Distribution of Mantle Up-welling Determined from Plate Motions: A Case for Large-scale Bénard Convection

—?The number and geometric distribution of putative mantle up-welling centers and the associated convection cell boundaries are determined from the lithospheric plate motions as given by the 14 Euler poles of the observational NUVEL model. For an assumed distribution of up-welling centers (called “cell-cores”) the corresponding cell boundaries are constructed by a Voronoi division of the spherical surface; the resulting polygons are called “Bénard cells.” By assuming the flow-kinematics within a cell, the viscous coupling between the flow and the plates is estimated, and the Euler poles for the plates are computed under the assumption of zero-net-torque. The positions of the cell-cores are optimized for the HS2-NUVEL1 Euler poles by a method of successive approximation (“subplex”); convergence to one of many local minima occurred typically after ～20,000 iterations. Cell-cores associated with the fourteen HS2-NUVEL1 Euler poles converge to a relatively small number of locations (8 to 10, depending on interpretation), irrespective of the number of convection cells submitted for optimized distribution (from 6 to 50). These locations are correlated with low seismic propagation velocities in tomography, uniformly occur within hotspot provinces, and may specifically be associated with the Hawaiian, Iceland, Reunion/Kerguelen (Indian Ocean), Easter Island, Melanesia/Society Islands (South Pacific), Azores/Cape Verde/Canary Islands, Tristan da Cunha (South Atlantic), Balleny Islands, and possibly Yellowstone hotspots. It is shown that arbitrary Euler poles cannot occur in association with mantle Bénard convection, irrespective of the number and the distribution of convection cells. Nevertheless, eight of the observational Euler poles – including the five that are accurately determined in HS2-NUVEL1 (Australia, Cocos, Juan de Fuca, Pacific, and Philippine) – are “Bénard-valid” (i.e., can be explained by our Bénard model). Five of the remaining six observational poles must be relocated within their error-ellipses to become Bénard-valid; the Eurasia pole alone appears to be in error by ～115°, and may actually lie near 40°N, 154°E. The collective results strongly suggest Bénard-like mantle convection cells, and that basal shear tractions are the primary factor in determining the directions of the plate motions as given by the Euler poles. The magnitudes of the computed Euler vectors show, however, that basal shear cannot be the exclusive driving force of plate tectonics, and suggest force contributions (of comparable magnitude for perhaps half of the plates) from the lithosphere itself, specifically subducting slab-pull and (continental) collision drag, which are provisionally evaluated. The relationship of the putative mantle Bénard polygons to dynamic chaos and turbulent flow is discussed.     

Plate-kinematic Constraints from Mantle Bénard Convection

General kinematic implications for plate tectonics are determined for Rayleigh-Bénard convection of the mantle. The continuum of all possible configurations of Bénard polygons is probed by large random samples of global configurations (450,000 to 54,000,000), for each of which the Euler poles are determined on the basis of viscous coupling across the asthenosphere. Two computationally related methods lead first, to Euler pole restrictions for fourteen plates, and second, to restrictions on the Bénard cell configuration. Result No. 1: Euler poles occur in global preference-patterns, which are determined exclusively by the shape of the plate. The observational HS2-NUVEL1 model poles occur near regions preferred by Bénard convection (Eurasia excluded); the agreement is best for the most accurate observational poles. Result No. 2: Seven specific mantle Bénard cells are indicated by present-day plate motions. The upwelling centers correlate with hotspot domains; the major global subduction zones correlate with Bénard model downwelling. This result is independent of the Euler pole accuracy used in its determination, and is consistent with the distribution of low seismic p-wave propagation velocities determined by tomography, and with shear-wave splitting analysis within the asthenosphere. Conclusions: The results suggest that the bulk mantle is divided into less than ten Bénard convection cells globally (cf., Fohlmeister and Renka, 2002), each of which extends from the asthenosphere to the core-mantle boundary; turbulent flow, and other perturbations of the Bénard kinematics appear to be limited. These primally poloidal flow kinematics provide basal shear forces as a major component in driving plate tectonics, and are specifically configured for the directions of plate motions. The Bénard model is incomplete without a dynamic contribution from the lithosphere, which represents a separate convection layer of the distinct polar kinematics of rigid plates. The complete hybrid mechanism for driving plate tectonics includes lithospheric buoyancy dynamics, specifically from the subducting Pacific plate slabs to compensate for plate-slowing due to the back-flow sector of the Hawaiian convection cell, and collision-drag dynamics principally for smaller plates or continental margins.     

