Cooperation in organisms, whether bacteria or primates, has been a difficulty for evolutionary theory since Darwin. On the assumption that interactions between pairs of individuals occur on a probabilistic basis, a model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game. Deductions from the model, and the results of a computer tournament show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established. Potential applications include specific aspects of territoriality, mating, and disease.

The Evolution of Cooperation

Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude ( M ), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement

Stable URL:http://links.jstor.org/sici?sici=0036-8075%2819750808%293%3A189%3A4201%3C419%3ACTOAEO%3E2.0.CO%3B2-NScience is currently published by American Association for the Advancement of Science.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/aaas.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgFri Jan 25 16:37:09 2008

https://science.sciencemag.org/content/sci/189/4201/419.full.pdf

Cenozoic Tectonics of Asia: Effects of a Continental Collision: Features of recent continental tectonics in Asia can be interpreted as results of the India-Eurasia collision.

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

A comprehensive study of the observations of seismology provides widely based strong support for the new global tectonics which is founded on the hypotheses of continental drift, sea-floor spreading, transform faults, and underthrusting of the lithosphere at island arcs. Although further developments will be required to explain certain part of the seismological data, at present within the entire field of seismology there appear to be no serious obstacles to the new tectonics. Seismic phenomena are generally explained as the result of interactions and other processes at or near the edges of a few large mobile plates of lithosphere that spread apart at the ocean ridges where new surficial materials arise, slide past one another along the large strike-slip faults, and converge at the island arcs and arc-like structures where surficial materials descend. Study of world seismicity shows that most earthquakes are confined to narrow continuous belts that bound large stable areas. In the zones of divergence and strike-slip motion, the activity is moderate and shallow and consistent with the transform fault hypothesis; in the zones of convergence, activity is normally at shallow depths and includes intermediate and deep shocks that grossly define the present configuration of the down-going slabs of lithosphere. Seismic data on focal mechanisms give the relative direction of motion of adjoining plates of lithosphere throughout the active belts. The focal mechanisms of about a hundred widely distributed shocks give relative motions that agree remarkably well with Le Pichon's simplified model in which relative motions of six large, rigid blocks of lithosphere covering the entire earth were determined from magnetic and topographic data associated with the zones of divergence. In the zones of convergence the seismic data provide the only geophysical information on such movements.

Two principal types of mechanisms are found for shallow earthquakes in island arcs: The extremely active zone of seismicity under the inner margin of the ocean trench is characterized by a predominance of thrust faulting, which is interpreted as the relative motion of two converging plates of lithosphere; a less active zone in the trench and on the outer wall of the trench is characterized by normal faulting and is thought to be a surficial manifestation of the abrupt bending of the down-going slab of lithosphere. Graben-like structures along the outer walls of trenches may provide a mechanism for including and transporting sediments to depth in quantities that may be very significant petrologically. Large volumes of sediments beneath the inner slopes of many trenches may correspond, at least in part, to sediments scraped from the crust and deformed in the thrusting.

Simple underthrusting typical of the main zone of shallow earthquakes in island arcs does not, in general, persist at great depth. The most striking regularity in the mechanisms of intermediate and deep earthquakes in several arcs is the tendency of the compressional axis to parallel the local dip of the seismic zone. These events appear to reflect stresses in the relatively strong slab of down-going lithosphere, whereas shearing deformations parallel to the motion of the slab are presumably accommodated by flow or creep in the adjoining ductile parts of the mantle. Several different methods yield average rates of underthrusting as high as 5 to 15 cm/yr for some of the more active arcs. These rates suggest that temperatures low enough to permit dehydration of hydrous minerals and hence shear fracture may persist even to depths of 700 km. The thickness of the seismic zone in a part of the Tonga arc where very precise hypocentral locations are available is less than about 20 km for a wide range of depths. Lateral variations in thickness of the lithosphere seem to occur, and in some areas the lithosphere may not include a significant thickness of the uppermost mantle.

The lengths of the deep seismic zones appear to be a measure of the amount of under thrusting during about the last 10 m.y. Hence, these lengths constitute another ‘yardstick’ for investigations of global tectonics. The presence of volcanism, the generation of many tsunamis (seismic sea waves), and the frequency of occurrence of large earthquakes also seem to be related to underthrusting or rates of underthrusting in island arcs. Many island arcs exhibit a secondary maximum in activity which varies considerably in depth among the various arcs. These depths appear, however, to correlate with the rate of underthrusting, and the deep maxima appear to be located near the leading (bottom) part of the down-going slab. In some cases the down-going plates appear to be contorted, possibly because they are encountering a more resistant layer in the mantle. The interaction of plates of lithosphere appears to be more complex when all the plates involved are continents or pieces of continents than when at least one plate is an oceanic plate. The new global tectonics suggests new approaches to a variety of topics in seismology including earthquake prediction, the detection and accurate location of seismic events, and the general problem of earth structure.

Seismology and the new global tectonics

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

Earthquake Prediction: A Physical Basis

Seismic data strongly support recent theories of tectonics in which large plates of lithosphere move coherently with respect to one another as nearly rigid bodies, spreading apart at ocean ridges, sliding past one another at transform faults, and underthrusting at island arcs. Boundaries between adjacent plates of lithosphere are defined by belts of high seismic activity. Redetermination of more than 600 hypocenters in the Middle America region and previous studies in the Galapagos and Caribbean regions define the boundaries of two relatively small, nearly aseismic plates in the region of interest. The first, the Cocos plate, is bordered by the East Pacific rise, the Galapagos rift zone, the north-trending Panama fracture zone near 82° W., and the Middle America arc; the second, the Caribbean plate, underlies the Caribbean Sea and is bounded by the Middle America arc, the Cayman trough, the West Indies arc, and the seismic zone through northern South America.

