On disturbances in a viscoelastic solid rod of Burger's type subjected to a magnetic field

Summary The propagation of disturbances in a semi-infinite visco-elastic rod of Burger's type has been investigated, when the rod is subjected to an initially static magnetic field, making use of the electro-magnetic equations of Maxwell, equations of elasticity and the stress-strain relations of the material.     

Intensity determination by continuous thermal cycling

The advent of cryogenic magnetometers with which remanence can be measured at high sensitivity statically permits continuous thermal demagnetization and, in principle, a continuous version of the classic stepwise method of intensity determination. In the technique we have initially tried a field is trapped in the superconducting shield of the magnetometer throughout the experiment. The sample is then thermally cycled over progressively higher temperature ranges so that the incremental acquisition of partial thermoremanence (PTRM) and loss of the natural remanence (NRM) of the sample can be compared. In control experiments we have found that bad intensity estimates arise because the presence of the field causes difficulty in reliable separation of remanent and induced moments. A better approach is to heat and cool the sample in the required fields outside of the magnetometer and to insert it into the magnetometer only for the measurement of remanence. In this way it will be possible to cycle the sample to progressively higher temperatures and measure at elevated temperatures without cooling to room temperature, but one will measure remanence directly in zero field.     

PML solution of longitudinal wave propagation in heterogeneous media

This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.     

Attenuation of compressional waves in peridotite measured as a function of temperature at 200 MPa

A technique has been developed to determine attenuation in rocks at high temperature using a gas-media, high-pressure apparatus. A pulse transmission technique and a spectral ratio method are used to study compressional seismic properties of rocks. Seismic waves are transmitted to and from the sample through buffer rods of mullite. The effect of seismic wave reflections within the sample assembly are cancelled out by taking ratios of the spectra measured at different temperatures. In order to obtain good signal-to-noise ratio for resolving the attenuation at high pressure and temperature, special care is taken in the sample assembly and the ultrasonic coupling between the sample, buffer rods and transducers. A very tight connection of the sample-buffer rod-transducer is essential for obtaining high frequency signals (>300 kHz) at high temperature. A small mass is attached to each outside end of the transducer to drive low frequency signals (<250 kHz) into the sample. Before attenuation measurements, the sample and the buffer rods are tightly compacted in a platinum tube at high pressure and room temperature to ensure pressure seal of the sample assembly. The frequency range of measurement covers 50 to 450 kHz for the sample. Attenuation is very small in the buffer rod compared to the sample for the entire temperature range of the study. Because of the small attenuation, a wide frequency band of 50 kHz to 3.2 MHz can be covered for investigating the attenuation in the buffer rod. The technique has been used to measure attenuation at high confining pressure, and temperatures including sub- and hyper-solidus of upper mantle rocks. Therefore, effects of partial melting on attenuation can be studied.The method is applied to the attenuation measurement in a peridotite as a function of temperature to 1225°C at 200 MPa confining pressure. At high temperature, signal amplitude decays more rapidly at high frequency than at low frequency, from which attenuation (andQ) can be determined using a spectral ratio method. No frequency dependence ofQ is resolved for both the sample and the buffer rod over the entire temperature and frequency ranges of the measurement. The results show thatQ decreases rapidly with increasing temperature even in the temperature range below the solidus of peridotites. Such temperature sensitivity ofQ is probably more useful to probe thermal structure in the upper mantle than that of conductivity at temperatures below the solidus. The results in this study are compared with available seismic velocity, electrical conductivity and solidus data for peridotites, suggesting that there is no discontinuous change in both mechanical and electrical properties of peridotites at the solidus temperature. Even at hypersolidus temperatures, it appears that velocity drops and conductivity increases continuously (not abruptly) with increasing melt fraction. This implies that mechanical and electrical properties of the upper mantle will gradually change at the boundary where the geotherm crosses the solidus.     

