Geomagnetic field analysis—IV. Testing the frozen-flux hypothesis

Summary. We present a model of the magnetic field at the core–mantle boundary, for epoch 1959.5, based on a large set of observatory and survey measurements. Formal error estimates for the radial field at the core are 50 μT, compared with 30 and 40 μT for our previous MAGSAT (1980) and POGO (1970) models.
Current work on the determination of the velocity of the core fluid relies on the assumption that the core behaves as a perfect conductor, so that the field lines remain frozen to the fluid at the core surface. This frozen-flux condition requires that the integrated flux over patches of the core surface bounded by contours of zero radial field remain constant in time. A new method is presented for constructing core fields that satisfy these frozen-flux constraints. The constraints are non-linear when applied to main field data, unlike the case of secular variation which was considered in an earlier paper. The method is applied to datasets from epochs 1969.5 and 1959.5 to produce fields with the same flux integrals as the 1980 model.
The frozen-flux hypothesis is tested by comparing the changes in the flux integrals between 1980/1969.5, 1969.5/1959.5 and 1980/1959.5 with their errors. We find that the hypothesis can be rejected with 95 per cent confidence. The main evidence for flux diffusion is in the South Atlantic region, where a new null flux curve appears between 1960 and 1970, and continues to grow at a rapid rate from 1970 to 1980. However, the statistical result depends critically on our error estimates for the field at the core surface, which are difficult to assess with any certainty; indeed, doubling the error estimates negates the statistical argument. The conclusion is therefore, at this stage, tentative, and requires further evidence, either from older data, if good enough, or from future satellite measurements.     

Motions at the core surface derived from SV data

Summary. Examples of core motions which generate the observed secular variation field – as given by various models for 1970 and 1980 – from the main field have been computed in the frozen flux approximation, assuming that the spectrum of the motion is of low degree and decreases with wave-number. No mode of degree > 4 in the expansion of the motion can be derived with any degree of confidence. Among the low degree modes, some appear to be stable (they come out with the same magnitude whatever the inversion scheme used). The flow made of these stable modes is then examined. An outstanding feature of the flow is the body westward drift. But it seems necessary, if one looks for such a regular flow, to consider both toroïdal and poloïdal components, which would imply upwelling and down-welling in the upper layers of the core. The toroïdal part of the flow appears to be enhanced by the 1969 impulse, although its geometry is nearly unchanged. On the contrary the geometry of the computed poloïdal part is different in 1980 and in 1970;     

Invariants in toroidal and tangentially geostrophic frozen-flux velocity fields

We derive two new types of invariant that must be obeyed by the radial magnetic field at the core-mantle boundary if the hypothesis of frozen flux is valid and the fluid motion is either toroidal or tangentially geostrophic there. These general invariants incorporate specific invariants that are already known and can, in principle, be tested using magnetic data that cover an interval of time.     

Geomagnetic field analysis - I. Stochastic inversion

Summary. Most of the Earth's magnetic field and its secular change originate in the core. Provided the mantle can be treated as an electrical insulator, stochastic inversion enables surface observations to be analysed for the core field. A priori information about the variation of the field at the core boundary leads to very stringent conditions at the Earth's surface. The field models are identical with those derived from the method of harmonic splines (Shure, Parker & Backus) provided the a priori information is specified appropriately.
The method is applied to secular variation data from 106 magnetic observatories. Model predictions for fields at the Earth's surface have error estimates associated with them that appear realistic. For plausible choices of a priori information the error of the field at the core is unbounded, but integrals over patches of the core surface can have finite errors. The hypothesis that magnetic fields are frozen to the core fluid implies that certain integrals of the secular variation vanish. This idea is tested by computing the integrals and their standard and maximum errors. Most of the integrals are within one standard deviation of zero, but those over the large patches to the north and south of the magnetic equator are many times their standard error, because of the dominating influence of the decaying dipole. All integrals are well within their maximum error, indicating that it will be possible to construct core fields, consistent with frozen flux, that satisfy the observations.     