Intraplate seismicity of the Pacific Basin, 1913–1988

We establish here a comprehensive database of intraplate seismicity in the Pacific Basin. Relocation and analysis of 894 earthquakes yield 403 reliable intraplate earthquakes during 1913–1988. These numbers do not include earthquake swarms, which account for another 838 events. Most of the remainder (304 events) are actually plate boundary earthquakes that have been erroneously located in intraplate regions. A significant number occur in recent years when location capabilities should have guarded against this situation. Relocations involve a careful linear inversion ofP andS arrivals, accompanied by a Monte Carlo statistical analysis. We have also attentively removed the high number of clerical errors and nuclear tests that exist in epicenter bulletins.A geographical examination of the relocated epicenters reveals several striking features. There are three NW-SE lineaments north of the Fiji Plateau and in Micronesia; diffuse seismicity and incompatible focal mechanisms argue against the southernmost, discussed byOkal et al. (1986) andKroenke andWalker (1986), as the simple relocation of the Solomon trench to the North. Besides another striking lineament, along the 130°W meridian, there is also a strong correlation between seismicity and bathymetry in certain parts of the Basin. In the Eastcentral Pacific and Nazca plates there are many epicenters on fracture zones and fossil spreading ridges, and hot spot traces like the Louisville, Nazca and Cocos Ridges also display seismicity.     

Forecasting thunderstorms and hailstorms by means of temperature and dew-point anomalies on a time-section chart

Summary Vertical time-section charts for temperature and dew-point anomalies have been plotted. The temperature anomaly decreasing upwards give convection according to Byers and Braham [1]²). The coincidence of temperature anomalies with central minimum and of dew-point anomalies with central maximum, or of upward decreasing trend in temperature anomalies and upward increasing trend in dewpoint anomalies, correspond to the convection associated with greater moisture influx, thus representing the case of a thunderstorm. The mentioned anomalies have been found to occur in such a way that cells with central maximum are followed by those with central minimum, and vice versa. Thus simultaneous occurrences of upward decreasing anomalies in temperature, i.e. occurrence of cells with central minimum of temperature, and upward increasing anomalies in dew-point, i.e. occurrence of cells with central maximum, can be observed at any station, hence the occurrences of thunderstorms at that station can be predicted. Moreover, the two kinds of anomalies can give the idea (along with that of convection, of coming of the synoptic situation having dry air aloft and moist air below, which is the ideal condition) for the occurrence of a hailstorm (Fawbush andMiller [2]).     

Upper mantle low anisotropy channels below the Pacific Plate

A new 3D anisotropic model has been obtained at a global scale by using a massive dataset of seismic surface waves. Though seismic heterogeneities are usually interpreted in terms of heterogeneous temperature field, a large part of lateral variations are also induced by seismic anisotropy of upper mantle minerals. New insight into convection processes can be gained by taking seismic anisotropy into account in the inversion procedure. The model is best resolved in the Pacific Plate, the largest and the most active tectonic plate. Superimposed on the large-scale radial (ξ parameter) and azimuthal anisotropy (of V_SV velocity) within and below the lithosphere, correlated with present or past Pacific Plate motions, are smaller-scale (<1000 km) lateral variations of anisotropy not predicted by plate tectonics. Channels of low anisotropy down to a depth of 200 km (hereafter referred to as LAC) are observed and are the best resolved anomalies: one east-west channel between Easter Island and the Tonga-Kermadec subduction zones (observed on both radial and azimuthal anisotropies) and a second one (only observed on azimuthal anisotropy) extending from the south-west Pacific up to south-east Hawaii, and passing through the Polynesia hotspot group for plate older than about 40 Ma. These features provide strong constraints on the decoupling between the plate and asthenosphere. They are presumably related to cracking within the Pacific Plate and/or to secondary convection below the rigid lithosphere, predicted by numerical and analog experiments. The existence and location of these LACs might be related to the current active volcanoes and hotspots (possibly plumes) in the Central Pacific. LACs, which are dividing the Pacific Plate into smaller units, might indicate a future reorganization of plates with ridge migrations in the Pacific Ocean.     

