Numerical simulations of full-wave fields and analysis of channel wave characteristics in 3-D coal mine roadway models

Currently, numerical simulations of seismic channel waves for the advance detection of geological structures in coal mine roadways focus mainly on modeling twodimensional wave fields and therefore cannot accurately simulate three-dimensional (3-D) full-wave fields or seismic records in a full-space observation system. In this study, we use the first-order velocity–stress staggered-grid finite difference algorithm to simulate 3-D full-wave fields with P-wave sources in front of coal mine roadways. We determine the three components of velocity V_x, V_y, and V_z for the same node in 3-D staggered-grid finite difference models by calculating the average value of V_y, and V_z of the nodes around the same node. We ascertain the wave patterns and their propagation characteristics in both symmetrical and asymmetric coal mine roadway models. Our simulation results indicate that the Rayleigh channel wave is stronger than the Love channel wave in front of the roadway face. The reflected Rayleigh waves from the roadway face are concentrated in the coal seam, release less energy to the roof and floor, and propagate for a longer distance. There are surface waves and refraction head waves around the roadway. In the seismic records, the Rayleigh wave energy is stronger than that of the Love channel wave along coal walls of the roadway, and the interference of the head waves and surface waves with the Rayleigh channel wave is weaker than with the Love channel wave. It is thus difficult to identify the Love channel wave in the seismic records. Increasing the depth of the receivers in the coal walls can effectively weaken the interference of surface waves with the Rayleigh channel wave, but cannot weaken the interference of surface waves with the Love channel wave. Our research results also suggest that the Love channel wave, which is often used to detect geological structures in coal mine stopes, is not suitable for detecting geological structures in front of coal mine roadways. Instead, the Rayleigh channel wave can be used for the advance detection of geological structures in coal mine roadways.     

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.     

Non-linear wave loads on large circular cylinders: a perturbation technique

The forces and overturning moments exerted by second order waves on large vertical circular cylinders are analysed. The mathematical equations governing the physical system are the three-dimensional Laplace's equation satisfied by the velocity potential ?(x,y,z,t) and the boundary conditions, namely the dynamic boundary condition which is obtained from the Bernoulli's equation, kinematic boundary condition, radiation condition, bottom boundary condition and the zero radial velocity condition on the surface of the cylinder. The non-linearity of the mathematical problem is evidenced in the free surface boundary conditions viz. dynamic and kinematic boundary conditions. Analytical solutions are obtained using the perturbation technique. These solutions are compared with various experimental data. The comparison shows favourable agreement between the theory and the experimental results.     

On the effects of a bumpy core-mantle interface

Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |?η/?χ| ? 1 and such that in the core [z < η(x)] a uniform flow (U₀, 0, 0) prevails in the presence of a uniform ‘toroidal’ field (B₀, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity Ω_H and a uniform small poloidal field B_p. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of Ω_H and B_p, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.     

Implications of turbulent shear on clay floc break-up along the Atlantic estuary (Bouregreg), Morocco

Water depth,salinity,current,and suspended sediment concentration(SSC)were measured along with the grain size distribution of bed sediment along an estuarine longitudinal section.The floc size increased with increase in the percentage of clay and silt,while decreased with increase in the percentage of sand content of bed sediment.The turbulent shear,G,had a direct effect on floc size with its value increasing with increase in G up to a G value of 15 s^-1,while an inverse relation existed between floc size and G at higher G(G>15 s^-1).Further,higher turbulence enabled sand to get resuspended and cause additional shear leading to the break-up of flocs.An attempt was made to modify G to account for the combined effect of water turbulence(G)and shear imparted by sand(Ga)and the impact of the modification of G on the predictability of floc size was evaluated.A new model was developed which explains floc size in terms of sediment concentration(C),salinity gradient(S),and G for different scenarios based on the value of G.Sensitivity analysis was done for observed floc size(FS)and predicted floc size using four approaches:(I)FSαC^x;(II)FSαC^xS-y;(III)FSαC^xS^-yGz for G<15 s^-1and FSαC^xS^-yG-z for G>15 s^-1;and(IV)FSαC^xS^-yG_m^-zfor G>15 s^-1and G_m=G+Ga,where x,y,and z are determined by calibration.It was observed that the predictability of the floc size improved when the turbulence was modified to account for shear imparted by sand so that the coefficient of determination was increased from 0.78 for model III to 0.89 for model IV.Further,the settling velocity was expressed as a function of suspended sediment concentration,turbulent shear,and salinity gradient.The predictability of settling velocity was improved(R2 increased from 0.77 to 0.86)when the additional turbulence created by sand was incorporated in the non-dimensional empirical equation.The study highlights the influence of sand in causing the break-up of flocs and suggests that for turbulence shear values high enough to resuspend sand,and G has to be modified to account for the additional shear imparted by sand in mixed sediment estuarine environments.     