Magneto-elastic waves and disturbances in initially stressed conducting media: II

Summary The paper is concerned with the investigation of the magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, (a) the steady state response to moving loads in a magneto-elastic initially stressed conducting medium under an uniaxial tension has been discussed. Secondly, (b) the Lamb's problem corresponding to a line load suddenly applied in a magneto-elastic initially stressed conducting half-space bounded by a plane under uniaxial tension has been investigated. The final results obtained in both cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

体应变仪大地震时两次自动调零数据的处理

仪器在较大波动幅度的影响下产生自动调零（电磁阀门开启）,与地震信息混在一起,难以直接使用原始数据。合理消除自动调零带来的影响,还原真实情况,成为台站必须解决的问题。采用确定校正值的方法,力图还原为连续记录,结果发现：处理后的资料可以和另外一台没有调零动作的体积应变仪器的原始资料相符合。     

Dynamic thermoelastic response of a cylinder

Pure and Applied Geophysics - In this paper, dynamic thermoelastic response of an infinite solid circular cylinder has been studied when the surface of the cylinder is kept at zero temperature...     

Constraints on velocity-depth trends from rock physics models

Estimates of depth, overpressure and amount of exhumation based on sonic data for a sedimentary formation rely on identification of a normal velocity–depth trend for the formation. Such trends describe how sonic velocity increases with depth in relatively homogeneous, brine‐saturated sedimentary formations as porosity is reduced during normal compaction (mechanical and chemical). Compaction is ‘normal’ when the fluid pressure is hydrostatic and the thickness of the overburden has not been reduced by exhumation. We suggest that normal porosity at the surface for a given lithology should be constrained by its critical porosity, i.e. the porosity limit above which a particular sediment exists only as a suspension. Consequently, normal velocity at the surface of unconsolidated sediments saturated with brine approaches the velocity of the sediment in suspension. Furthermore, porosity must approach zero at infinite depth, so the velocity approaches the matrix velocity of the rock and the velocity–depth gradient approaches zero. For sediments with initially good grain contact (when porosity is just below the critical porosity), the velocity gradient decreases with depth. By contrast, initially compliant sediments may have a maximum velocity gradient at some depth if we assume that porosity decreases exponentially with depth. We have used published velocity–porosity–depth relationships to formulate normal velocity–depth trends for consolidated sandstone with varying clay content and for marine shale dominated by smectite/illite. The first relationship is based on a modified Voigt trend (porosity scaled by critical porosity) and the second is based on a modified time‐average equation. Baselines for sandstone and shale in the North Sea agree with the established constraints and the shale trend can be applied to predict overpressure. A normal velocity–depth trend for a formation cannot be expressed from an arbitrary choice of mathematical functions and regression parameters, but should be considered as a physical model linked to the velocity–porosity transforms developed in rock physics.     

初始应力及磁场作用下导电粘弹体内的平面波

本文研究初始应力及磁场作用下导电粘弹体内的波动特性。首先导出有初始应力及磁场作用下导电粘弹体运动的基本方程,然后用它去研究流体静压力及单轴初始应力下波动方程的解,从平面简谐波的频散方程,分析了初始应力及磁场对波动传播的影响。粘弹体用Kelvin-Voigt模型,外磁场假定为均匀。所得结果表明,初始应力对波的影响随应力性质不同而有所差异,它既影响波的相速也影响波的衰减。磁场影响的大小决定于外磁场的强弱。从本文所得公式中,令外磁场为零,可得初始应力对波特性的影响;如令初始应力为零,就得到磁场对波的影响结果;令两者同时为零,即得粘弹波的经典结果。     

On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation

Pure and Applied Geophysics - Deflection and bending moments of a thin isotropic rectangular plate, having its edges simply supported and maintained at zero temperature, have been investigated in...     

