Continuous wavelet-like filter for a spherical surface and its application to localized admittance function on Mars

We have developed a 2D isotropic continuous wavelet-like transform for a spherical surface. The transform is simply defined as the surface convolution between the original field and a kernel, based on the zeroth-order Bessel function with a spherical correction. This spherical correction violates the geometric similarity for the various scales of the kernels, which becomes more apparent at longer wavelengths. We found numerically that this transform is practically equivalent to a Gaussian bandpass filter in the spherical harmonic domain. We have applied this wavelet-like transform on the recently acquired Martian gravity and topography fields. Using a ratio constructed locally from these two fields, we have constructed a map describing the lateral variations of the localized admittance function on Mars.     

Influence of spatial variations of microtopography and infiltration on surface runoff and field scale hydrological connectivity

Surface runoff on agricultural fields arises when rainfall exceeds infiltration. Excess water ponding in and flowing through local microtopography increases the hydrological connectivity of fields. In turn, an increased level of hydrological connectivity leads to a higher surface runoff flux at the field boundaries. We investigated the functional hydrological connectivity of synthetical elevation fields with varying statistical properties. For this purpose, we developed an object-oriented ponding and redistribution model to which Philip’s infiltration model was coupled. The connectivity behaviour is determined by the presence of depressions with a large area and spatial organization of microtopography in rills or channels. The presence of microdepressions suppresses the effect of the spatial variation of infiltration properties. Connectivity behaviour of a field with a varying spatial distribution of infiltration properties can be predicted by transforming the unique connectivity function that was defined for a designated microtopography.     

Magnetic and Electric Fields Produced in the Sea During Geomagnetic Disturbances

— To understand geomagnetic effects on systems with long conductors it is necessary to know the electric field those systems experience. For surface conductors such as power systems and pipelines this can easily be calculated from the magnetic field variations at the surface using the surface impedance of the earth. However, for calculating the electric fields in pipelines and submarine cables at the seafloor it is necessary to take account of the attenuating effect of the conducting seawater. Assuming that the fields are vertically propagating plane waves, we derive the transfer functions between the electric and magnetic fields at the seafloor and the magnetic field variations at the sea surface. These transfer functions are then used, with surface magnetic field data, to determine the power spectra of the seafloor magnetic and electric fields in a shallow sea (depth 100 m) and in the deep ocean (depth 5 km) for different values of the Kp magnetic activity index. For the period range considered (2 min to 3 hrs) the spectral characteristics of the seafloor magnetic and electric fields for a 100 m deep sea are very similar to those of the surface fields. For the deep ocean the seafloor spectra show a faster decrease in spectral density with increasing frequency compared to the surface fields. The results obtained are shown to be consistent with seafloor observations. Assessment of the seafloor electric fields produced by different levels of geomagnetic activity can be useful in the design of the power feed equipment for submarine cables and cathodic protection for undersea pipelines.     

On the downward continuation of electromagnetic fields1

A concise derivation is given for the downward continuation of the tangential fields on the surface to yield expressions for the fields at a specified depth. A homogeneous slab region is assumed for the analysis.     

On the problem of the existence and uniqueness of a discrete,surface, optimum wiener filter,applied to the filtering of geophysical fields

Summary Proof is given of the existence and uniqueness of a discrete, surface, optimum (in the Wiener sense) filter for filtering geophysical fields considering a spectral approach to the construction of the said filter. It is also shown that the filtration coefficients and the filtration errors of the filter, constructed with the help of statistical estimates of the required spectral densities, converge towards their theoretical values. From the mathematical point of view, this paper concludes the building-up of the mathematical model of the discrete Wiener optimum surface filtration, suitable for geophysical fields.     

Constraints on the origins of lunar magnetism from electron reflection measurements of surface magnetic fields

Apollo 15 and 16 subsatellite measurements of lunar surface magnetic fields by the electron reflection method are summarized. Patches of strong surface fields ranging from less than $\text{1}\text{4}$° to tens of degrees in size are found distributed over the lunar surface, but in general no obvious correlation is observed between field anomalies and surface geology. In lunar mare regions a positive statistical correlation is found between the surface field strength and the geologic age of the surface as determined from crater erosion studies. However, there is a lack of correlation of surface field with impact craters in the mare, implying that mare do not have a strong large-scale uniform magnetization as might be expected from an ancient lunar dynamo. This lack of correlation also indicates that mare impact processes do not generate strong magnetization coherent over ～ 10 km scale size. In the lunar highlands fields of >100 nT are found in a region of order 10 km wide and >300 km long centered on and paralleling the long linear rille, Rima Sirsalis. These fields imply that the rille has a strong magnetization (>5 × 10^?6 gauss cm³ gm^?1 associated with it, either in the form of intrusive, magnetized rock or as a gap in a uniformly magnetic layer of rock. However, a survey of seven lunar farside magnetic anomalies observed by the Apollo 16 subsatellite suggests a correlation with inner ejecta material from large impact basins. The implications of these results for the origin of lunar magnetism are discussed.     

