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.     

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.     

Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation

Summary In this paper, the problem of a normal load moving over the surface of a layer of ice, lying on a rigid foundation, has been considered. FollowingHearmon, the ice is taken to be transversely isotropic. Two cases have been considered-in the first case, the rigid foundation is taken to be smooth, and in the second case, it is taken to be in welded contact with the layer of ice. Expressions have been obtained in both cases for the stresses at any point of the layer. From detailed numerical calculations, it has been found that the value of the normal stress at a point directly below the moving load falls of approximately as that of 1/z with increase in the depthz below the surface. On calculating the normal stress at the boundary between the layer of ice and the foundation, it is found that the normal stress falls off rapidly as we move away along the boundary from the point directly below the load.     

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.     

On the stresses produced by a moving stress discontinuity at the boundary between two transversely isotropic media

Summary This paper deals with the stresses produced by a moving stress discontinuity between two semi-infinite transversely isotropic media. The solutions for the stresses have been obtained in simple closed forms for certain types of moving stress discontinuity. Discontinuities in the normal stress as well as in the shear stress has been considered. The case in which one or both of the media are isotropic may be deduced as a special case from the results obtained here.     

Diffraction ofSH-waves originating from a moving point source by a rigid quarter space

Summary ApplyingWiener-Hopf techniques the diffraction ofSH-waves originating from a moving point source due to the presence of a step change in the elevation of the surface of a homogeneous half-space have been obtained. An interesting feature of resonance associated with the motion of a load at a velocityv ₀ ^–1 approachingv ₀ ^–1 has been observed.     

Formation of cracks due to moving source over a thick crust

Summary In this paper the problem of a point source of stress moving over the surface of a thick aelotropic plate resting of a rigid foundation has been considered. Following the method ofAleksandrov & Vorovich (1960) the stress componentsZ _x andZ _z have been expanded in series of ascending powers of 1/h when the source velocity is less than (c ₄₄/)^1/2. When the velocity exceeds (c ₄₄/)^1/2 it has been shown that two cracks are produced in different directions and their successive reflections at the upper and lower surface are also obtained.     

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.     

Die äquatoriale Beschleunigung bei Sonne,Jupiter und Saturn nebst Betrachtungen über die Form der Kontinente

Zusammenfassung Ausgehend von derEmden'schen Theorie der äquatorialen Beschleunigung der Sonne und einer früheren Anwendung derselben auf den Planeten Jupiter, wird auch die Beschleunigung bei Saturn hier erstmalig diskutiert und der Versuch gemacht, dieselbe Theorie zur Erklärung der Ostabweichung der Kontinente der Erde im äquatorialen Gebiet anzuwenden. Das ist nur möglich, wenn man 1.) auf die archaische Periode der Erdentwicklung zurückgreift, bei der aber die wesentlichen Höhenunterschiede der Erdoberfläche schon ausgebildet waren, 2.) der Pol im wesentlichen die jetzige Lage hatte und 3.) der Reibungskoeffizient der festen Erdkruste aber wesentlich geringer war: 10¹⁴ gegen etwa 10²⁰ c.g.s.

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Summary The hypothesis ofR. Emden to explain the equatorial acceleration of the sun has newly been discussed by the author and 11 years ago applied to the rotation ot the planet Jupiter. It is possible to apply her also to the planet Saturn and to the earth in the archaic period of evolution. The earth shows a striking eastern curvature of the continents in the equatorial zone, which possibly has originatet in times, when the earth crust was capable to yield to the same forces, which drive the equatorial zone forwards in rotating gaseous and liquid spheres, as the sun and the great planets. It is nenessary to suppose an invariable position of the pole and the principal height differences of the crust already developed. It is found, that the viscosity of the earth in that time has been small in comparison to its present value (10¹⁴ to 10²⁰ c.g.s.).

     

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.     

Rayleigh wave propagation in a two-layer anisotropic media

Summary The possibility of propagation of Rayleigh waves in an incompressible crust of constant density and rigidity varying exponentially with depth lying on a semi-infinite transversely isotropic base has been discussed in this paper. Frequency equation has been derived and numerical calculations are made. The result obtained in this case is compared with that ofNewlands [3]²) andDutta [4].     

On the evaluation of planetary albedo of the earth from turbidity measurements in India

Summary The planetary albedo of the earth has been evaluated from the turbidity measurements in India by usingÅngström's empirical relation [1]²) and the same has been presented in this paper. The diurnal and seasonal variations of the planetary albedo have been discussed. It has been found that during the morning hours, albedo is usually more than that during afternoon hours. Further, it shows a minima during winter season and a maxima during hot summer months.     

Thermoelastic stresses and strains in a gravitating earth

Summary The stress and strain fields in various earth models are studied under the assumption of an elastic mantle and the existence of thermal stresses which are proportional to the difference between the initial and present temperatures. The thermoelastic equilibrium equation for a 49-layered earth with spherical symmetry is integrated and programmed for various combinations of velocities, densities and temperatures. Results show that the strains in the upper mantle depend to a great extent on the thermal model. Central radial strain ranges from 5.2 to 7.3 per cent and the central pressure ranges between 3.1 and 3.7×10¹² dynes/cm² for all models. It is established that the thermal history of the earth could not have changedBullen's pressures by more than 0.4×10¹² dynes/cm².Contribution No. 1095, Division of Geological Sciences, California Institute of Technology, Pasadena, California.     

