Elastische Multipolwellen in einem Medium,das aus homogenen,isotropen, planparallelen Schichten besteht

Zusammenfassung Gegeben ist ein festes, elastisches Medium, das aus homogenen, isotropen, planparallelen Schichten aufgebaut ist. Im Innern einer Schicht wird ein punktförmiger Störungsherd von Multipolcharakter angenommen. Die Störung setzt zur Zeitt=0 ein. Unter Anwendung der Laplace-Transformation werden nach dem Verfahren vonCagniard «Exponentialkoeffizienten» und «Übertragungsfaktoren» berechnet, die gestatten, die elastischen Verschiebungen der an den verschiedenen Unstetigkeitsflächen reflektierten und gebrochenen Wellen zu bestimmen.

---

Summary (Elastic waves of multiplet type in a solid consisting of homogeneous isotropic layers with plane parallel boundaries) — An unlimited elastic solid consists of homogeneous isotropic layers, separated by plane parallel boundaries. A point in the interior of one layer is a multiple source of elastic waves. The disturbance begins att=0. By aid of Laplace-transforms, «exponential coefficients» and «transmission factors» have been calculated according to the method shown byCagniard. By aid of the «transmission factors» we can determine the elastic displacements of the waves reflected and refracted at the boundaries.

     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

Onlamb's problem in a magneto-elastic initially stressed conducting medium

Summary The object of the present paper is to investigate the so-called planeLamb's problem in an initially stressed magneto-elastic semi-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical planeLamb's problem when the semi-space is supposed to be initially unstressed and non-magnetic.     

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.     

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.     

An effective approach to determine the dynamic source parameters

In this study, we present a new and effective method to determine the dynamic source parameters (i.e., stress drop and strength distribution). We first assume that the kinematic source parameters, i.e., the slip and rupture time distributions on the fault plane, are known from the previous source inversion studies. Then, using the seismic source representation theorem we determine the dynamic stress field on a fault plane from known kinematic parameters. Finally, we determine the strength of the fault defined as the peak stress just before the rupture. We have tested the validity of this method by using an illustrative two-dimensional analytical example. To assess the applicability of this method, we have applied it to study the 1979 Imperial Valley earthquake, and obtained consistent results with those ofMiyatake's (1992) andQuin's (1990). Compared with previous methods, this new method is simple, straightforward and accurate, and needs much less calculation. Therefore, it is expected to be useful in exploring the seismic source process.     

Seismic prospection by Wiechert-Herglotz method of calculus

Summary TheWiechert-Herglotz method to investigate seismically the Earth structure, is adapted for refraction prospecting. The case of a single layer bounded by a sloping interface is considered. The velocity is assumed to be an increasing function of depth within the layer and constant beneath. A general procedure of computation is outlined. Special formulae are given in addition for the case in which the dromochroneD ₁ corresponding to disturbances propagated only through the layer are of parabolic shape. Table I was calculated using them and assuming an horizontal interface. It may be seen there that valuesh ₁ of the layer thickness furnished by these formulae may become considerably greater than those based on D₁ rectilinear. Computation ofh ₁ may easily be performed by means of the same table.     

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.

---

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.

     

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.     

Ueber Anwendungen einer Formel zur Berechnung des Vertikal-gradienten der Schwere

Summary A formula is derived, which allows to calculate the vertical gradient of gravity from gravity anomalies with consideration of the whole gravitational field of the earth. It is shown that the formula given byEvjen for a plane surface in practical cases is nearly always sufficient. The accuracy of calculation is to be checked with regard to the geophysical applications. Two examples give an idea of the variations of the vertical gradient at the earth's surface. FurthermoreEvjen's method of direct structural calculation by means of the vertical gradient is discussed.

---

Résumé On déduit une formule qui permet de calculer, par rapport au champ total de gravité de la Terre, le gradient vertical de la pesanteur résultant des anomalies gravimétriques. Il s'en suit que la formule donnée parEvjen pour une surface plate est presque toujours suffisante dans les cas pratiques. On examine la précision du calcul à l'égard des applications géophysiques. Deux examples nous donnent une idée des variations du gradient vertical sur la surface de la Terre. Enfin on discute la méthode d'Evjen de calculer directement la structure a l'aide du gradient vertical.

