On the propagation of Love waves in a non-homogeneous internal stratum of finite depth lying between two semi-infinite isotropic media

Summary The possibility of propagation of Love waves in a non-homogeneous internal stratum of finite depth lying between two semi-infinite isotropic media has been studied in this paper. The density and rigidity of the internal stratum are taken to vary exponentially with depth.     

The disturbance due to periodic surface traction in a semi-infinite medium of varying elasticity and density

Summary In this paper, the shear displacement due to a transverse periodic surface traction on a semi-infinite elastic solid, in which the rigidity and density vary exponentially with the depth has been obtained. The normal modes are calculated for high frequencies and the surface displacement obtained numerically in a particular case for a low frequency.     

On S. H. point source in heterogeneous medium

Summary A S.H. point source in heterogeneous elastic medium where the modulus of rigidity and density vary exponentially with depth has been considered. The form of disturbance due to such a point source in a semi-infinite medium has been obtained in integral form. The integrals are evaluated by contour integration.     

On the torsional vibration of a finite circular cylinder of non-homogeneous material by a particular type of twist on one of the plane ends

Summary In this paper the torsional vibration of a finite circular cylinder of non-homogeneous material whose rigidity and density vary linearly with the depth has been considered. One end of the cylinder is fixed while a periodic shearing force acts along the circumference of a circle on the other end.     

On the propagation of Love type waves in an infinite cylinder with rigidity and density varying linearly with the radial distance

Summary The propagation of Love type waves in an infinite non-homogeneous circular cylinder with a central core is investigated here. The rigidity and density of the outer mentle are supposed to vary linearly with the radial distance, while those of the inner core are taken to be constant. Phase velocity curve against wave number is drawn.     

On the propagation of love waves in a heterogeneous layer lying on a homogeneous medium

Summary The present note is devoted to find out the possibility of propagation of love waves in a heterogeneous layer of finite depth lying on a homogenous semi-infinite elastic medium, the rigidity and density in the upper layer varying as (1–sinz), where is a constant andz is the vertical distance from the interface. The numerical results for the phase velocity for some special Earth models are given.     

Motion in a non-homogeneous elastic medium by a twisting impulsive force on the surface of a spherical cavity

Summary In this paper, the propagation of disturbance due to a twisting impulsive force on the surface of a spherical cavity, in a non-homogeneous isotropic medium, in which the rigidity and density vary inversely as the distance from the centre is investigated. Numerical solution is done by the method suggested byKromm.     

Parabolic density function in sedimentary basin modelling

For modelling sedimentary basins of large thickness from their gravity anomalies, the concept of parabolic density function which explains the variation of true density contrast of the sediments with depth in such basins is introduced inBott's (1960) procedure. The analytical expression the gravity anomaly of a two-dimensional vertical prism with parabolic density contrast needed to estimate the gravity effect of the basin in modelling procedure is derived in a closed form. Two profiles of gravity anomalies, one across San Jacinto Graben, California and the other across Tucson basin, Arizona where the density of sediments is found to vary with depth are interpreted.     

Solutions of the heat conduction equation in a non-uniform soil

A class of analytic, periodic solutions of the heat conduction equation in a non-uniform soil is derived. The class may be characterized by the fact that the speed of the temperature wave varies according to the square root of the soil diffusivity (a function of soil depth). In addition it is shown that the constant soil solution is the limiting case when the rate of change with depth of diffusivity and thermal conductivity become very small. The solutions may be regarded as general whenever temperature analysis is restricted to small values of depth or whenever the soil parameters vary slowly. For all other cases the class of solutions possess the additional property that the rate of change of conductive capacity varies directly as the product of the bulk density and specific heat of the soil. A particular temperature profile is given for the case when the diffusivity varies as the nth power of depth.     

On propagation of love-type waves on a spherical model with rigidity and density both varying exponentially with the radial distance

Summary The propagation of Love type waves on a spherical model' in the mantle of which the rigidity and density vary exponentially with the radial distance while in the core they remain constant — has been investigated. The frequency equation that has been worked out has been examined in detail for the existence of root in the particular cases when they involve Bessel Functions of smallest and largest orders.     