Study on the sunny-shady slope effect on the subgrade of a high-speed railway in a seasonal frozen region

The temperature distributions of different parts of a subgrade were analyzed based on the results of three years of monitoring data from the Harbin-Qiqihaer Passenger Dedicated Line, a high-speed railway, including the slope toes, shoulders, and natural ground. The temperature variation with time and the maximum frozen depths showed that an obvious sunny-shady effect exists in the railway subgrade, which spans a seasonal frozen region. Development of frost heave is affected by the asymmetric temperature distribution. The temperature field and the maximum frozen depths 50 years after the subgrade was built were simulated with a mathematical model of the unsteady phase transition of the geothermal field.     

改进的热惯量模式及遥感土壤水分

本文提出一个考虑地表显热通量及潜热通量的热惯量模式。模式利用了地面定标的方法并充分利用了热象图的空间分布信息,因而较大幅度地提高了估算土壤水分含量的精度。     

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

Summary. Previous studies, both geomagnetic and seismic, have been unable to show conclusively whether or not there is fluid upwelling at the core-mantle boundary. Here a new method is developed, in which an attempt is made to invert geomagnetic secular variation data measured at the Earth's surface for a frozen-flux purely toroidal core-mantle boundary (CMB) velocity field, under the assumption that the mantle is electrically insulating and flux is frozen in at the CMB. These data have previously been inverted for the core-mantle boundary radial secular variation, from which the appropriate fit between model and data is known. Two different main field models were used to assess the effect of uncertainty in its radial component at the CMB. The conclusions were the same in both cases: frozen-flux purely toroidal motions provide a poor fit. A statistical test allows very firm rejection of the hypothesis that the residuals are not significantly larger, whereas there is no statistical difference between the residuals of inversions for radial secular variation and frozen-flux velocity fields at the CMB if upwelling and down-welling is included. The inherent non-uniqueness in the velocity field obtained is not of concern, since only their statistical properties are utilized and no physical significance is attached to the flows obtained.     

Wind velocity and sand transport on a barchan dune

We present measurements of wind velocity and sand flux performed on the windward side of a large barchan dune in Jericoacoara, northeastern Brazil. From the measured profile, we calculate the air shear stress using an analytical approximation and treat the problem of flow separation by an heuristic model. We find that the results from this approach agree well with our field data. Moreover, using the calculated shear velocity, we predict the sand flux according to well-known equilibrium relations and with a phenomenological continuum saltation model that includes saturation transients and thus allows for nonequilibrium conditions. Based on the field data and theoretical predicted results, we indicate the principal differences between saturated and nonsaturated sand flux models. Finally, we show that the measured dune moves with invariant shape and predict its velocity from our data and calculations.     

Equation for the field lines of an axisymmetric magnetic multipole

Summary. An exact equation is derived for the magnetic field lines of the general axisymmetric magnetic multipole of arbitrary degree ( n ). This new result has important applications in studies of the possible nature of solarterrestrial physics during geomagnetic polarity reversals. In the limiting case of a magnetic dipole ( n=1 ), the equation for the magnetic field lines of the general axisymmetric magnetic multipole simplifies correctly to the well-known dipolar form, which is used extensively in geomagnetism, magnetospheric physics and cosmic-ray physics as a first-order approximation to the actual configuration of the geomagnetic field.
It is also shown theoretically that suites of similar magnetic field lines of the general axisymmetric multipole attain their maximum radial distances from the origin on a set of circular conical surfaces, with coincident vertices at the centre of the Earth; this set includes the equatorial plane if the degree ( n ) of the multipole is odd. The magnetic field is horizontal everywhere on all these surfaces.
Palaeomagnetic studies have suggested that during some polarity reversals the magnetic field in the inner magnetosphere can be represented approximately either by a single, non-dipolar, low-degree (2 < n < 4), axisymmetric magnetic multipole or by a linear combination of such multipoles. In this situation, the equation for the field lines of an axisymmetric magnetic multipole of low degree (2 < n < 4) would be as fundamental to a proper understanding of magnetospheric, ionospheric and cosmic-ray physics during polarity reversals as is the equation for dipolar field lines in the case of the contemporary geomagnetic field.     