Least square criterion for isostasy

Summary Least square criterion has been introduced to specify the order of isostatic compensation of mountains. The hydrostatic stability of the mountains is of basic significance in plate tectonics. However different concepts of isostasy differ in the evaluation of its order. An elegant and rapid technique is developed which extends the symmetric matrix method of root estimation byNegi andGarde [1]³) to provide a stability test through the mathematical expectation of the root increment. Application is illustrated for Rocky Mountains, United States.     

On the geodynamic setting of kimberlite genesis

The emplacement of kimberlites in the North American and African continents since the early Palaeozoic appears to have occurred during periods of relatively slow motion of these continents. The distribution of kimberlites in time may reflect the global pattern of convection, which forces individual plates to move faster or slower at different times. Two-dimensional numerical experiments on a convecting layer with a moving upper boundary show two different regimes: in the first, when the upper boundary velocity is high, heat is transferred by the large-scale circulation and in the second, when the upper boundary velocity is lower, heat is predominantly transferred by thermal plumes rising from the lower boundary layer. For a reasonable mantle solidus, this second regime can give rise to partial melting beneath the moving plate, far from the plate boundaries. The transition between these modes takes place over a small range of plate velocities; for a Rayleigh number of 10⁶ it occurs around 20 mm yr^?1. We suggest that the generation of kimberlite magmas may result from thermal plumes incident on the base of a slowly moving plate.     

Quantitative estimates of interplate coupling inferred from outer rise earthquakes

Interplate coupling plays an important role in the seismogenesis of great interplate earthquakes at subduction zones. The spatial and temporal variations of such coupling control the patterns of subduction zone seismicity. We calculate stresses in the outer rise based on a model of oceanic plate bending and coupling at the interplate contact, to quantitatively estimate the degree of interplate coupling for the Tonga, New Hebrides, Kurile, Kamchatka, and Marianas subduction zones. Depths and focal mechanisms of outer rise earthquakes are used to constrain the stress models. We perform waveform modeling of body waves from the GDSN network to obtain reliable focal depth estimates for 24 outer rise earthquakes. A propagator matrix technique is used to calculate outer rise stresses in a bending 2-D elastic plate floating on a weak mantle. The modeling of normal and tangential loads simulates the total vertical and shear forces acting on the subducting plate. We estimate the interplate coupling by searching for an optimal tangential load at the plate interface that causes the corresponding stress regime within the plate to best fit the earthquake mechanisms in depth and location.We find the estimated mean tangential load over 125–200 km width ranging between 166 and 671 bars for Tonga, the New Hebrides, the Kuriles, and Kamchatka. This magnitude of the coupling stress is generally compatible with the predicted shear stress at the plate contact from thermal-mechanical plate models byMolnar andEngland (1990), andVan den Buekel andWortel (1988). The estimated tectonic coupling,F _tc , is on the order of 10¹²–10¹³ N/m for all the subduction zones.F _tc for Tonga and New Hebrides is about twice as high as in the Kurile and Kamchatka arcs. The corresponding earthquake coupling forceF _ec appears to be 1–10% of the tectonic coupling from our estimates. There seems to be no definitive correlation of the degree of seismic coupling with the estimated tectonic coupling. We find that outer rise earthquakes in the Marianas can be modeled using zero tangential load.     

Free convection along a non-uniformly heated vertical plate with a variable transverse magnetic field

Summary In this article, we have solved the problem of natural convection along a vertical plate with variable temperature and a transverse non-uniform magnetic field. It also represents a unified analysis of the works of other including the present author, on natural convection with or without transverse magnetic field, and with uniform or non-uniform plate temperature.The author is indebted to Prof.K. B. Ranger, Department of Mathematics, for his continuous and active interest in my research work. I am also grateful to him for offering me a fellowship from his N.R.C. (Canada) research fund.     

平均热点参考基准的建立和岩石圈西向漂移的研究

对于大地测量应用来说,目前IERS机构在定义地球参考系时推荐采用岩石圈无整体旋转(No-Net-Rotation-NNR)约束条件,然而对于地球物理应用来说,相对于NNR参考基准的绝对板块运动数据可能会对地幔对流等研究结果产生误导.考虑到热点的运动,提出建立平均热点(MHS-Medial HotSpot)参考基准的方法,给出建立该基准的约束准则,分别以地学模型NNR-NUVEL1A和实测模型ITRF2005VEL为基础,建立了平均热点参考基准MHS-NUVEL1A和MHS-ITRF2005,并与其它基于热点的绝对板块运动模型进行了比较和分析;讨论了岩石圈的西向漂移,给出了岩石圈相对于下地幔整体旋转的更精确的定量估计,即基于实测的热点参考架MHS-ITRF2005和地学模型NNR-NUVEL1A之间的整体旋转为0.26°/Ma,旋转极在(50°S, 62°E),这与由板块的受力模型给出的岩石圈的整体旋转的旋转极很接近,旋转速率大致快了10%.     