Oceanography of coastal and riverine waters around Timika, West Central Irian Jaya, Arafura Sea

Oceanographic studies have been carried out in coastal and riverine waters of the area around Timika, West Papua in November 1999, March–April, July and November 2000. The temperature of the seawater along the coast is around 28 °C in winter (November 99), rising to 30.0 °C (November 00). In the open sea, 30 miles off the coast at 40 m water depth, the temperature is >30 °C with no stratification. Water temperature near the coast is consistently lower than in the open sea. This is thought to be due the cooling effect of the land, being densely covered by mangrove forest. In the upper parts of the Kamora, West Tipuka, East Tipuka, Ajkwa, Minajerwi, Mawati and Otakwa Rivers, at salinity zero psu, water temperature varies between 24.6 and 26.2 °C, which is as cold as the temperature in the upwelling Banda Sea to the NW. Some of these rivers are fed by glacial melt water from the high mountains to the east. At mid estuary, warm seawater is found under the cooler river water.Salinity near this coast varied between 24 and 30, and offshore salinity was 31–33 with no stratification. Inshore surface waters were turbid (11–14 ntu), and near bottom waters were generally much more turbid from river sediment supply and tidal resuspension. The Ajkwa River estuary has the highest turbidity (750 ntu) at zero salinity. Offshore waters were very clear (5.0–6.0 ntu), and there was no increase in turbidity near the bottom.     

A new model for the acquisition of thermoremanence by multidomain magnetite

Isothermal remanence (IRM) induced in multidomain grains at high temperature (T_i) decreases on cooling in zero field. The intensity and stability (against temperature change) of the IRM depend on whether the temperature (T_i) was reached from higher temperature or from lower temperature. These results cannot be explained by the existing multidomain theories. A new model of a thermoremanence (TRM) acquisition mechanism, in which domain wall interactions play the major role, is proposed. This model explains the main features of the experimental results very well, predicting an almost linear relationship between TRM and the inducing field, up to relatively high fields.     

滞变—摩擦基底隔震支座的试验和模型

本提出了一种滞变－摩擦基底隔震支座。这种支座由钢棒和摩擦元件组成，钢棒容许摩擦元件水平滑动，同时又限制这种滑动；摩擦元件承受结构的竖向荷载，作完成了钢棒滞变恢复力特性的试验，并给出了钢棒的滞变恢复力模型的模型参数的计算公式，该模型与常用的折线模型有所不同，它仅用一个非线性微分方程来描述滞变恢复力，而不需要复杂的规则。     

A new investigation on drift of base-line value in geomagnetic observation

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Finite strain theories and comparisons with seismological data

All the finite strain equations that we are aware of that are worth considering in connection with the interior of the Earth are given, with the assumptions on which they are based and corresponding relationships for incompressibility and its pressure derivatives in terms of density. In several cases, equations which have been presented as new or independent are shown to be particular examples of more general equations that are already familiar. Relationships for deriving finite strain equations from atomic potential functions or vice versa are given and, in particular it is pointed out that the Birch-Murnaghan formulation implies a sum of power law potentials with even powers. All the equations that survive simple plausibility tests are fitted to the lower mantle and outer core data for the PEM earth model. For this purpose the model data are extrapolated to zero temperature, using the Mie-Grüneisen equation to subtract the thermal pressure (at fixed density) and the pressure derivative of this equation to substract the thermal component of incompressibility. Fitting of finite strain equations to such zero temperature data is less ambiguous than fitting raw earth model data and leads immediately to estimates of the low temperature zero pressure parameters of earth materials. On this basis, using the best fitting equations and constraining core temperature to give an extrapolated incompressibilityK ₀=1.6×10¹¹Pa, compatible with a plausible iron alloy, the following numerical data are obtained: Core-mantle boundary temperature 3770 K Zero pressure, zero temperature densities: lower mantle 4190 kg m^–3 outer core (solidified) 7500 kg m^–3 Zero pressure, zero temperature incompressibility of the lower mantle 2.36×10¹¹PaHowever, an inconsistency is apparent betweenP() andK() data, indicating that, even in the PEM model, in which the lower mantle is represented by a single set of parameters, it is not perfectly homogeneous with respect to composition and phase.     