Statistical relations between the probability of occurrence of Pc3-4 pulsations at high latitudes in the antarctic regions and the solar wind and IMF parameters

Geomagnetic pulsation in the Pc3-4 bands have been studied at high Antarctic latitudes during the local summer. The statistical relation between the occurrence probability of Pc3 and Pc4 pulsations and the solar wind (SW) and IMF parameters has been revealed by verifying the hypothesis that an indication is identical in two distributions. Different dependences of the occurrence probability of high-latitude Pc3 and Pc4 pulsations on the IMF value and orientation and SW density and velocity have been found out. It has been indicated that these dependences remain unchanged in the range of geomagnetic latitudes from 66° to 87°. It has been established that the Pc3 observation probability at small (20°–50°) IMF cone angles (θ = cos^?1(B _x/|B|)) is a factor of 1.5 higher than the average statistical probability and depends on the IMF value, which confirms the hypothesis that the Pc3 source is the turbulent region upstream of the magnetospheric quasiparallel low shock. On the contrary, the probability of occurrence of Pc4 weakly depends on the IMF cone angle and is maximal at θ ～ 0° and ～90°. With increasing negative B _z values, the generation probability increases in the Pc4 band and tends to decrease in the Pc3 band. It has been found out for the first time that the dependence of the Pc4 occurrence probability on the IMF clock angle (? = tan^?2 (B/B _z) is identical in the regions of projections of closed and open field lines, whereas this dependence is different for Pc3. In the region of projections of closed field lines, the Pc3 occurrence probability increases at B _z < 0 and B _y > 0 (the condition under which the cusp shifts on the dawn side) and at B _y < 0 and B _z > 0 (which is typical of the formation of the low-latitude boundary plasma sheet). In the region of projections of open field lines such a probability increases at B _y < 0 and B _z < 0 (which results in the formation of the high-latitude boundary plasma sheet). Based on the discovered regularities, the conclusion has been made that the sources of generation of high-latitude Pc3 and Pc4 pulsations are different.     

An observational study of 300 mb winds in the tropical belt. Part I: Kinematic parameters

This study is diagnostic in character and entails a systematic investigation of the kinematic parameters of the mean monthly 300 mb horizontal-motion field for the global tropical region during January, April, and October. The kinematic parameters analysed include the horizontal velocity divergence, relative vorticity, velocity potential, and stream function. The magnitude of relative voritcity has been observed to be nearly equal to that of the horizontal velocity divergence in the equatorial latitudes and an order of magnitude larger in the subtropics. The magnitudes of?u/?x, ?v/?y, and horizontal velocity divergence are comparable and vary very little with latitude, while that of?u/?y is an order of magnitude larger than that of?v/?x, confirming its dominance in the computation of relative vorticity. The latitudinal position of zero absolute vorticity isopleth fluctuates within 5 degrees of the equator and is confined more to the winter hemisphere than to the summer hemisphere. The rotational component of wind is large compared with the divergent wind component. The magnitude of the rotational vector wind is four times that of the divergent vector wind in the equatorial latitudes and an order of magnitude larger in the subtropical latitudes.     