Bilateral propagation of a spontaneous two-dimensional anti-plane shear crack under the influence of cohesion

Summary. We consider the problem of the bilateral extension of a two-dimensional anti-plane shear crack that initiates spontaneously at a point and extends under the influence of cohesive forces at the edges. An approximation to the stresses in the regions beyond the edges of the crack has been found that simplifies the calculation. The exact stresses in these regions are also found iteratively. In the cases of uniformly propagating cracks, the estimates of cohesive forces obtained from the approximation are close to the exact values for high crack speeds but are significantly different for low crack speeds. It is also found that if healing is initiated due to the encounter of one end of a uniformly propagating crack with an unbreakable barrier, the static stress drop in the torn region is constant but may either overshoot or undershoot the dynamical stress drop. In these cases, the final static slip distribution is obtained by freezing the dynamic solution along a characteristic line through the location of the barrier. We find that the crack length cannot be unambiguously derived from the far field spectral properties.     

极尖纬度午后极光嘶声的极大发生率

极尖纬度午后区是一个异常等离子体过程区，已发现该区在低地磁扰动条件下，多种空间物理现象活动强度极大（相对邻区）：强的向上场向电流，向下低能电子流极大，向上离子通量极大，Ｆ层电子密度极大等等。导致该区异常的根本原因尚不清楚。本文利用南极点站（磁纬约７５°）的极光嘶声的电场强度进行统计分析，发现该区３１－３８ｋＨｚ波段极光嘶声的发生率极大。本文还分析了该区极光嘶声发生率与地磁活动指数Ａｐ的关系，结果表明，它们之间有明显的相关关系。     

塔克拉玛干沙漠腹地土壤热通量变化特征

利用2009-2011年塔克拉玛干沙漠大气环境观测试验站测得的土壤热通量数据,分析了塔克拉玛干沙漠腹地土壤热通量在不同天气条件下的变化特征。结果表明：（1）塔克拉玛干沙漠腹地1 cm处土壤热通量年平均值为1.9 W·m^-2,5、20、40 cm处分别为1.0、0.4、0.4 W·m^-2;1 cm处土壤热通量年最大值为334.1 W·m²,年最小值为-184.2 W·m^-2;土壤热通量基本表现为夏季 > 春季 > 秋季 > 冬季。（2）各土层土壤热通量具有明显的日变化特征。随着土壤深度的加大,土壤热通量的日变化幅度明显减小,最大值出现的时间有一定的滞后性。土壤热通量5 cm出现最大值的时间比1 cm处延迟3 h,延迟速率为0.75 h·cm^-1,20 cm比5 cm出现最大值的时间晚2 h,延迟速率约为0.13 h·cm^-1。（3）不同天气情况下的土壤热通量日变化特征有一定的差异,晴天较为规则,阴天、雨天、沙尘天则较不规则,且1 cm处土壤热通量受天气影响最显著。晴天1 cm处土壤热通量平均值为9.0 W·m^-2;阴天、雨天、沙尘天1 cm处土壤热通量值平均值分别为5.1、-6.1、-1.9 W·m^-2。     

华北平原典型农田水、热与CO2通量的测定

在中国科学院栾城农业生态试验站用波文比-能量平衡法与涡度相关技术对净辐射通量（Rn)，潜热通量（λE），感热通量（H），土壤热通量（G）与冠层CO2通量（Fco2)进行了长期定位研究，结果显示Rn大部分用于作物潜热的消耗，连续2年4个生长季λE/Rn都在70%以上，在作物生育盛期，夏玉米λE/Rn略高于冬小麦，H/Rn都在15%左右，G/Rn在5%-13%之间，且冬小麦G/Rn明显高于夏玉米。蒸发比值（EF）在不同的理想环境条件下，随着可供能量（Rn-G)的增加表现出先迅速下降，后缓慢下降，最后趋于稳定的趋势，并在冬小麦环境条件下得到了验证，直角双曲线模型可以模拟Fco2随光通量密度（PPFD）的响应过程。晴天冠层水分利用效率（WUE）不是在正午出现最高值，当PPFD达到1500μmolm^-2s^-1左右时，WUE却略有下降。     