     

The thermal diffusivity of red sandy soil at Waltair

Summary The study of heat exchanges or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature change produced in any layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil from range and lag methods suggested byJohnson andDavies [15]²) andCoutis [7] respectively. The values of diffusivity cbtained from these methods agree well with each other. The effect of soil moisture on diffusivity has been studied. The diffusivity increases with the increase of moisture in the surface layers of the scil. The ratio of ranges of soil temperature at different depths is found to be approximately constant which is in agreement with the theory of heat flow into the soils. The results of diffusivity obtained from these methods agree well with those results of past workers. The mean value of the thermal diffusivity of red sandy soil at the experimental site of Waltair is found to be 6.336×10^–3 cm²/sec.     

Magneto-viscoelastic disturbances in a ‘hereditary layer’

Summary The dynamical response due to the interaction of viscoelastic field and magnetic field in a layer ofVito Volterra's hereditary model is analysed by making use of Laplace-transform.     

Energieakkumulation in Grundschicht und Nullschicht

Zusammenfassung Grundschicht und Nullschicht wurden bereits früher als zwei Schichten erkannt, die in bezug auf den Massenhaushalt der hochreichenden Hoch — und Tiefdruckgebiete von polar entgegengesetzter Bedeutung sind: In der Grundschicht erfolgt ein ageostrophischer Massenfluss vom hohen zum tiefen Druck, in der Nulischicht ein solcher vom tiefen zum hohen Druck. Beide Schichten weisen aber auch Gemeinsamkeiten auf. Sie liegen unter den markantesten Inversionen der Troposph?re (Peplopause bzw. Tropopause). Da eine Inversion als Sperrschicht des nach oben gerichteten Flusses der kinetischen Energie wirkt, kommt es unter ihr zu einem Stau kinetischer Energie, der eine ageostrophische Erh?hung der Windgeschwindigkeit gegenüber den vertikal benachbarten Schichten mit sich bringt. Anhaltspunkte für eine derartige Erh?hung der Windgeschwindigkeit unterhalb der Peplopause liegen vor.

---

Summary Ground layer and zero layer were recognized in the past already as two layers that are of directly opposite relevance to the mass exchange in high-reaching high and low pressure areas; taking place in the ground layer is an ageostrophic mass transport in the direction high to low pressure, while in the zero layer the opposite motion is accurring, i.e., from low to high pressure. Yet, the two layers have some communities too. They are located below the most significant inversions of the troposphere (Peplopause and/or Tropopause). Since an inversion will act upon the flow upward of kinetic energy as an intercepting layer, a congestion of kinetic energy will be produced below it, involving an ageostrophic increase in the wind speed, as compared with vertically adjoining layers. There are a number of clues for such an increase of wind speed actually occurring below the peplopause.

---

---

Prof. Dr.Karl Schneider-Carius,Bad Kissingen Erhardstr. 3.

---

Dr.Heinrich Faust, Deutscher Wetterdienst,Frankfurt a.M., Taunusanlage 18.     

Inversion of source process and related studies of the Taiwan Strait earthquake using genetic algorithm