Mantle flow with existence of plates and generation of the toroidal field

The observed plate velocities contain two types of motions. The poloidal component is related to the formation of ridges and subduction zones and the toroidal field expresses the shearing of surface plates. One very important consideration in modeling flow in the earth's mantle is the existence and motion of the lithospheric plates. The motion of plates represents a large-scale circulation with strong viscous coupling to the mantle underneath. The mantle flow probably is neither a purely free convection driven by buoyancy forces due to nonadiabatic temperature gradients in the mantle nor a forced convection generated by boundary forces, but a mixed convection that combines the effects of boundary and buoyancy forces. We present, in this paper, the mixed convection model resulting in a surface velocity field that contains both the observed poloidal and toroidal components.     

Global vorticity budget over the tropics and subtropics at 200-mb during northern hemisphere summer

The large-scale terms in the vorticity equation are evaluated usingKrishnamurti's (1971a, b) summer mean winds at 200 mb for a global belt from 25°S to 45°N. The production of vorticity by the divergent wind field is found to be imbalanced over all of the tropical and subtropical belt. As a result there is a requirement for a sub-grid scale (space or time) mechanism which removes negative vorticity from the regions of strong divergence (Tibetan and Mexican highlands) and removes positive vorticity from the regions of strong convergence (mid-oceanic troughs) at 200 mb during northern summer at a rate of approximately 4×10^–10 sec^–2. As suggested byHolton andColton (1972), in regions of strong and persistent convection, such as the Tibetan Plateau, deep cumulus clouds can account for this transport. However, the mechanism for removing positive vorticity in the vicinity of the upper tropospheric mid-oceanic troughs is still an intriguing and open question.On leave-of-absence at the National Science Foundation, Climate Dynamics Research Section.     

Migration of historical earthquakes in California

Most large earthquakes of magnitude 6.0 in California during 1852–1987 appear to show a southeast-to-northwest tendency of epicenter migration. This finding is consistent with earlier findings ofSavage (1971) for a relatively few large earthquakes along the west coast of North America, and ofWood andAllen (1973) for smaller events along the San Andreas fault in central California. The average speed of migration is approximately 130 km/yr, which is within the range of speeds observed for other major seismic zones in the world. The epicenter migration in California may be the result of some small but broad-scaled episodic strain changes associated with creep waves induced by magma injections at the East Pacific Rise and propagating northwestwardly along a broad transform boundary between the Pacific and North American plates at subseismogenic depths as proposed bySavage (1971).     

A new ultrasonic interferometer for the determination of equation of state parameters of sub-millimeter single crystals

A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 10⁵ in travel time measurements is achievable in single crystals (thickness of 200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities.The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting andSpetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.     

Predicted near-field ground motion for dynamic stress-drop models

We propose a finite difference method, using a hexagonal grid, to compute displacements (stresses, velocities, accelerations) in the near-field of a 2-D in-plane stress-drop crack, in both whole space (constant stress-drop) and half-space (depth-dependent stress-drop). To exercise the method, the stress field distribution is evaluated for both fundamental 2-D shear cracks, anti-plane. In order to test the method's reliability, the results are compared with some analytical and numerical solutions available in the literature (Kostrov, 1964;Virieux andMadariaga, 1982). For the in-plane source, the results emphasize that the method can resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. Synthetic motions are computed on the fault, but also in an infinite medium and at the free surface. The rather complex waveforms generated in the near-field, even by simple sources, emphasize the contribution of all wave terms (near, intermediate and far-field) to the motion. The presence of near-field and the numerical procedure explain the significant low frequency content of the computed seismograms. The set of treated problems proves the method is stable and accurate.     