Gaussian beams, complex rays, and the analytic extension of the Green's function in smoothly inhomogeneous media

Summary. Some relations between Gaussian beams, complex rays and the analytic extension of the Green's function in smoothly inhomogeneous media are shown in this paper. It is found that: (1) a single Gaussian beam is a paraxial approximation of the analytical extension of the ray-approximated Green's function in smoothly inhomogeneous media by putting the source point into a complex space. The Gaussian beam approximation of the Green's function has an advantage in computational efficiency and stability and can avoid the singularity problems at caustics, but also introduces a parabolic approximation to the wavefront and an angle-dependent amplitude damping. Therefore the validity of the Gaussian beam approximation should be checked using other methods. (2) Complex-ray tracing, which does not involve the paraxial approximation, can also avoid the singularity problemsm though without the computational efficiency. Therefore, it should be used to verify the Gaussian beam approximation, whenever possible. (3) The decomposition of a plane wave into an ensemble of Gaussian beams is equivalent to approximating the Green's function (the kernel of the ray-Kirchhoff method) with a single Gaussian beam. This introduces a parabolic approximation to the wavefront and a Gaussian windowing for arrival angles which may cause some problems in modelling wave propagation and scattering and has no advantages over other methods. (4) The representation of a point source field by a superposition of Gaussian beams, on the other hand, is equivalent to approximating the Green's function with a bundle of overlapped Gaussian beams. This representation is similar to a Maslov uniform asymptotic representation. It has no caustics and has improved accuracies at the caustics for quasi-plane waves compared to the extended WKBJ method.     

Dynamic processes of a simple linear dune—a study in the Taklimakan Sand Sea, China

Samples of dune sands, surveys of the morphology and field measurements of wind velocity and direction of a simple linear dune in Taklimakan Sand Sea show that the airflow and sand flux vary with the change of wind direction on the dune surface. Decrease of the airflow stress on the lee flank does not result in much decrease of the sand flux because of the low threshold shear velocities and the airflow conditions. There are no significant relations between the sand flux on the lee flank and the angle of incidence of the airflow. The low threshold shear velocities and the maintenance of the sand flux at the lee flank are the main mechanisms keeping the linear shape of the dunes. Measurements of the sand flux shows that it reaches a maximum on the crest of the dune. The grain size of the transported sands has some differences compared to that of the dune surface. The sands transported are finer than that on the dune surface, but better sorted under the influence of the medium to low wind activity. The field experiment results exhibit that it is possible for the dunes to be shaped as linear dunes during the processes of accumulation and elongation.     

Maximum entropy regularization of the geomagnetic core field inverse problem

The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey-scale image). The problem of reconstructing the magnetic field at the core–mantle boundary from surface data is a problem where the target image, the value of the radial field B_r , can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.     

二维沙丘迎风坡沙粒跃移运动的数值模拟

为了研究沙丘迎风坡面上沙粒的跃移运动,本文根据风工程和空气动力学的最新理论,给出了沙丘迎风坡面上风场的空间分布规律,在此基础上对沙粒跃移运动进行了数值计算。由于沙丘周围流场情况较为复杂,各处的风速廓线也不同,故选取不同的坡面位置进行跃移计算,其中各处的起沙率由已有的实验结果或拟合公式给出。计算结果表明：从坡脚到坡顶,平均风速加速比和摩阻风速逐渐增加,到沙丘顶部达到最大值;同时沿坡面向上,各截面处单宽输沙率和距离当地地面相同高度处输沙浓度逐渐加强,这与已有文献报道的结果吻合良好。     

Unilateral extension of a two-dimensional shear crack under the influence of cohesive forces

Summary. We consider the problem of the unilateral extension of a two-dimensional anti-plane crack that initiates spontaneously at a point. The crack extends under the influence of cohesive resistance at the edge and dynamical friction along the crack walls. The stresses in the region beyond the edge of the crack are approximated so that they are exactly equal to the cohesive stresses near the edge of the crack, and are zero on the wavefront. An exact method of solving such problems is also given and can be used to determine the validity of the approximation. We find that the crack will not grow if the cohesion exceeds some critical value; this is consistent with an earlier result obtained by Knopoff, Mouton & Burridge for a similar one-dimensional model of crack propagation.     