Multiplatform observation of the surface circulation in the Gulf of Naples (Southern Tyrrhenian Sea)

The Gulf of Naples (Southern Tyrrhenian Sea) is a highly urbanised area, where human activities and natural factors (e.g. river runoff, exchanges with adjacent basins) can strongly affect the water quality. In this work we show how surface transport can influence the distribution of passively drifting surface matter, and more in general if and how the circulation in the basin can promote the renovation of the surface layer. To this aim, we carried out a multiplatform analysis by putting together HF radar current fields, satellite images and modelling tools. Surface current fields and satellite images of turbidity patterns were used to initialise and run model simulations of particle transport and diffusion. Model results were then examined in relation to the corresponding satellite distributions. This integrated approach permits to investigate the concurrent effects of surface dynamics and wind forcing in determining the distribution of passive tracers over the basin of interest, identifying key mechanisms supporting or preventing the renewal of surface waters as well as possible areas of aggregation and retention.     

Statistical characteristics of geophysical fields in Hilbert's space

Summary A review of the terms of functional analysis, which can be exploited for statistical treatment of geophysical fields, is given. The procedure for determining the statistical characteristics of the fields, defined by a single realization, which does not require the limiting assumption of homogeneity to be introduced, is outlined.     

The fractal geometry of the soil—covered landscape

The soil-covered landscape surface can be idealized from two viewpoints. The intuitive view is of a smooth, absolutely continuous surface with continuous contour lines and measurable in integral dimensions. The alternative view emphasizes the roughness, a surface of little regularity and at the limit of no contours, the appropriate measure being that of fractional Hausdorff dimension. Regularity is a local property and both idealizations need to stop far short of the limit to avoid awkward consequences. The dichotomy of viewpoint can be matched in the theory of Gaussian random fields. These, if they are smooth, are very smooth but if they are irregular they are highly irregular (erratic); there is no middle ground. This Belayev dichotomy is defined and both modes applied to the soil-covered landscape. On the one hand, if the landscape is subject to a general diffusive type degradation or more generally a Davisian downwasting regime then the curvature of the landscape surface is progressively straightened and the distribution of gradient (increments) along a typical traverse will eventually adopt a Gaussian form. Then from the irregular viewpoint the surface is ultimately well represented by a fractional Brownian surface of low Hausdorff dimension (2·0 < dim < 2·3). The Hausdorff dimension is directly related to the entropy of the landscape and as degradation proceeds both quantities decrease in value. On the other hand, if the surface is regarded as smooth and well represented by an absolutely continuous Gaussian field then the mean value of the number of upcrossings of a level or the extent of an excursion set will also be Gaussian. This analysis is restricted to one dimension; the number of times a profile curve crosses or the amount of time it spends above any given level. Predictions from both viewpoints are substantially corroborated in a map analysis of 15 sites on varied terrains in Southern England and the map analysis checked against one based upon digital tape data for one of the sites.     

Simulation of individual particle movement in a gravel streambed

A two‐dimensional simulation model of travel distances of individual particles in a gravel‐bed river is presented. The model is based on a number of rules, which include particle size, entrainment, trajectory, distance of movement and entrapment. Particle interactions are controlled by resistance fields defined about each obstacle and critical elevation defined in the model. Resistance fields, particle dropping and critical elevation rules control particle interactions. The interaction rules cause the particles to develop pebble clusters, stone cells and transverse structures (transverse ribs). The simulated travel distances of individual particles are consistent with reported field results. Individual particle travel distances were simulated using two different models; one without interactions between the individual particles and the stationary bed and one with interactions. The case without interactions demonstrates the random nature of sediment transport, and narrow ranges of travel distances. Wider ranges of travel distances, similar to those for natural situations, were obtained for the cases with interactions. The more intense the interaction between the mobile stones and the stationary ones, the wider the range of distances of travel for a given particle size. Modelling the mean travel distance yielded a result similar to that published previously, which was based on empirical data. Well developed bed‐surface structures were obtained for relatively poorly sorted sediment with intense interactions between particles. Transverse structures developed when relatively large particles were allowed to move. Copyright © 2002 John Wiley & Sons, Ltd.     

