to determine best fit regional principal stress directions and R = (σ2–σ1)/(σ3–σ1), a measure of relative stress magnitudes, under the assumption of uniform stress in the source region. This analysis allows for the possibility that failure occurs on preexisting zones of weakness of any orientation. In the inversion we perform a grid search of stress models to find the one which requires the smallest total rotation of all the fault planes that is needed to match the observed and predicted slip directions; the method allows for errors in orientations of both the fault planes and slip directions. We have an objective means for identifying the more likely of the two possible fault planes from each focal mechanism relative to a given stress model; thus we do not face the problem of ambiguity of nodal planes which plagues other analyses of this kind. By using a grid search of stress models rather than a linearization scheme, we are able to perform a realistic error analysis and thus establish confidence limits for the preferred regional stresses. The method can be used to investigate possible stress inhomogeneities during earthquake sequences by analyzing subsets of the data population. The technique has been applied to 76 events from the San Fernando earthquake sequence for which we have found best fit stresses (plunge and azimuth): σ1, = 7,187; σ2 = 27,281; σ3 = 62,84; and R = 0.65. The average misfit between this stress model and all the data is about 8°, and all but eight of the aftershocks have misfits of less than 20°. These values are considerably less than the uncertainty of the focal mechanism determinations; therefore significant stress inhomogeneities are not required by the data. Our analysis does not support the suggestion of a change in stresses during the aftershock sequence, as proposed by others on the basis of an apparent change in focal mechanisms.

An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando Earthquake Sequence

Summary

The dispersion of Love and Rayleigh waves in the period range 17–167 s is used to detect the change in the structure of the upper mantle as the age of the sea-floor increases away from the mid-ocean ridge Using the single station method, the group and phase velocities of Rayleigh waves were measured for 78 paths in the east Pacific In order to describe the observed Rayleigh wave dispersion, both a systematic increase in velocities with the age of the sea-floor and anisotropy of propagation are required The maximum change in velocity with age is about 5 per cent, with the contrast between age zones decreasing with increasing period The greatest change occurs in the first few million years, due to the rapid cooling and solidification of the upper part of the lithosphere In the 0–5 My age zone, the average thickness of the lithosphere can be no greater than 30 km, including the water and crustal layers Within 10 My after formation, the lithosphere reaches a thickness of about 60 km As the mantle continues to cool, the shear velocity within the lithosphere increases Within the area of this study, no change occurs in the upper mantle deeper than about 80 km



Rayleigh waves travel fastest in the direction of spreading The degree of anisotropy in Rayleigh wave propagation is frequency-dependent, reaching a maximum of 2–0±0–2 per cent at a period of about 70 s Several models are constructed which can reproduce this frequency-dependent anisotropy



The regional phase velocities of the fundamental and first higher Love modes have been simultaneously measured using a new technique The Love wave data is inconsistent with the Rayleigh wave data unless SH velocity is higher than SV velocity within the uppermost 125 km of the mantle Anisotropy deeper than 250 km is suggested, but not required, by the data

The Early Structural Evolution and Anisotropy of the Oceanic Upper Mantle

The flexural rigidity of the lithosphere is often estimated from the linear transfer function (admittance) between gravity anomalies and topography. Admittance estimates strongly weight provinces with large topographic relief, which will tend to be those provinces with low flexural rigidity if the cause of the topography is subsurface variations in density. If the observed admittance of continents is modeled in terms of surface loading of an elastic plate, there is a strong bias toward low flexural rigidities. Models incorporating both surface and subsurface loading yield much higher rigidities. Although the two models may match the observed admittance equally well, only those with both surface and subsurface loading are consistent with the observed pattern of coherence between gravity and topography as a function of wavelength. A new method of analysis shows that surface and subsurface loading are approximately equal in importance in the vicinity of the Kenya rift valley. The flexural rigidity of the East African lithosphere is about 2×1023 N m, or an effective elastic thickness of the plate of 25–30 km. Data from the conterminous United States are consistent with the presence of provinces with a wide range of flexural rigidities, averaging tens of kilometers in effective elastic thickness.

Subsurface loading and estimates of the flexural rigidity of continental lithosphere

SUMMARY Anisotropic inversions of surface wave data show that the variations in vertical shear velocity, pv, and anisotropy of the oceanic upper mantle in the Pacific are much smoother and more systematic functions of the age of the seafloor than has been reported in previous studies. The data used in this analysis are the pure-path results of previous studies on the lateral distribution of fundamental-mode Love and Rayleigh wave phase velocities (Nishimura & Forsyth 1985, 1988). The pure-path models include parameters which describe the variations with age, azimuthal anisotropy and residual depth anomalies. The calculated velocity models of the upper mantle are constrained to vary smoothly with depth and to represent the minimum deviation from an isotropic starting model. Inversions were performed using the method of Tarantola & Valette (1982). The two best resolved parameters of the computed transversely isotropic model are the shear wave velocity terms, fiv and 5. The results indicate that pv above 200 km progressively increases as a function of the age of the seafloor with the pattern qualitatively mimicking isotherms of theoretical thermal cooling models. If one selects the depth to the maximum negative gradient in shear velocity as being the best available indicator of lithospheric thickness, then the thickness increases from about 15-35 km beneath 0-4 Myr old seafloor to 70-110km in the oldest seafloor. The magnitude of the shear wave anisotropy term, 5, rapidly increases in the first 20 Myr until some apparent constant value is reached in the older regions. A more realistic upper mantle structure is calculated using a priori information on the correlation between changes in shear and compressional wave velocities and the expected nature of the anisotropy. The general results are the same as the previous inversion without a priori constraints. Finally, the effect of attenuation is included, the primary result being an overall increase in 6". The maximum change occurs at around 150 km depth, which reduces the velocity contrast between the lithosphere and asthenosphere. It is therefore more difficult to make a distinction between the plate and low-velocity zone when the effect of attenuation is included. An estimate of the azimuthal anisotropic structure is obtained by inverting for the Rayleigh wave cos 2v coefficients using derivatives calculated by the method of Montagner & Nataf (1986). The reference frame used to constrain the azimuthal effect is that of fossil seafloor spreading direction. The results indicate that in regions of the Pacific less than 80 Myr in age, there is significant anisotropy down to 200 km depth. In regions older than 80 Myr, azimuthal anisotropy is confined to the upper SO km. The transverse and azimuthal anisotropy structures can be explained by an oceanic upper mantle containing olivine with different orientations.

/pdf/the-anisotropic-structure-of-the-upper-mantle-in-the-pacific-4fc3os61f9.pdf

Donald W. Forsyth

Papers

On the Relative Importance of the Driving Forces of Plate Motion

An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando Earthquake Sequence

The Early Structural Evolution and Anisotropy of the Oceanic Upper Mantle

Subsurface loading and estimates of the flexural rigidity of continental lithosphere

The anisotropic structure of the upper mantle in the Pacific