Transient disturbance produced in an elastic half-space by impulsive shearing traction distributed over a circular region

The displacement produced in a semi-infinite, homogeneous, isotropic elastic medium by the application of shearing traction over a circular portion of the half-space has been evaluated in exact form by Cagniard's Technique (Cagniard, 1962;Gakenheimer andMiklowitz, 1969).     

On the disturbances in an infinite viscoelastic medium due to transient normal forces and transient twists on the surface of a spherical cavity

Summary In this note the disturbances in an infinite viscoelastic medium ofViogt type with a spherical cavity have been considered. The problem has been solved separately for (1) transient radial forces and (2) transient twist acting on the inner spherical surface of the cavity. Exact solutions have been obtained in both cases.     

On the propagation of plane waves in a porous visco-elastic material containing a fluid and deformed by a magnetic field

Summary In the present note, an attempt has been made to investigate the wave-motions in a poro-viscoelastic medium traversed by a static magnetic field, by using the equations ofMaxwell, and those ofBiot.     

A fluid-filled fracture as possible mechanism of ground deformation at Phlegraean Fields,Italy

Two uplift episodes have recently been recorded at Phlegraean Fields, a volcanic region near Naples (south-central Italy). The first episode occurred in 1970 and lasted up to 1972; the second has begun at the end of 1982 and is still in progress.An attempt to model the ground deformations which occurred during the 1970–1972 event is made in this paper. The source has been assumed to be a two-dimensional fluid-filled fracture, similar to a sill. A good fit with experimental data has been obtained for a short (1–2 km long) shallow (3 km deep) source and a driving pressure ranging from 60 to 210 bars. Rigidity values have been fixed at 3.5–4.0 × 10¹⁰ c.g.s., with Poisson ratio equal to 0.3.This solution which differs from previous approaches byMogi (1958) andWalsh andDecker (1971) is non-unique, but the present results are in good agreement with observed horizontal and vertical displacements. Notwithstanding the oversimplification made in assuming a homogeneous elastic semi-infinite medium, the predicted stress field seems to be in agreement with the fault-plane solutions and the pattern of epicenters determined for the uplift-seismic swarm episode that is still in progress.     

Propagation of a fracture in an infinite medium

Summary The displacement produced in an infinite homogeneous, isotropic elastic medium due to a steadily progressing crack has been obtained in a closed form by using Laplace transforms andCagniard's method. Numerical values of the displacement have been obtained and presented graphically.     

On disturbances produced in an elastic medium by twists applied on the inner surface of a spherical cavity

Summary In this note, disturbances generated in an isotropic elastic medium by some simple types of twisting forces applied on the inner surface of a spherical cavity have been investigated. Prof.S. K. Chakraborty, Surendranath College, 24 Harrison Road,Calcutta (India).     

Wave propagation in two layered medium under initial stresses

Summary In this paper, the frequency equation for phase velocity of waves propagated in a laminated medium consisting of two eleastic layers of finite thickness under initial stresses, has been obtained. It has been shown that when wave length becomes very small compared to the thickness of each layer, the wave approaches two Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface. The propagation ofSH-waves in the composite medium under initial stresses has also been discussed. A particular case has been taken to find the velocity of Love wave in the homogeneous half space under initial compressive stresses.Biot's incremental deformation theory has been used.     

The electrostatic force between a charged conducting sphere and a charged dielectric sphere in an arbitrarily oriented external electric field

Summary The electrostatic force between a charged conducting sphere and a charged dielectric sphere in a uniform, arbitrarily oriented external electric field is obtained and presented in terms of force coefficients which depend only on the relative geometry of the two spheres and the dielectric constants of the dielectric sphere and the medium. When the dielectric constant of the dielectric sphere is allowed to approach infinity, the resulting computed force agrees with that ofDavis (1964) for two conducting spheres, and when the external field and the charge on the dielectric sphere are set to zero, the resulting force agrees with that ofHall andBeard (1975) for a charged conducting sphere near an uncharged dielectric sphere.     

Note on the propagation of waves from a spherical cavity in an infinite solid

Summary The present note, as its title implies, is concerned with the investigation of disturbances in an infinite elastic medium containing an initial magnetic field in the axial direction. The equations ofMaxwell, those of elasticity have been effectively made use of to solve the problem.     

Moving load on a porous,liquid-saturated solid

Summary The object of this paper is to study the stresses produced in a porous liquid-saturated solid of the type considered byBiot [1]²) by a normal load moving along the surface of such a solid. Two cases have been considered. In the first case, the porous solid is taken to be semi-infinite, while in the second case we consider a layer of the liquid-saturated porous solid resting on a smooth rigid foundation. Expressions have been obtained for the stresses at any point in the medium due to a normal load moving along the free surface of the porous solid. Detailed numerical calculations have been carried out for liquid-saturated sandstone, using the data given byFatt [9] for such a medium. These calculations show that the normal stress zz in the solid falls off approximately as 1/z with increase in the depthz below the free surface, and that the stresses in the solid and in the liquid fall off rapidly as we move away from the point directly below the moving load.     