Focal mechanisms of 70 earthquakes in these regions were determined to ascertain the relative motion of these two plates with respect to the surrounding regions or plates. The results show underthrusting of the Cocos plate beneath Mexico and Guatemala in a northeasterly direction and beneath the rest of Central America in a more north-northeasterly direction. The Cocos plate is spreading away from the rest of the Pacific floor at the East Pacific rise and at the Galapagos rift zone. Motion is right-lateral strike-slip along the Panama fracture zone, a transform fault connecting the Galapagos rift zone and the Middle America arc. At the same time, the Caribbean plate is moving easterly with respect to the Americas plate, which is here taken to include both North and South America and the western Atlantic. Left-lateral strike-slip motion along steeply dipping fault planes is observed on the Cayman trough. The Americas plate is underthrusting the Caribbean in a westerly direction at the Lesser Antilles and near Puerto Rico. Unlike the Lesser Antilles, however, motion at present is not perpendicular to the Puerto Rico trench but instead is almost parallel to the trench along nearly horizontal fault planes.

Computations of rates of motion indicate that underthrusting is at a higher rate in southeastern Mexico and Guatemala than in western Mexico and that the Caribbean is moving at a lower rate relative to North America than is the Cocos plate.

Tectonics of the Caribbean and Middle America Regions from Focal Mechanisms and Seismicity

The mechanisms of 17 earthquakes on the mid-oceanic ridges and their continental extensions were investigated using data from the World-Wide Standardized Seismograph Network of the U. S. Coast and Geodetic Survey and from other long-period seismograph instruments. Mechanism solutions of high precision can now be obtained for a large number of earthquakes with magnitudes as small as 6 in many areas of the world. Less than 1% of the data used in this study are inconsistent with a quadrant distribution of first motions of the phases P and PKP; in many previous investigations 15 to 20% of the data were often inconsistent with the published solutions. Ten of the earthquakes that were studied occurred on fracture zones that intersect the crest of the mid-oceanic ridge. The mechanism of each of the shocks that is located on a fracture zone is characterized by a predominance of strike-slip motion on a steeply dipping plane; the strike of one of the nodal planes for P waves is nearly coincident with the strike of the fracture zone. The sense of strike-slip motion in each of the ten solutions is in agreement with that predicted for transform faults; it is opposite to that expected for a simple offset of the ridge crest along the various fracture zones. The spatial distribution of earthquakes along fracture zones also seems to rule out the hypothesis of simple offset. Two well documented solutions for earthquakes that are located on the mid-Atlantic ridge but that do not appear to be located on fracture zones are characterized by a predominance of normal faulting. The mechanisms of four earthquakes on extensions of the mid-oceanic ridge system—one near northern Siberia and three in East Africa—are also characterized by a predominance of normal faulting. The inferred axes of maximum tension for these six events are approximately perpendicular to the strike of the mid-oceanic ridge system. The results are in agreement with hypotheses of sea-floor growth at the crest of the mid-oceanic ridge system.

Mechanism of earthquakes and nature of faulting on the mid-oceanic ridges

We compile a worldwide catalog of shallow (depth < 70 km) and large ( Ms ≥ 7) earthquakes recorded between 1900 and 1989. The catalog is shown to be complete and uniform at the 20-sec surface-wave magnitude Ms ≥ 7.0. We base our catalog on those of Abe (1981, 1984) and Abe and Noguchi (1983a, b) for events with Ms ≥ 7.0. Those catalogs, however, are not homogeneous in seismicity rates for the entire 90-year period. We assume that global rates of seismicity are constant on a time scale of decades and most inhomogeneities arise from changes in instrumentation and/or reporting. We correct the magnitudes to produce a homogeneous catalog. The catalog is accompanied by a reference list for all the events with seismic moment determined at periods longer than 20 sec. Using these seismic moments for great and giant earthquakes and a moment-magnitude relationship for smaller events, we produce a seismic moment catalog for large earthquakes from 1900 to 1989. The catalog is used to study the distribution of moment released worldwide. Although we assumed a constant rate of seismicity on a global basis, the rate of moment release has not been constant for the 90-year period because the latter is dominated by the few largest earthquakes. We find that the seismic moment released at subduction zones during this century constitutes 90% of all the moment released by large, shallow earthquakes on a global basis. The seismic moment released in the largest event that occurred during this century, the 1960 southern Chile earthquake, represents about 30 to 45% of the total moment released from 1900 through 1989. A frequency-size distribution of earthquakes with seismic moment yields an average slope ( b value) that changes from 1.04 for magnitudes between 7.0 and 7.5 to b = 1.51 for magnitudes between 7.6 and 8.0. This change in the b value is attributed to different scaling relationships between bounded (large) and unbounded (small) earthquakes. Thus, the earthquake process does have a characteristic length scale that is set by the downdip width over which rupture in earthquakes can occur. That width is typically greater for thrust events at subduction zones than for earthquakes along transform faults and other tectonic environments.

Lynn R. Sykes

Papers

Seismology and the new global tectonics

Earthquake Prediction: A Physical Basis

Tectonics of the Caribbean and Middle America Regions from Focal Mechanisms and Seismicity

Mechanism of earthquakes and nature of faulting on the mid-oceanic ridges

Seismic moment catalog of large shallow earthquakes, 1900 to 1989