A conceptual–numerical model to simulate hydraulic head in aquifers that are hydraulically connected to surface water bodies

In this paper, we present a conceptual‐numerical model that can be deduced from a calibrated finite difference groundwater‐flow model, which provides a parsimonious approach to simulate and analyze hydraulic heads and surface water body–aquifer interaction for linear aquifers (linear response of head to stresses). The solution of linear groundwater‐flow problems using eigenvalue techniques can be formulated with a simple explicit state equation whose structure shows that the surface water body–aquifer interaction phenomenon can be approached as the drainage of a number of independent linear reservoirs. The hydraulic head field could be also approached by the summation of the head fields, estimated for those reservoirs, defined over the same domain set by the aquifer limits, where the hydraulic head field in each reservoir is proportional to a specific surface (an eigenfunction of an eigenproblem, or an eigenvector in discrete cases). All the parameters and initial conditions of each linear reservoir can be mathematically defined in a univocal way from the calibrated finite difference model, preserving its characteristics (geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses). We also demonstrated that, in practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. The reduced computational cost of these solutions can help to integrate the groundwater component within conjunctive use management models. Conceptual approximation also facilitates understanding of the physical phenomenon and analysis of the factors that influence it. A simple synthetic aquifer has been employed to show how the conceptual model can be built for different spatial discretizations, the parameters required, and their influence on the simulation of hydraulic head fields and stream–aquifer flow exchange variables. A real‐world case was also solved to test the accuracy of the proposed approaches, by comparing its solution with that obtained using finite‐difference MODFLOW code. Copyright © 2011 John Wiley & Sons, Ltd.     

区域面波群速度反演的球谐函数法

一个定义在球面局部区域的复杂的面波速度函数如果直接利用球谐函数拟合可能需要展开到很高阶的球谐系数．通过保角变换，把一个球面局部区域扩展到球面上更大的区域上，变换过程中面波速度保持不变，在变换后的球面域上用球谐函数来拟合速度函数，达到降低球谐系数阶数的目的，使面波群速度的反演变成了球谐系数的线性化反演.通过球谐系数分析，可得到反演的分辨率.该方法不仅适用于面波群速度反演，同样适用于各种球面区域场的分析.     

Classification of Harmonic Functions in the Exterior of a Unit Sphere and Its Application to the Description of the External Magnetic Field of the Earth

Geomagnetism and Aeronomy - The magnetic fields of a subterranean source observed on the Earth’s surface or from the orbit of a satellite are studied. We analyze the space of all harmonic...     

Tangential discontinuities and the optical analogy for stationary fields IV. High speed fluid sheets

Abstract

It was shown in the previous paper that a sufficiently strong pressure maximum applied to an equilibrium flux surface, by the fields on either side of the surface, produces a gap in the flux surface. The fields on either side make contact through the gap to produce a surface of tangential discontinuity (current sheet). It is shown in the present paper that there is a high speed sheet of fluid and field sliding over the surface of discontinuity when the applied pressure moves slowly across the flux surface. Conditions in the active X-ray corona of the sun suggest that such sheets are generally present, with velocities of the order of 10² km/sec, but with thicknesses too small to be observed. More substantial high speed sheets of fluid may occur in solar flares.     

Determination of regional net radiation and soil heat flux over a heterogeneous landscape of the Tibetan Plateau

This paper explores the potential for documenting regional fields of surface energy fluxes over the Tibetan plateau using published algorithms and previously calibrated empirical formulae with data from NOAA‐14 AVHRR and atmospheric data collected during the GAME‐Tibet field experiment. Comparison with observations at three field sites suggests errors in the resulting estimates are less than 10% in the clear sky conditions necessary for application of this approach. Because of the need for clear skies, it was only possible to calculate the desired regional fields for one satellite scene during the 5 month study period. Maps of surface energy fluxes, and frequency analyses of these maps, are presented for this scene. The need for an alternative, more consistently applicable, satellite‐based method to map surface energy fields is highlighted. Copyright © 2002 John Wiley & Sons, Ltd.     