Gravity anomaly and density structure of the San Andreas fault zone

A densely spaced gravity survey across the San andreas fault zone was conducted near Bear Valley, about 180 km south of San Francisco, along a cross-section where a detailed seismic reflection profile was previously made byMcEvilly (1981). WithFeng andMcEvilly's velocity structure (1983) of the fault zone at this cross-section as a constraint, the density structure of the fault zone is obtained through inversion of the gravity data by a method used byParker (1973) andOldenburg (1974). Although the resulting density picture cannot be unique, it is better constrained and contains more detailed information about the structure of the fault than was previously possible. The most striking feature of the resulting density structure is a deeply seated tongue of low-density material within the fault zone, probably representing a wedge of fault gouge between the two moving plates, which projects from the surface to the base of the seismogenic zone. From reasonable assumptions concerning the density of the solid grains and the state of saturation of the fault zone the average porosity of this low-density fault gouge is estimated as about 12%. Stress-induced cracks are not expected to create so much porosity under the pressures in the deep fault zone. Large-scaled removal of fault-zone material by hydrothermal alteration, dissolution, and subsequent fluid transport may have occurred to produce this pronounced density deficiency. In addition, a broad, funnel-shaped belt of low density appears about the upper part of the fault zone, which probably represents a belt of extensively shattered wall rocks.     

地幔对流与岩石层板块的相互耦合及影响──（Ⅱ）地幔混合对流理论及其应用

观测到的板块运动包含两种能量分布几乎相等的运动形态：极型场和环型场．纯粹的由热驱动的地幔自由对流不能预期和解释环型运动的产生．本文提出地幔混合对流理论，既考虑了热驱动的自由对流，也考虑了由板块自身激发的强迫对流．根据板块处于动力学平衡状态的观测事实，建立了相应的模型．数值结果表明，根据混合对流模型所预期的板块速度场，既能产生极型场，也能产生环型场，而且在空间分布特征及功率谱分布上与观测资料符合相当好．地幔物质的上升流动基本和洋脊对应，而下降流动和俯冲带对应．     

地幔对流与岩石层板块的相互耦合及影响──（Ⅱ）地幔混合对流理论及其应用

观测到的板块运动包含两种能量分布几乎相等的运动形态：极型场和环型场．纯粹的由热驱动的地幔自由对流不能预期和解释环型运动的产生．本文提出地幔混合对流理论，既考虑了热驱动的自由对流，也考虑了由板块自身激发的强迫对流．根据板块处于动力学平衡状态的观测事实，建立了相应的模型．数值结果表明，根据混合对流模型所预期的板块速度场，既能产生极型场，也能产生环型场，而且在空间分布特征及功率谱分布上与观测资料符合相当好．地幔物质的上升流动基本和洋脊对应，而下降流动和俯冲带对应．     

Mineralogy and physical nature of clay gouge

Fault gouges have been observed in the surface outcrops, in shallow excavations, and in deep (300 meters below the surface) tunnels and mines in fault zones. The 2-microns fractions in these fault gouges may compose a few percent to more than fifty percent of the total mass in the outcrops, and the mineralogy of the 2-microns fractions consists of a variety of clays (the common ones are montmorillonite, illite, kaolinite, chlorite, vermiculite and mixed-layer clays) and some quartz, feldspars, etc.Although we cannot yet conclude directly from the studies of gouges that similar gouges exist at depths where many large shallow earthquakes are generated, there is a strong possibility that they do, based on (1) available equilibrium data on various clays — for example, kaolinite has been found to exist at 4 kb and 375°C (±15°C) (Thompson, 1970) and montmorillonite + kaolite has been found to exist at 450°C and 4 kb (Velde, 1969); (2) the compatibility of laboratory velocity data in gouge (Wang et al., 1977) with those in a model for central California (Healy andPeake, 1975); (3) the capability of clays to undergo sudden earthquake-like displacements (Summers andByerlee, 1977); (4) the petrology of intrafault cataclastic rocks in old fault zones (Kasza, 1977); and (5) the compatibility of gouge mineralogy with the mineralogy of hydrothermal clay deposits.If clay gouges are indeed significant components of the fault zone at depth, then the mechanical properties of clays under confining pressures up to 4 kb are important in the behavior of faults. Very few experiments have been performed under such high pressures. But from the physical makeup of clays, we can infer that (1) the range of possible behavior includes stable sliding with vermiculite and montmorillonite (asByerlee andSummers, 1977, have proven) to stick-slip-like behavior with kaolinite, chlorite, etc.; (2) the absence or presence of water will greatly affect the strengths of gouges — it is possible that water may reduce the strength of gouge to a fairly small value.