The α-effect in 2D fast dynamos

We look at the large-scale dynamo properties of spatially periodic, time dependent, helical 2D flows of the form u(x, t)?=?(? _y ?ψ?(x, y, t), ?? _x ?ψ?(x, y, t), ?ψ (x, y, t). These flows act as kinematic fast dynamos and are able to generate a mean magnetic field uniform and constant in the xy-plane but whose direction varies periodically along z with wavenumber k. Using Mean Field Electrodynamics, the generation mechanism can be understood in terms of a k-dependent α-effect, which depends on the magnetic Reynolds number, R _m . We calculate this effect for different motions and investigate how its limit as k?→?0 depends on R _m and on the properties of the flows such as their spatial structure or correlation time. This work generalises earlier studies based on 2D steady flows to motions with time dependence.     

Dynamic analysis of offshore wind turbine in clay considering soil–monopile–tower interaction

A comprehensive study is performed on the dynamic behavior of offshore wind turbine (OWT) structure supported on monopile foundation in clay. The system is modeled using a beam on nonlinear Winkler foundation model. Soil resistance is modeled using American Petroleum Institute based cyclic p–y and t–z curves. Dynamic analysis is carried out in time domain using finite element method considering wind and wave loads. Several parameters, such as soil–monopile–tower interaction, rotor and wave frequencies, wind and wave loading parameters, and length, diameter and thickness of monopile affecting the dynamic characteristics of OWT system and the responses are investigated. The study shows soil–monopile–tower interaction increases response of tower and monopile. Soil nonlinearity increases the system response at higher wind speed. Rotor frequency is found to have dominant role than blade passing frequency and wave frequency. Magnitude of wave load is important for design rather than resonance from wave frequency.     

An analogue model study of electromagnetic induction in the Tasmania region

Laboratory analogue model magnetic measurements are carried out for a model of the region including Tasmania, Bass Strait with its highly conductive deep sedimentary basins, and the south coast of mainland Australia. The model source frequencies used simulate naturally occurring geomagnetic variations of periods 5–120 min. In-phase and quadrature magnetic H_x, H_y and H_z field measurements for the modelled region are presented for an approximately uniform overhead horizontal source field for E-polarization (electric field of the source in the N-S direction) and for H-polarization (electric field of the source in the E-W direction). Large anomalous in-phase and quadrature model magnetic fields are observed over Bass Strait and the coastal regions at short periods for both E- and H-polarization, but with increasing period, the field anomalies decrease more rapidly for E-polarization, than for H-polarization. The difference in response with polarization for the Bass Strait region is attributed to current induced in the deep ocean, for all periods, being channelled through Bass Strait for H-polarization but not for E-polarization. The persistent large coastal field anomalies elsewhere, for H-polarization, can be accounted for by the coastal current concentrations due to currents induced in the deep ocean for all periods deflected to the south and to the north by the shelving sea-floor and channelled through Bass Strait and around the southern coast of Tasmania. The phenomena of current deflection and channelling for H-polarization for the geometry of the southern Australia coastline and associated ocean bathymetry is particularly effective in producing field anomalies for a large period range.The coastal horizontal H_x and H_y field anomalies, present for E-polarization at short periods and for H-polarization at all periods, do not extend far inland, and thus, for inland station sites somewhat removed from the coast, should not present serious problems for magnetic soundings in field work. The sharp vertical field (H_z) gradient over Tasmania at short periods, which is predominantly in the E-W direction for E-polarization and the N-S direction for H-polarization, is strongly frequency dependent, becoming almost undetectable at 60 min. The behaviour of the H_z field gradients, however, are very similar from traverse to traverse over inland Tasmania, and thus, the effects of the ocean should not present too serious a problem in the interpretation of field station studies. The discrepancies between model and field station results should be useful in mapping geological boundaries in the region.     