Non-linear soil-structure-interaction analysis using dynamic stiffness or flexibility of soil in the time domain

The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. Alternatively, a flexibility formulation for the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. The dynamic-stiffness or flexibility coefficient in the time domain is calculated as the inverse Fourier transform of the corresponding value in the frequency domain. The dynamic-stiffness coefficient's asymptotic behaviour for high frequencies determines the singular part whose transformation exists only in the sense of a distribution. As the dynamic-flexibility coefficient converges to zero for the frequency approaching infinity, the corresponding coefficient in the time domain is simpler to calculate, as no singular part exists. The salient features of the dynamic-stiffness and flexibility coefficients in the time domain are illustrated using a semi-infinite rod with exponentially increasing area. The dynamic-flexibility coefficients in the time domain are calculated for a rigid circular disc resting on the surface of an elastic halfspace and of a layer built-in at its base. Material damping is also introduced using the three-parameter Kelvin and the Voigt models.     

One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer

An analytical solution for the space-time variation of contaminant concentration in one-dimensional transient groundwater flow in a homogenous semi-infinite aquifer, subjected to time-dependent source contamination, is derived. The uniform and time varying dispersion along transient groundwater flow is investigated under two conditions. First, the flow velocity distribution in the aquifer is considered as a sinusoidally varying function, and second, the flow velocity distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free, so the initial background concentration is considered as an exponentially decreasing function of the space variable which is tending to zero at infinity. It is assumed that dispersion is directly proportional to the square of the velocity, noting that experimental observations indicate that dispersion is directly proportional to the velocity with a power ranging from 1 to 2. The analytical solution is illustrated using an example and may help benchmark numerical codes and solutions.     

Transient waves in a rod subjected to impulsive end loading

Herein the propagation of transient waves in a rod due to impulsive end loading is investigated using the method of wavefront expansion. The Mindlin–Herrmann equations which include the Poisson effect are used to model the rod. Since this rod theory is restricted to lower values of Poisson's ratio (< 0.283), the present work also has the same restriction. The impulsive end loading on the rod can be prescribed in the form of stress, strain, velocity or acceleration boundary conditions. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variables and their derivatives. These discontinuities are determined from a set of recurrence relations which are in turn generated by the use of time harmonic asymptotic series solutions to the equations of motion. Transients due to both velocity and strain (or stress) boundary conditions are treated. Numerical examples are presented to illustrate the method of solution. The results indicate the distortion of the transient waves due to the dispersive nature of the governing equations. Transients due to other boundary conditions at the rod end can be treated by using the results presented in the paper.     

Numerical versus field studies of delayed yield in response to a moving water-table

As pumping proceeds in an unconfined aquifer the water-table is lowered and slowly drains out of the initially saturated material giving a delayed yield from storage. Although considerable work has been carried out on delayed yield, a definitive solution is still lacking. The unsaturated zone was treated here as a significant factor in delayed yield analysis. The one-dimensional unsaturated flow equation was solved numerically to simulate the flow in the zone located between successive water levels in the unconfined aquifer for the case with zero flux at the upper boundary. The moisture content distribution curve was integrated numerically to determine the amount of water drained with time. The study shows that the numerical results are in close agreement with the monitored field data, which implies the important role of the unsaturated zone and the reliability of the numerical simulation in describing this physical phenomenon. The results show that the relationship between the flux and time is sensibly in exponential form, which agrees with the general applicability of Boulton's assumption.     

民乐盆地短水准测量精度分析与改进措施

根据误差理论及在民乐盆地等测量场地的观测试验结果，对影响短水准测量精度的各种因素进行了分析研究。结果表明，短水准测量精度主要受４种干扰因素影响：（１）温度变化引起水准标尺尺长误差；（２）仪器单面受热的影响；（３）尺桩升降的影响；（４）地面折光的影响。特别是第４种因素的影响尤为显著。针对上述４种干扰，本文提出了一些相应的改进措施。作者将这些措施应用到实际观测中，收到了较明显的效果。