Planetary Boundary Layer Flows in the Atmosphere and the Ocean at the Equator

—The boundary layer flows created by the frictional dissipation of the wind speed at the surface in the atmosphere and by surface wind stress in the ocean at the equator and in the equatorial region, are obtained by taking the influence of the surface friction on the zonal velocity as being balanced by vertical transport for the long-term mean flow and by a corresponding time variation for time-dependent flow fields. Solutions are expressed in terms of the velocities in zonal and vertical directions and the divergence of the horizontal current in the two media. It is found that under the ever present easterly flow in the lower atmosphere, the boundary layer flow in the atmosphere is convergence and ascending motion in the lower troposphere, and divergence at the surface and uplift in ocean, and in reverse directions for the westerly flow. Similar results are obtained for time-dependent wind fields and they give way to the steady asymptotic solutions when the period of the variation exceeds 10 months.     

大地电磁有限差分数值解对比

基于网格精度、形成系统方程的方式、边界条件以及预条件线性算子等,文中对大地电磁（MT）有限差分数值解作了对比.对不同网格剖分方式下的三个均匀半空间模型的一维MT响应对比显示,在降低首层厚度的同时保持层间厚度变化在合理范围可以同时提高主场和辅助场的精度.在利用正常中心网格法（主场和辅助场都定义在单元顶面的中心）计算二维（2-D）TM模式响应时,应该从Maxwell一次差分方程开始组建二次差分方程,这样可以更充分考虑模型电阻率的变化.在对边界值如何影响数值解的测试表明,仅仅提高一维（1-D）边界值的精度对提高2-D MT有限差分数值解的精度是有限的.线性算子对提高MT解的效率十分重要,简单的对比进一步表明合适的预条件再配合好的线性算子（如文中求解2-D MT时所采用的DILU-BICGSTAB方法）不仅可以加速收敛,而且可以降低迭代次数.     

多层弹性半空间中的地震波（一）

为了了解地震震源和地球介质的性质,很有必要对地震波的辐射、传播和衰减问题作仔细的分析。作为一种近似,可以暂且忽略地球的曲率,把传播地震波的地球介质视为多层半空间。为简便起见,地震波的衰减问题另作考虑。这样,便需要研究多层、均匀、各向同性和完全弹性半空间中地震震源辐射的地震波传播问题。 用哈斯克尔（Haskell）矩阵法解多层介质中弹性波的传播问题是很方便的。如果     

2008年汶川地震近断裂区域变形场的空间分布

应用Yoshimitsu Okada及Steketee静态断裂位错模型及目前汶川地震研究成果,理论上反演龙门山近断裂区域在汶川地震中从震源深处至地表的变形(应变)场分布.通过矢量合成及坐标变换方法将Yoshimitsu Okada单一静态断裂位错模型应用于龙门山断裂带错裂研究中,重点研究汶川地震中因龙门山中央主断裂中、北段和山前断裂中段共同错动形成的应变场.模拟揭示了应变场平面和垂直分量的空间分布特征.研究发现:应变场垂直分量的幅值在震源深处大于地表,但在地表分布范围较大;应变场沿断裂走向分量的幅值和影响范围由震源深度至地表均逐渐增加;应变场垂直于断裂走向分量的变化情况类似于垂直向应变场;震源深度附近的大变形可能为龙门山断裂在地震中强烈挤压形成的塑性变形.研究表明从震源至地表,所有应变场分量从断裂两侧附近位置至远离断裂,幅值均迅速衰减;其中地表部分的最大变形与现有计算成果近似,变形场的变化特征与地表科考近似,断裂两盘变形方向与震后InSAR资料揭示的情况一致.     

Structure of the Hellenic Subduction Zone from Gravity Gradient Functions and Seismology

The Normalized Full Gradient (NFG) method has widespread applications in the analysis of potential fields, especially the gravity and magnetic fields. This method is used to identify the lateral and horizontal density variations in the crust and lithosphere. In this study, the NFG method was applied to the gravity data of the Cretan Arc and its surroundings. Because of the tectonic features of the eastern Mediterranean, the Cretan Arc and the neighboring areas are seismically very active. Especially the subduction zone and the complicated crustal features have been defined applying many different geophysical methods. In this study, first the NFG method is tested with synthetic prisms (two cubes). After that, the NFG method was applied to the Bouguer gravity data of the Cretan Arc and its subduction zone (Hellenic subduction zone) and Hellenic subduction zone was defined with the foci depth data (USGS) along the south–north direction. Thus, geometry of the focal depth distribution has been created to determine probable media depths and their localizations. According to the NFG results, vertical structural transitions were observed at a depth ranging between 10 and 180?km. Also, these results were compared with the foci depth model and the other results of the related publications. Finally, some considerations in vertical solution with the NFG method have been presented and locations of the different structures at horizontally have been defined with application of the NFG method.