Applying genetic algorithm to inversion of seismic moment tensor solution and using the data of P waveform from digital network and initial motion directions of P waves of Taiwan network stations, we studied the moment tensor solutions and focal parameters of the earthquake of M=7.3 on 16 September of 1994 in Taiwan Strait and other four quakes of M _L≥5.8 in the near region (21°–26°N, 115°–120°E). Among the five earthquakes, the quake of M=7.3 on September 16, 1994 in Taiwan Strait is the strongest one in the southeastern coast area since Nan’ao earthquake of M=7.3 in 1918. The results show that moment tensor solution of M=7.3 earthquake is mainly double-couple component, and is normal fault whose fault plane is near NW. The strike of the fault plane resembles that of the distributive bands of earthquakes before the main event and fracture pattern shown by aftershocks. The tension stress axis of focal mechanism is about horizontal, near in NE strike, the compressive stress axis is approximately vertical, near in NWW strike. It seems that this quake is controlled by the force of Philippine plate’s pressing Eurasian plate in NW direction. But from the viewpoint of P axis of near vertical and T axis of near horizontal, it is a normal fault of strong tensibility. There are relatively big difference between focal mechanism solution of this quake and those of the four other strong quakes. The complexity of source mechanism solution of these quakes represents the complexity of the process of the strait earthquake sequences. Contribution No. 98A01001, Institute of Geophysics, State Seismological Bureau, China. The subject is supported and helped by Academician Yun-Tai CHEN, Profs. Qing-Yao HONG, Zhen-Xing YAO, Tian-Yu ZHENG, Yao-Lin SHI, Ji-An XU, Bo-Shou HUANG and colleague Mei-Jian AN, Xue-Reng DING, Rui-Feng LIU. De-Chong ZHANG and Ming Li provided the digital data warm-heartedly. Lin-Ying WANG offered us the catalogue of earthquakes in southeastern coastal area in China. Xi-Li WANG and Tong-Xia BAI provided us the issued annual reports data. The authors would like to express their gratitude to all of these people. This paper is sponsored by the National Natural Science Foundation of China and Scientific and Technological Commission of Shantou, Guangdong Province.     

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.     

On the singing phenomenon in the offshore seismic experiments

Summary Offshore areas are sometimes found in which seismic record assumes the appearance of a sine wave or a simple combination of sine waves. It is more interesting to note that the dominant frequency on the singing records is the third harmonic of a fundamental whose wave length is four times the water depth. In this paper it has been proved that this peculiar phenomenon happens due to the slope of the sedimentary layer near the observational points. Using the method introduced byCovert (1958) of finding the Green's function for built in bodies, pressure field has been obtained in the water layer for a two dimensional point source in the same medium and it has been proved that due to the slope of the sedimentary layer singing is caused by waves of wave-length equal to four times the water depth.     

Propagation of Rayleigh waves in an axially symmetric heterogeneous layer lying between two homogeneous halfspaces

Summary The propagation of Rayleigh type waves in an axially symmetric inhomogeneous layer lying between two halfspaces is studied. The halfspaces are supposed to be identical in their elastic properties. The variation of the parameters in the layer is assumed to be of the form where is a constant andz is the distance measured from one interface into the layer. With this assumption, the vector wave equation for the layer is separable. The solution is obtained in terms ofWhittaker's functions and the frequency equation of Rayleigh type waves is derived.     

On plane waves in thermo-viscoelastic solids deformed by magnetic fields

Summary In the present paper,Maxwell's electromagnetic equations together with the equation of motion of two types of viscoelastic solids have been used to deal with the propagation of magneto-thermoviscoelastic plane waves.     

Principal horizontal stresses in Southern Africa

A review ofin situ stress measurements at eight regional localities in Africa south of the 15°S parallel shows that average directions of the horizontal pricipal stresses are N-S and E-W. These directions agree with principal stress orientations deduced from earthquake fault plane solutions. However, the maximum and minimum principal horizontal stresses are not consistently oriented parallel to either the N-S or E-W direction; they may vary within an individual region because of local geological structures and from region to region. At the sites within the Witwatersrand sediments (all at depths greater than 500 m) the maximum stress tends to lie NW-SE but at three of the four sites outside the Witwatersrand sediments (all at depths less than 500 m) this stress is oriented approximately N-S.The data reported here are compared with horizontal stresses predicted for Southern Africa bySolomon, Sleep andRichardson (1975) from various plate tectonic driving force models. The agreement between orientations is fair for all sites but only the deép sites in the Witwatersrand sediments have comparable stress magnitudes.     

Love wave dispersion: Errors due to assumption of isotropy

Summary Frequency equation for Love waves, propagating in a transversely isotropic homogeneous layer which is embedded between two isotropic homogeneous half spaces, is obtained. Errors, in rigidity (h), density and thickness of the anisotropic layer, which arise due to the assumption of isotropy of the medium are calculated by numerically analyzing the frequency equation. The results show that the errors increase with the increasing frequencies, and their signs depend upon the value (whether less than or greater than 1) of the anisotropy co-efficient of the medium of the layer.