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].     

Propagation of love waves in a non-homogeneous stratum of finite depth sandwitched between two semi-infinite isotropic media

Summary The aim of this paper is to study a problem in which the intermediate layer is non-homogeneous, the rigidity varying exponentially with depth i.e. ₂=₂ v ₀ ² e ^2pz , the density being constant, velocity varies also exponentially with depth according to the law =v ₀ e ^pz . The variability ofKH with the change of phase velocity is shown graphically.     

Hybrid Method for Love Wave Dispersion in Vertically Inhomogeneous Media

—Love wave dispersion in a vertically inhomogeneous multilayered medium is studied by a combination of analytical and numerical methods for arbitrary variation of rigidity and density with depth. The problem is reduced to a boundary value problem for a differential equation and solved numerically. The method compares favourably with other methods in use. Simple particular cases are considered and interesting results are exhibited graphically.     

Gravity interpretation of nonoutcropping sedimentary basins in which the density contrast decreases parabolically with depth

The decrease in density contrast of sedimentary rocks with depth in many sedimentary basins can be approximated by a parabolic density function. Analytical gravity expression of an outcropping two-dimensional vertical step along which the density contrast decreases parabolically with depth is derived in the space domain. A modification ofBott's (1960) method of gravity interpretation is proposed by considering two outcropping vertical steps on either side of the first and last observation points in addition toN outcropping vertical prisms in order to interpret the gravity anomalies of nonoutcropping basins. The thicknesses of the two outcropping vertical steps are made equal to the thicknesses of the two outcropping vertical prisms placed below the first and last observation points. The initial depth estimates of the sedimentary basin are calculated by the infinite slab formula ofVisweswara Rao et al. (1993). The gravity effects of theN outcropping prisms and the two outcropping vertical steps are calculated at each anomaly point and the depth to the floor of the basin are adjusted based on the differences between the observed and calculated anomalies. A gravity anomaly profile of Los Angeles basin, California is interpreted.     

Dependence of the Love numbers upon the inner structure of the Earth and comparison of theoretical models with results of measurements

Summary The question this paper is examining is the following: to what extent are the Love numbers dependent on certain characteristics of the inner structure of the Earth? It has been proven — on the basis of calculations carried out by the author-that these quantities are only in a small degree dependent on the density values measured on the surface of the Earth and on the selection of the density function in the mantle of the Earth. On the other hand the value of Love numbersh, k andl is considerably influenced by the assumptions made about the core of the Earth, namely by the position of the boundary between the core and the mantle and by the magnitude of the rigidity coefficient presumed in the core in the vicinity of the core-mantle boundary.The results of the calculations are compared with those mean values of Love numbers obtained from the data of stations operating at different places of the Earth. By reason of this it can be assumed that the core of the Earth has, in the vicinity of the core-mantle boundary, a coefficient of effective rigidity of the order of 10¹⁰ dyn/cm², if the core-mantle boundary is placed at the relative Earth radius of 0.545 from the centre of the Earth.     

On forced torsional oscillation of a cylindrical shell of non-homogeneous material by the application of a periodic shearing force at one end

Summary In the present note the author has considered the torsional vibration of a cylindrical shell of non-homogeneous material whose rigidity and density vary linearly with distance from the axis of the shell. It is assumed that one end of the shell is fixed while the other end is acted on by a periodic shearing force, both the inner and the outer curved surface being free from stress at all times.     

洱海4种沉水植物叶片的光合色素组成及C、N、P化学计量特征对水深的响应

水深与水体的多个环境要素(如光照、温度等)密切关联.因而水深会影响沉水植物的生长、繁殖和生理生化特征,包括叶片的光合色素组成和C、N、P化学计量特征.本研究通过对洱海4种沉水植物苦草(Vallisneria natans)、微齿眼子菜(Potamogeton maackianus)、光叶眼子菜(Potamogeton lucens)和篦齿眼子菜(Potamogeton pectinatus)在不同水深梯度的叶片色素组成和C、N、P化学计量特征进行分析,以阐明水深对这些指标的影响规律和机制.结果表明:水深对4种沉水植物叶片光合色素组成和C、N、P化学计量特征的影响具有种间差异性;苦草、微齿眼子菜和光叶眼子菜叶片N含量,苦草和光叶眼子菜叶片P含量都与叶片叶绿素含量呈显著正相关;苦草叶片N含量随水深增加而增加,可能是由苦草为应对深水弱光胁迫而加强光合色素和蛋白的合成导致的,而磷含量的增加可能还受其他因素的影响.     

