Coherency of rupture and seismic spectrum

In considering the seismic spectrum, one of the methods to incorporate irregularity of fault motion statistically is to introduce the concept of coherency of fracture. In a classic paper,Aki (1967) investigated the scaling law of seismic spectrum on the basis of a statistical model in which an exponentially decaying function is fitted to the autocorrelation function of the dislocation velocity. It is found, however, thatAki's model does not necessarily express irregular fault motion, but corresponds to a smooth dislocation. We show that an analytical function of dislocation velocity gives the same autocorrelation function and the same seismic spectrum as those ofAki's model. In actual fault motion, there is considerable evidence which indicates that the dislocation is not continuous and smooth over the whole fault plane, but is often segmented in several parts. In order to take into consideration this feature we introduce a generalized autocorrelation function of the dislocation velocity in which many coherent fractures smaller than the size of the fault dimension are included. It is shown that the more small-scale coherent fractures, the larger the seismic wave energy in the high frequency range.Kanamori andAllen (1986) showed that a large ratio of seismic wave energy relative to the seismic moment means a large effective stress drop. On the other hand, it is well known that when a fault plane is segmented in several parts, stress drop becomes large (e.g.,Madariaga, 1979;Rudnicki andKanamori, 1981). These two results are fused in our model, because we find that large seismic wave energy is obtained when the fault motion includes small-scale fractures.Kanamori andAllen (1986) also showed that there is a tendency for earthquakes with long repeat times to have a large effective stress drop. Our model implies that a fracture corresponding to earthquakes with long recurrence intervals is more complex, and the strength is large, as also suggested byCao andAki (1986) using a numerical simulation. It should be noted that to the zeroth order, an approximate scaling relation is observed among earthquakes, which means that a large earthquake consists of a relatively large-scale coherent fracture. This fact seems to suggest that the condition of occurrence of a large earthquake is related to the maturing of a source region in which a large coherent fracture becomes feasible.     

Seismic excitation of the polar motion, 1977–1993

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed byChao andGross (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0–1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards 140°E, away from the actually observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field byChao andGross (1987), manifests some geodynamic behavior yet to be explored.     

Grundschicht und Nullschicht der Atmosphäre

Zusammenfassung NachdemSchneider-Carius die von ihm in mehreren Untersuchungen behandelte und von ihm so bezeichnete «Grundschicht» als das Hauptausgleichniveau für die Druckgegensätze zwischen Hoch und Tief in den unteren Luftschichten nachgewiesen hat, entstand naturgemäß die Frage, wie und in welcher Höhensicht der notwendige Massenfluß vom Tief zum Hoch erfolgt. Ohne denselben würden sich die Druckgebilde wegen der ageostrophischen Windkomponente vom Hoch zum Tief in der Grundschicht binnen kürzester Zeit auflösen.H. Faust fand diese Schicht über Mitteleuropa in 10 km Höhe. Sie ist identisch mit dem Sitz des hochtroposphärischen Windmaximums und weist das Maximum des ageostrophischen Massenflusses vom Tief zum Hoch auf. Da in ihr die für das Wettergeschehen so fundamental wichtigen Vertikalbewegungen Null sind, nannteFaust die Schicht «Nullschicht». In der Grundschicht und der Nullschicht sind somit zwei atmosphärische Schichten gefunden, die in polarer Wechselwirkung miteinander für die Dynamik der Wettervorgänge von entscheidender Bedeutung sind.

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Summary Especially whenSchneider-Carius had shown in several papers the ground layer to be the main levelling layer of pressure contrasts, the question arose where the seat of mass transport from low to high pressure is located. ThenFaust found a layer 10 kms above Central Europe, where vertical motion in highreaching cyclones and anticyclones averages zero. Because of the fundamental significance of vertical motion, he called it the «zero layer». This zero layer, which is identical with the wind maximum in the upper troposphere, turned out to be the principal seat of ageostrophic mass transport from low to high pressure. Also, the angle between true and geostrophic wind (the ageostrophic component) has its maximum in the zero layer. As the processes in the zero layer produce and/or increase pressure contrasts, it is the direct counterpart of the ground layer. It is shown that both layers are exercising reciprocal effects upon each other, with action in one layer producing the appropriate reaction in the other layer. As both layers are the principal seat of ageostrophic mass transport between areas of high and low pressure, their mutual action proves to be of basic importance for the dynamics of the whole weather trend.

     

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.     