On the propagation of spherical waves due to large underground explosion

Summary When a high explosive pressure acts on the boundary of a spherical cavity in an elastic medium, the material in a region around the charge behaves plastically and thereafter an elastic wave is propagated. Not only that but the elastic plastic boundary moves also with a certain velocity which is less than the elastic wave velocitySabodash [3]²). In this paper, firstly the case when the elastic plastic boundary moves with a velocityV ₀. (V ₀<c) has been dealth with. The pressure in the elastic medium on this boundary has been assumed to be constant and equal toP ₀. Secondly the case when the elastic plastic boundary moves with an exponentially decaying velocity has been considered. The pressure in the elastic medium on this boundary has also been assumed to be of exponential character.     

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.     

The value ofStreptococcus faecalis as an indicator bacterium in heavily polluted water

Summary Experiments on cultivation in various media, and under various experimental conditions ofSt. faecalis isolated from heavily polluted localities are described. It is rendered probable that it is not the high incubation temperature (45°C) which is the reason for the low counts found on cultivation in standard sodium-azide medium, but the fact thatSt. faecalis which has been adapted to growth in sodiumazide medium cannot—or at any rate can only with difficulty—grow when transferred into MacConkey medium (confirmatory test). It is concluded thatHajna’s [10] BAGG medium, which contains glycerol, is the only one of the tested media which yields reliable counts from heavily polluted localities. In experiments with identification tests to separate the two human streptococciSt. faecalis andSt. faecium, it was found in accordance withMannweiler [15] andDeibel [7] that strains often failed to grow under one or more of the tolerance conditions. Therefore, in routine work one may consider streptococci growing at incubation temperatures of 10°C and 45°C as identical withSt. faecalis and those at 10°C and 50°C as identical withSt. faecium.

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Zusammenfassung Kulturversuche in verschiedenen Medien und unter verschiedenen Versuchsbedingungen mitStreptococcus faecalis, der aus Abwasserteichen mit stark verschmutztem Abwasser stammt, werden beschrieben. Es ist m?glich, dass nicht die hohe Inkubationstemperatur von 45°C der Grund für die niedrige Ausz?hlung auf dem Standard-Natrium-Azid-Medium ist, sondern die Tatsache, dassS. faecalis, das sich diesem Medium angepasst hat, nicht oder allenfalls nur mit Schwierigkeit wachsen kann, wenn es auf das MacConkey-Medium übertragen wird (Best?tigungstest). Daraus wird geschlossen, dassHajnas [10] BAGG-Medium, welches Glyzerin enth?lt, das einzige der getesteten Medien ist, welches zuverl?ssige Ausz?hlungen aus schwer verunreinigtem Abwasser ergibt. In Identifikationsversuchen zur Trennung der beiden menschlichen Streptokokken,S. faecalis, undS. faecium, wurde in übereinstimmung mitMannweiler [15] undDeibel [7] gefunden, dass St?mme unter einer oder mehreren der Toleranzbedingungen nicht wuchsen. Daher k?nnen Streptokokken bei Routinearbeiten bei Inkubationstemperaturen von 10°C und 45°C als mitS. faecalis, bei solchen von 10°C und 50°C als mitS. faecium identisch betrachtet werden.

     

Displacement produced in an elastic half-space by the impulsive torsional motion of a circular ring source

Summary In this paper the problem of disturbance in an elastic semi-infinite medium due to the torsional motion of a circular ring source on the free surface of a medium are studied. Two cases, when the medium is either homogeneous or inhomogeneous, are treated. In order to solve the problem, the Laplace transform and the Hankel transform and the Laplace inversion by Cagniard's method as modified byDe Hoop (1959) are applied. Finally, the integrals for displacement are evaluated numerically. The displacement on the free surface as a function of time is shown by means of graphs, in the case of both a homogeneous and an inhomogeneous medium, indicating clearly the variation in displacement due to the presence of an inhomogeneity.     

On the strongSH-motion in clay overlying hard elastic material due to explosions

Summary Kisslinger and others have observed that there is strongSH-motion in clay resulting in fracture of the surface when a strong shot is made inside. To explain this phenomenon, it has been assumed that the thickness of this visco-elastic clay above the comparatively harder elastic medium is not uniform. This non-uniformity of thickness contributes to a term in the displacement which becomes theoretically very large for certain wave-lengths.     

Tomography and the Herglotz-Wiechert inverse formulation

In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (seeHerglotz, 1907;Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.     

Generation of rayleigh waves due to stress-discontinuity in a semi-infinite elastic medium

Summary In this paper, the displacements produced at the surface of a semi-infinite, clastic medium by the sudden creation and subsequent motion of discontinuities in the normal and tangential stresses have been obtained in the form of definite integrals byCagniard's method. Numerical values are given in a particular case.Published with the kind permission of the Director General, Geological Survey of India, Calcutta.     

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.     

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.     

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.