Curie Point Depths of Albania Inferred from Ground Total Field Magnetic Data

Ground total magnetic field data of Albania were used to produce estimates of the Curie point isotherm. The strategy followed was to estimate the depth to the bottom of the deepest magnetic sources. Firstly, the average depth to the top of the deepest crustal block, z_t, was computed by linear fitting to the second lowest-frequency segment of the azimuthally averaged power spectrum of the total magnetic field data. Then, the depth to the centroid of the deepest crustal block, z₀, was computed by linear fitting to the lowest-frequency segment of the azimuthally averaged power spectrum of a distribution of magnetic dipoles. Finally, the depth to the bottom, the inferred Curie point depth, z_b, was calculated from z_b=2z₀−z_t. Curie depth estimates for Albania vary from about 17 to 25.5 km (below sea level). These results are consistent with the depths inferred by extrapolating geothermal gradient and heat-flow values, suggesting that the Curie point depth analysis is useful to estimate the regional thermal structure. It also suggests that the approach was valid and that ground total magnetic field data can be used for this purpose.     

Cone morphologies associated with shallow marine eruptions: east Pico Island, Azores

Eruptions in shallow water typically produce cones of volcaniclastic material. In order to identify any systematic effects of water depth and other environmental parameters on cone morphology, we have measured the heights and widths of cones in multibeam echo-sounder data from a submarine ridge extending southeast from Pico Island, Azores. XRF analyses of dredged samples show that lavas here vary compositionally from alkali basalt to trachybasalt and trachyandesite. Cones in deeper water are generally steep-sided with upper flanks close to 30°, the dip of talus at the angle of repose. However, height/width ratios of cones vary more in shallow water (200?C400-m summit depth) with extreme values below 0.1; while some shallow-water cones are steep-sided as in deep water, others are much flatter. Three such cones lie on a bench at 300-m depth immediately east of Pico Island and have flank slopes of only 10?C20°. We speculate that exceptionally shallow cone slopes here were produced by forced spreading of the erupting columns on reaching the water?Cair density barrier.     

Volumetric displacement of flow depth by obstacles,and the determination of friction factors in shallow overland flows

Large roughness elements such as stones or plant stems (obstacles) influence the depth of overland flows in two ways. The first effect is a dynamic one, involving frictional retardation of the flow and associated reduction in flow speeds. The second influence is static, and arises from the upward volumetric displacement of flow depth because of the submerged volume of the obstacles. Depending upon the distribution of submerged obstacle volume with height above the soil surface, the proportion of the flow volume occupied (and so, the perturbation of flow depth arising from volumetric displacement) can vary irregularly or systematically with flow stage. Furthermore, the amount of volumetric displacement of flow depth would vary among surfaces carrying different cover fractions of identical obstacles. Consequently, estimates of the change in friction factors arising from the drag on flow traversing varying obstacle cover fractions are confounded with the parallel shift volumetric displacement. To understand the true frictional drag arising from obstacles, a correction must be made for the volumetric displacement. A method for making this correction is outlined. New laboratory experiments provide precise observations of depths and friction coefficients in laminar flows passing fields of regular obstacles. After making the proposed correction for volumetric displacement, increases of 40 to 75 per cent in the derived value of the Darcy–Weisbach friction factor, f, are found for an obstacle cover of 20 per cent. Many published studies of friction coefficients in shallow overland flows, such as those on stone‐covered dryland soils, involve larger obstacle cover fractions, and evidently involve the significant confounding effect of volumetric displacement. Copyright © 2002 John Wiley & Sons, Ltd.