Some hydrodynamic problems for a nepheloid zone

Summary A layer of a few hundred meters thickness with suspended matter (a nepheloid zone) was discovered byEwing andThorndike [4]³⁾ near the bottom on the continental slope of the North Atlantic. A downward pressure gradient is produced in this layer due to increment of water density with suspensoid. When only the Coriolis force balances with this pressure gradient, a bottom nepheloid current flows southwestward parallel to the depth contours with a velocity of about 10 (cm/sec) for a slope of one degree. The pressure gradient for fluid with locally variable density above a sloping bottom is treated and an extra term due to density gradient along the slope is derived. The vertical profiles of the nepheloid current with an effect on the vertical eddy viscosity are computed. Two kinds of vertical distributions of eddy viscosity are determined from the observed nepheloid distributions and used in the calculations: constant but different values at two layers and those increasing with height. The effect of the change of density along the bottom is treated by introducing dimensionless variables. Rossby number of the nepheloid current becomes about 10^–2 indicating inertia terms to be negligible. Rossby number of turbidity currents ranges from 2 (in a decaying area) to 5 (developing area), suggesting that inertia terms are more important than Coriolis terms. The trajectories of turbidity currents are computed from motion of a mass of mud under the Coriolis force and friction, and the results are applied to those inferred byHand andEmery [6] in the San Diego Through off California.LGO Contribution Number 925.     

The longitudinal proper motion of sunspots and the solar rotation rate

Summary The longitudinal proper motion of sunspot groups has been shown to be a function of their size and relative extension in longitude. Two theories are proposed to explain these effects, which theories assume that the wind circulation of the spots and the wind field surrounding the spots are intimately connected, and dynamically interact. The retardation in the motion of large spot groups is hypothesized to be due to the effect of the latitudinal variation of the Coriolis parameter (on a rotating spherical body) and an assumed vortical circulation around the spots. The more rapid longitudinal motion of extended spot groups is suggested to be the result of the preferential occurrence and development of such groups in regions of above-average horizontal wind and wind shear. If these theories are essentially correct, the real solar rotation rate—i.e., the longitude- and time-averaged fluid motion field—should be derived from the motions of small spot groups, and is 1% to 11/2% higher than the usually accepted rate whichNewton andNunn derived.     

Focal mechanism study of South American earthquakes

Summary This study presents the focal mechanism solutions of four South American earth-quakes. These solutions have been determined using the sign of the initial motion ofP wave, and the polarization angle ofS wave. A regional study of the strike of the fault plane, the direction of motion, and the regional stress pattern has been made in which the focal mechanism solutions determined byStauder andBollinger were also used.     

Über die Bindung der Aerosolteilchen auf der Oberfläche der Wolkenelemente

Summary The importance ofStefan's flow by collection of insoluble aerosol particles on the surface of the evaporating droplets by condensation has recently been emphasized mainly in connection with the possible wash-out mechanism in the atmosphere. A simple theory is deduced for the collection efficiency of insoluble particles on droplets under theStefan's force and a comparision is made with the binding of aerosol particles byBrown's motion and microturbulence of air flow. In general we must take in account the influence ofStefan's flow by calculating the wash-out efficiency.     

Correlation between terrestrial heat flow and thermal conductivity

Summary The significant correlation coefficient between the terrestial heat flow and thermal conductivity computed from the continental heat flow data byHorai andNur [1]²) may be explained as a natural consequence of terrestrial heat flow through a random medium. The theory predicts a value of 0.40 for the correlation coefficient. A simple statistical test shows that the majority of the computed coefficients belong to the statistical population whose mean is equal to the theoretical correlation coefficient. There are, however, a few observations of unsually high correlation coefficient which cannot be explained by the above hypothesis.     

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.     

On the energy flux of Hide waves

Summary There are two ways to define the energy flux for Hide waves, one from its equations of motion and the other by multiplying its mean energy density by group velocity and these lead to different results FollowingLonguet-Higgins we point out that this is due to certain arbitrariness in the definition of the energy flux and that their difference is just a solenoidal vector.Dedicated to the memory of Dr.V. A. Wynne, 1945–1972.     