Taking into account truncation problems and geomagnetic model accuracy in assessing computed flows at the core-mantle boundary

SUMMARY
Since the time Roberts & Scott (1965) first expressed the key 'frozen flux' hypothesis relating the secular variation of the geomagnetic field (SV) to the flow at the core surface, a large number of studies have been devoted to building maps of the flow and inferring its fundamental properties from magnetic observations at the Earth's surface. There are some well-known difficulties in carrying out these studies, such as the one linked to the non-uniqueness of the flow solution [if no additional constraint is imposed on the flow (Backus 1968)] which has been thoroughly investigated. In contrast little investigation has been made up to now to estimate the exact importance of other difficulties, although the different authors are usually well aware of their existence. In this paper we intend to make as systematic as possible a study of the limitations linked to the use of truncated spherical harmonic expansions in the computation of the flow. Our approach does not rely on other assumptions than the frozen flux, the insulating mantle and the large-scale flow assumptions along with some simple statistical assumptions concerning the flow and the Main Field. Our conclusions therefore apply to any (toroidal, steady or tangentially geostrophic) of the flow models that have already been produced; they can be summarized in the following way: first, because of the unavoidable truncation of the spherical harmonic expansion of the Main Field to degree 13, no information will ever be derived for the components of the flow with degree larger than 12; second, one may truncate the spherical harmonic expansion of the flow to degree 12 with only a small impact on the first degrees of the flow. Third, with the data available at the present day, the components of the flow with degree less than 5 are fairly well known whereas those with degree greater than 8 are absolutely unconstrained.     

Simulated effect of soil freeze-thaw process on surface hydrologic and thermal fluxes in frozen ground region of the Northern Hemisphere

Soil freeze-thaw process is closely related to surface energy budget,hydrological activity,and terrestrial ecosystems.In this study,two numerical experiments(including and excluding soil freeze-thaw process)were designed to examine the effect of soil freeze-thaw process on surface hydrologic and thermal fluxes in frozen ground region in the Northern Hemisphere based on the state-of-the-art Community Earth System Model version 1.0.5.Results show that in response to soil freeze-thaw process,the area averaged soil temperature in the shallow layer(0.0175?0.0451 m)decreases by 0.35℃in the TP(Tibetan Plateau),0.69℃in CES(Central and Eastern Siberia),and 0.6℃in NA(North America)during summer,and increases by 1.93℃in the TP,2.28℃in CES and 1.61℃in NA during winter,respectively.Meanwhile,in response to soil freeze-thaw process,the area averaged soil liquid water content increases in summer and decrease in winter.For surface heat flux components,the ground heat flux is most significantly affected by the freeze-thaw process in both summer and winter,followed by sensible heat flux and latent heat flux in summer.In the TP area,the ground heat flux increases by 2.82 W/m2(28.5%)in summer and decreases by 3.63 W/m2(40%)in winter.Meanwhile,in CES,the ground heat flux increases by 1.89 W/m2(11.3%)in summer and decreases by 1.41 W/m2(18.6%)in winter.The heat fluxes in the Tibetan Plateau are more susceptible to the freeze-thaw process compared with the high-latitude frozen soil regions.Soil freeze-thaw process can induce significant warming in the Tibetan Plateau in winter.Also,this process induces significant cooling in high-latitude regions in summer.The frozen ground can prevent soil liquid water from infiltrating to deep soil layers at the beginning of thawing;however,as the frozen ground thaws continuously,the infiltration of the liquid water increases and the deep soil can store water like a sponge,accompanied by decreasing surface runoff.The influence of the soil freeze-thaw process on surface hydrologic and thermal fluxes varies seasonally and spatially.