б-sharpen immersed boundary method(б-SIBM)—New method for solving the horizontal pressure-gradient force(PGF) problem of б-coordinate

Althoughб-coordinate is one of the most popular methods used in marine and estuarine modeling,it has long suffered from the so-called"steep boundary problem",namely,the PGF problem.In this paper,a new method called the"б-sharpen immersed boundary method"(б-SIBM)is put forward.In this method,the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain.By this,бHбx of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem,which is,in turn,solved by the SIBM.The accuracy and efficiency of theб-sharpen immersed boundary method(б-SIBM)has been showed by both comparative theoretical analysis and classical numerical tests.First,it is shown that theб-SIBM is more effective than the z-level method,in thatб-SIBM needs special treatment only in the steep section,but the z-level method needs the special treatment in each grid note.Second,it is superior to theб-method in that it is not restricted by the density distribution.This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force(PGFE)and their long-term effects on circulation.It can be seen that,as for the maximum erroneous velocity and kinetic energy,the value ofб-SIBM is much less than that of the z-level method and the traditionalб-method.sharpen immersed boundary method(SIBM),immersed boundary method(IBM),direct forcing method,б-coordinate,     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

APPROXIMATION OF THE GRAVITATIONAL ATTRACTION OF GEOLOGICAL BODIES*

The gravitational attraction produced by a geological body of irregular shape can be easily determined by dividing it into cubes of small size. The exact expression of the effect of a cube is very complicated, but it can be calculated by using an electronic computer. 4851 values of the gravitational attraction were determined for different positions of a cube with the side of 2l and the center in M(x₀, y₀, z₀), for x₀∈[0;20], y₀∈[0;20] and z₀∈[0;10]. Using these values, templates in double logarithmic representation were drawn, with x₀ and z₀ as parameters and y₀ as abscissa, and with x₀ and y₀ as parameters and z₀ in abscissa; this double set of templates permits a good interpolation for all cubes in the considered domain of M. The use of templates was tested to approximate the effect produced by a theoretical model of spherical shape and in a real case of a three-dimensional salt body of known shape based on a large number of boreholes. In both cases very good results were obtained.     

Influence of the solar wind plasma density on the auroral precipitation characteristics

Based on the DMSP F6 and F7 satellite observations, the characteristics of precipitating particles in different auroral precipitation regions of the dayside sector have been studied depending on the solar wind plasma density. Under quiet geomagnetic conditions (|AL| < 100 nT and B _z > 0), a considerable increase in the fluxes of precipitating ions is observed in the zones of structured auroral oval precipitation (AOP) and soft diffuse precipitation (SDP). A decrease in the mean energy of precipitating ions is observed simultaneously with the flux growth in these regions. The global pattern of variations in the fluxes of precipitating ions, which shows the regions of effective penetration of solar wind particles into the magnetosphere at a change in the solar wind density from 2 to 20 cm^?3, has been constructed. The maximal flux variation (ΔJ _i = 1.8 · 10⁷ cm^?2 s^?1, i.e., 3.5% of an increase in the solar wind particle flux) is observed in the SDP region on the dayside of the Earth. The dependence of precipitating ion fluxes in the low-latitude boundary layer (LLBL), dayside polar cusp, and mantle on the solar wind density at positive and negative values of the IMF B _z component has been studied. In the cusp region, an increase in the precipitating ion flux is approximately 17% of an increase in the solar wind density. The IMF southward turning does not result in an appreciable increase in the ion precipitation fluxes either in the cusp or in the mantle. This fact can indicate that the reconnection of the geomagnetic field with southward IMF is not the most effective mechanism for penetration of solar wind particles into these regions.     

消除海底起伏影响的海洋地震波场正反向延拓

为了解决海底起伏变化对地震波场的影响问题,本文提出将（x-z）域中的曲网格映射成（ξ,η）域中的矩形网格,推导出（ξ,η）域中的二维标量声波方程,根据推导出来的波动方程采用逆时有限差分法将海面上采集到的地震波场在（ξ,η）域中向下延拓至海底面,延拓时采用海水的速度,然后采用顺时有限差分法将延拓后的地震波场再反延拓到海面上,延拓时采用海底面以下地层的速度,从而消除了海底起伏带来的负面影响。模型及实际地震资料的计算分析表明该方法不但能够校正由于海底起伏所引起的海底面下地层反射波场的不连续性还能够校正由于海底起伏所引起的地震波的动力学特征的变化。对延拓前后的地震波场进行速度反演,延拓后反演的地层速度比延拓前反演的地层速度的精度提高很多,延拓前后地震波场的叠加剖面对比表明该延拓方法能够明显提高地震波场的成像质量。     