Non-adiabatic motion of charged particles traversing a weak magnetic field: Pitch angle scattering

Summary A charged particle moves with velocityv in a constant non-uniform magnetic fieldH, spiralling with Larmor radiusR. IfR is small compared with the scale lengthL of the field, the magnetic moment associated with the Larmor motion of the particle is nearly constant. Consequently , the (pitch) angle betweenv andH, varies as arcsinH ^1/2. Hence in such adiabatic motion is approximately the same at points on the path whereH has the same value. But the magnetic moment and the pitch angle may differ materially at two such points, each in the region whereR/L is small, if between them the particle traverses a region whereR/L is not small. This region of non-adiabatic motion scatters the pitch angles.Such scattering is investigated for regions of weak field (R large), with and without the presence of a neutral line along whichH=0. Either type of region, it is found, can scatter the pitch angles. This gives support to the theory proposed byAkasofu andChapman to explain why auroral arcs and bands are very thin.The scattering here examined is of interest also in connection with magnetic mirror devices for nuclear energy transformation. It may also have applications to phenomena of solar and stellar atmospheres.     

Dynamic vibrations and stresses in a circular annulus of non-isotropic elastic material

Summary FollowingCinelli, we have discussed here the radial motion and stresses in a nonisotropic circular annulus subjected to dynamic loads on the surfaces.     

A determination of the wind-driven ocean circulation from the vorticity budget of the atmosphere

Summary The annual mean distribution of the surface stress curl over the Northern Hemisphere has been estimated from the horizontal vorticity advection in the atmosphere by using the upper-wind statistics as published byCrutcher [2]³). The results are used to compute the wind-driven mass transport (Sverdrup transport) in North Atlantic and North Pacific. The calculated intensity of the Gulf Stream is largest at the latitude 35°N, where a mass transport of 45×10⁶ tons sec^–1 is obtained; for the maximum intensity of the Kuroshio current a value of 60×10⁶ tons sec^–1 is obtained.Research supported in part by the Section of Atmospheric Sciences, National Science Foundation, Grant GP-2561.The research for this study was started by the author at the Department of Meteorology and Oceanography, The University of Michigan, Ann Arbor, Mich.     

Double boundary layers in standing surface waves

Summary The double boundary-layer theory ofStuart (1963, 1966) andRiley (1965, 1967) is employed to investigate the mass transport velocity due to two-dimensional standing waves in a homogeneous fluid. The double boundary-layer structure occurs only at the bottom, and the existence of jet-like motions is predicted, due to the nature of the mean flows in the bottom boundary layers. A vector equation governing mean motions in the secondary layer is derived for threedimensional wave motions.     

A critical analysis of the concept of planetary wave breaking

The concept of planetary wave breaking (McIntyre andPalmer, 1983; 1984) is critically reviewed. It is concluded that the wave breaking signature is not unique to any particular dynamic event in the stratosphere. Therefore, the classification of stratospheric transport events, such as wave breaking, groups fundamentally different events together. Better qualification of the wave breaking signature and a more solid theoretical basis of planetary wave breaking must be presented if the concept is to be of significant utility in describing stratospheric tracer transport.     

The constant temperature-sum as a basis for forecasting flowering date

Summary Hertlein's thesis is discussed and criticized on points where apparently significance is attached to results which require stronger statistical proofs.     

Hotspots,mantle convection and plate tectonics: A synthetic calculation

A model is developed that unifies vigorous hotspots with global-scale mantle convection and plate tectonics. The convection dynamics are assumed to generate flow patterns that emerge as closely packed polygonal cells in approaching the asthenosphere, and whose geometry is completely determined by a defining set of vigorous hotspots. Overlying viscously coupled rigid plates are driven with unique velocities (Euler vectors) at which the area integral of the shear forces is zero; these velocities are dynamically stable. The computed plate velocities, resulting from convection based on 15 hotspots, are compared with the velocities of plate motion models AM1-2 (Minster andJordan, 1978) and HS-NUVEL1 (Gripp andGordon, 1990), which combine transform fault geometries, magnetic anomalies and seismic data. The comparison shows a striking agreement for a majority of the plates. Geophysical implications of this numerical exercise are discussed.     

Resolution of tidal high water anomaly

Summary As a preliminary calculation of the Equilibrium Theory of Tides, a fictitious Earth-Moon configuration is analyzed byThomson andTait [1]²), in which non-sphericity of oceans is attributed to the attraction exerted by a stationary Moon. A rise of level is found at the which Earth-Moon orbital motion is accounted. This feature, which is utterly contradictory to fact according toG. H. Darwin [2] prompted him to remark that the equilibrium theory is nearly as much wrong as possible, in respect to the time of high water. An elementary analysis is given which, in demonstrating an exactly opposite finding, suggests a manner of removing one of the long-standing obscurities of the Laplace theory, remarked upon byHough andAiry, and in recent times byC. Eckart [3].