Disturbances produced by variable body forces in a layer of finite thickness resting on a rigid foundation

Summary The disturbances produced by time-dependent torsional body forces in a layer of elastic material lying on a rigid foundation have been discussed in this paper. Solutions have been obtained first for a general type of body force, and the solutions for an impulsive cylindrical source and an impulsive torsional line source of finite length have been deduced. It has been found that for any point in the layer, there is no disturbance up to a certain instant, after which there is a sudden displacement, which gradually falls off and tends to zero as the timet increases.     

Morphology and emplacement of an unusual debris-avalanche deposit at Jocotitlán volcano,Central Mexico

A pre-historic collapse of the northeastern flank of Jocotitlán Volcano (3950 m), located in the central part of the Trans Mexican Volcanic Belt, produced a debris-avalanche deposit characterized by surficial hummocks of exceptional size and conical shape. The avalanche covered an area of 80 km², had an apparent coefficient of friction (H/L)_of 0.11, a maximum runout distance of 12 km, and an estimated volume of 2.8 km³. The most remarkable features of the Jocotitlán debris avalanche deposit are: the several steep (29–32°) conical proximal hummocks (up to 165 m high), large tansverse ridges (up to 205 m high and 2.7 km long) situated at the base of the volcano, and the steep 15–50 m thick terminal scarp. Proximal conical hummocks and parallel ridges that can be visually fitted back to their pre-collapse position on the mountain resulted from a sliding mode of emplacement. Steep primary slopes developed as a result of the accumulation of coarse angular clasts at the angle of repose around core clasts that are decameters in size. Distal hummocks are commonly smaller, less conical, and clustered with more diffuse outlines. Field evidence indicates that the leading distal edge of the avalanche spilled around certain topographic barriers and that the distal moving mass had a yield strength prior to stopping. In the NE sector, the avalanche was suddenly confined by topographically higher lacustrine and volcaniclastic deposits which as a result were intensely thrust-faulted, folded, and impacted by large clasts that separated from the avalanche front. Post-emplacement loading also induced normal faulting of these soft, locally water-rich sediments. The regional tectonic pattern, N-NE direction of flank failure, and the presence of a major normal fault which intersects the volcano and is parallel to the orientation of the Acambay graben located 10 km to the N suggest a genetic relationship between the extensional tectonic stress regime and triggering of catastrophic slope failure. The presence of a 3-m-thick sequence of pumice and obsidian-rich pyroclastic surge and fall tephra directly overlying the debris-avalanche deposit indicates that magma must have been present within the edifice just prior to the catastrophic flank failure. The breached crater left by the avalanche has mostly been filled by dacitic domes and lava flows. The youngest pryroclastic surge deposits on the upper flanks of the volcano have an historical C¹⁴ age of 680±80 yearsBp (Ad 1270±80). Thus Jocotitlán volcano, formerly believed to be extinct, should be considered potentially active. Because of its close proximity to Mexico-City (60 km), the most populous city in the world, reactivation could engender severe hazards.     

‘Bedload’ dynamics: Grain impacts,momentum transfer and derivation of a grain froude number

A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū²/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration.     

Displacement due to impulsive loadings on the surface of elastic half-space

Summary The displacement due to vertical impulsive load has been obtained by function theoretic method. Graphs have been drawn for horizontal as well as for vertical displacement. It has been shown thatPekeris's [12]²) method is easier to apply than that ofCagniard [2] for the same purpose.     

Self-induced Deformation on the Fault Plane During an Earthquake Part II: Continuous Tangential Displacements

— This paper regards the on-fault displacement field generated by an earthquake on its own fault plane, with special attention to the tangential displacement vector. It is the continuation and the completion of a previous paper (Armigliato et al., 2003) concerning the analysis of the normal on-fault displacement component. It is here recognised that in addition to the discontinuous shear displacement, which is the main contribution to the seismic dislocation on the fault, there is a tangential displacement contribution that is continuous across the fault. The continuous tangential displacement is exclusively produced by the presence of the free earth's surface. The tangential displacement vector has non-vanishing components in both directions, parallel as well as perpendicular to the imposed uniform shear slip, the first being predominant on the second. We perform a set of computations aimed at evaluating the dependence of the tangential displacement magnitude on the relevant fault parameters for basic cases of rectangular faults embedded in a homogeneous half-space.     

On the topographic coupling at the core-mantle interface

The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U₀ relative to the mantle. Ω and B possess vertical and horizontal components.The vertical (poloidal) component B_p is uniform and has a value of 5 G while the horizontal (toroidal) field B_T = B_pαz, where α is a constant. When |α| ? 1, the mean horizontal stresses are found to have the same order of magnitude (10^?2 N m^?2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions.The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10^?2 N m^?2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ? 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.     

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).