Dependence of geomagnetic disturbances on extreme values of the solar wind <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> component

The dependence of the zonal geomagnetic indices (AE, Ap, Kp, Kn, and Dst) on the solar wind parameters (the electric field E _y component, dynamic pressure P _d and IMF irregularity σB) has been studied for two types of events: magnetic clouds and high-speed streams. Based on the empirical relationships, it has been established that the AE, Ap, Kp, and Kn indices are directly proportional to the E _y value at E _y < 12 mV m^?1 and are inversely proportional to this value at E _y > 12 mV m^?1 for the first-type events. On the contrary, the dependence of Dst on E _y is monotonous nonlinear. A linear dependence of all geomagnetic indices on E _y is typical of the second-type events. It has been indicated that the specific features of geoeffectiveness of magnetic clouds and high-speed solar wind streams are caused by the dependence of the electric field potential across the polar cap on the electric field, solar wind dynamic pressure, and IMF fluctuations.     

Numerical solution of the complete equations for nearly horizontal flows

The complete mathematical model for the non steady hydrodynamic circulation due to wind, waves and density gradients in a coastal area or a lake is solved by the combined application of the weighted residuals—Galerkin method and the finite difference method. The computation of u and v velocity components in x, y, z, t space is achieved through expansion in series of base functions times undetermined coefficients over the depth. The computation of these coefficients giving the vertical variation of the velocity is done by the Galerkin method. The rapid convergence of this procedure permits a quick and economic evaluation of 3-D flows on a 2-D grid (in x, y space). The capabilities of the method were demonstrated by applying it to a tidal flow in an estuary.     

Noncausal f–x–y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data

Seismic noise attenuation is very important for seismic data analysis and interpretation, especially for 3D seismic data. In this paper, we propose a novel method for 3D seismic random noise attenuation by applying noncausal regularized nonstationary autoregression (NRNA) in f–x–y domain. The proposed method, 3D NRNA (f–x–y domain) is the extended version of 2D NRNA (f–x domain). f–x–y NRNA can adaptively estimate seismic events of which slopes vary in 3D space. The key idea of this paper is to consider that the central trace can be predicted by all around this trace from all directions in 3D seismic cube, while the 2D f–x NRNA just considers that the middle trace can be predicted by adjacent traces along one space direction. 3D f–x–y NRNA uses more information from circumjacent traces than 2D f–x NRNA to estimate signals. Shaping regularization technology guarantees that the nonstationary autoregression problem can be realizable in mathematics with high computational efficiency. Synthetic and field data examples demonstrate that, compared with f–x NRNA method, f–x–y NRNA can be more effective in suppressing random noise and improve trace-by-trace consistency, which are useful in conjunction with interactive interpretation and auto-picking tools such as automatic event tracking.     

Theoretical grain size limits for single-domain,pseudo-single-domain and multi-domain behavior in titanomagnetite (x = 0.6) as a function of low-temperature oxidation

A theoretical model of grain size variation of domain transitions in titanomagnetite (x = 0.6) as a function of oxidation (z) is presented. The superparamagnetic (SP) to single-domain (SD) transition d_s, the SD to two-domain (TD) transition d₀, the TD to three-domain (3D) transition and the pseudo-single domain (PSD) to multi-domain (MD) transition are calculated as a function of z. It is shown that all the transition grain sizes increase with z, except for the PSD-MD transition for z > 0.6. The calculations predict that d_s increases from 0.044 to 0.197 μm, d₀ increases from 0.54 to 13 μm, the TD-3D transition increases from 1.6 to 49 μm as z varies from 0 to 0.8. The PSD-MD transition increases from 42 μm at z = 0 to 150 μm at z = 0.6, whereas between z = 0.6 to z = 0.8, the PSD-MD transition decreases to 49 μm. Qualitatively, the model explains some of the trends in magnetic properties of submarine basalts with low-temperature oxidation. Quantitatively, the model does give reasonable estimates of the PSD-MD boundary and d₀, which are close to the experimental values for x = 0.6 and z = 0. Furthermore, the model predicts that psarks or two-domain grains could be the major contributors to the remanence of oxidized submarine pillow basalts.