Spontaneous tangential discontinuities and the optical analogy for static magnetic fields. VI. Topology of current sheets

Abstract

The electric surface current in a tangential discontinuity in a force-free magnetic field is conserved. The direction of the current is halfway between the direction of the continuous fields on either side of the surface of discontinuity. Hence the current sheets, i.e. the surface of tangential discontinuity, have a topology that is distinct from the lines of force of the field. The precise nature of the topology of the current sheet depends upon the form of the winding patterns in the field. Hence, invariant winding patterns and random winding patterns are treated separately. Current sheets may have edges, at the junction of two or more topological separatrices. The current lines may, in special cases, be closed on themselves. The lines of force that lie on either side of a current sheet somewhere pass off the sheet across a junction onto another sheet. In most cases the current sheets extending along a field make an irregular honeycomb.

The honeycomb pattern varies along the field if the winding pattern of the field varies. The surface current density in a tangential discontinuity declines inversely, or faster, with distance from its region of origin. The edges of weaker tangential discontinuities (originating in more distant regions) are bounded by the stronger tangential discontinuities (of nearby origin).

An examination of the force-free field equations in a small neighborhood of the line of intersection of two tangential discontinuities shows that the lines of force twist around to cross the line of intersection at right angles. If the angle between the tangential discontinuities exceeds π/2, there is also the possibilitity that the lines twist around so as to come tangent to the line of intersection as they cross it.     

Neural network classification of discontinuities in space plasma parameters

The artificial neural network technique is applied to dividing discontinuities in space plasma and magnetic field parameters into classes corresponding to known types of magnetohydrodynamic discontinuities. Parameter discontinuities registered on the WIND spacecraft between 1996 and 1999 are classified using a network of the Kohonen Layer type. An algorithm for determining the orientation of discontinuity surfaces on the basis of one-dimensional observations of solar wind parameter discontinuities on board spacecraft is proposed.     

基于方向模板的保持边缘平滑后地震图像的不连续性检测

鉴于地震数据不连续性检测的重要性,本文提出了一种保持和检测地震图像不连续性(如:岩层,断层,河道等)的方法.通常在图象不连续的地方,象素值会有较大的差异,文中用4×4的方向模板计算目标点周围六个方向上的差值,当最大差值超过某个门限值时,则可认为该点为不连续点,由此来检测地震图像的不连续性.由于包含重要信息的区域受噪声的影响通常比其他地方严重,而且基于差值的不连续性检测算法对噪声较为敏感,所以在不连续性检测之前降低地震图像的噪声是很重要的.普通的平滑去噪方法会造成边缘模糊,不利于不连续性检测.本文采用旋转模板的非线性平滑方法,用四个六边形和一个八边形模板在目标像素周围旋转,用与目标像素标准差最小(最同类)的模板内那些点的均值代替目标像素的值,从而实现对地震图象的保边缘平滑去噪处理.理论模型和实际数据处理结果表明:与Y、Luo等人提出的保边缘平滑方法相比,本文的保边缘平滑处理方法提高了计算效率和峰值信噪比;将文中提出的保边缘平滑方法和基于方向模板的不连续性检测方法结合使用,得到的不连续性检测结果比直接检测更清晰.地震数据解释人员可根据检测到的不连续性来识别断层、岩层、河道等.     

Topography of the Moho and Conrad discontinuities in the Kyushu district,Southwest Japan

The first P-arrival time data from local earthquakes are inverted for two-dimensional variation of the depths to the Conrad and Moho discontinuities in the Kyushu district, southwest Japan. At the same time, earthquake hypocenters and station corrections are determined from the data. The depths to the discontinuities are estimated by minimizing the travel time residuals of first P-arrival phases for 608 earthquakes observed at 57 seismic stations. In the land area of Kyushu, the Conrad and Moho discontinuities are located within the depth ranges of 16–18 and 34–40 km, respectively. The Conrad discontinuity is not as largely undulated as the Moho discontinuity. The depth to the Moho is deep along the east coast of Kyushu, and the deepest Moho is closely related to markedly low velocity of P wave. We regard the deepest Moho as reflecting the Kyushu–Palau ridge subducting beneath the Kyushu district, together with the Philippine Sea slab. In western Kyushu, the shallow Moho is spreading in the north–northeast–south–southwest direction in the Okinawa trough region. Based on the presence of low-velocity anomaly in three-dimensional velocity structure and seismogenic stress field of shallow crustal earthquakes, the shallow Moho is interpreted as being due to lower crustal erosion associated with a small-scale mantle upwelling in the Okinawa trough region. The velocity discontinuity undulation basically has insignificant effect on hypocenter determination of the local earthquakes, but the Moho topography makes changes in focal depths of some upper mantle earthquakes. The depth variation of the Moho discontinuity has a good correlation with the Bouguer gravity anomaly map; i.e., the shallow Moho of western Kyushu and the deep Moho of eastern Kyushu closely correlate with the positive and negative Bouguer gravity anomalies, respectively.     

Determining the amplitude and timing of streamflow discontinuities: A cross wavelet analysis approach

Records of natural processes, such as gradual streamflow fluctuations, are commonly interrupted by long or short disruptions from natural non‐linear responses to gradual changes, such as from river‐ice break‐ups, freezing as a result of annual solar cycles, or human causes, such as flow blocking by dams and other means, instrument calibrations and failure. The resulting abrupt or gradual shifts and missing data are considered to be discontinuities with respect to the normal signal. They differ from random noise as they do not follow any fixed distribution over time and, hence, cannot be eliminated by filtering. The multi‐scale resolution features of continuous wavelet analysis and cross wavelet analysis were used in this study to determine the amplitude and timing of such streamflow discontinuities for specific wavebands. The cross wavelet based method was able to detect the strength and timing of abrupt shifts to new streamflow levels, gaps in data records longer than the waveband of interest and a sinusoidal discontinuity curve following an underlying modeled annual signal at ±0.5 year uncertainty. Parameter testing of the time‐frequency resolution demonstrated that high temporal resolution using narrow analysis windows is favorable to high‐frequency resolution for detection of waveband‐related discontinuities. Discontinuity analysis on observed daily streamflow records from Canadian rivers showed the following: (i) that there is at least one discontinuity/year related to the annual spring flood in each record studied, and (ii) neighboring streamflows have similar discontinuity patterns. In addition, the discontinuity density of the Canadian streamflows studied in this paper exhibit 11‐year cycles that are inversely correlated with the solar intensity cycle. This suggests that more streamflow discontinuities, such as through fast freezing, snowmelt, or ice break‐up, may occur during years with slightly lowered solar insolation. Copyright © 2013 John Wiley & Sons, Ltd.     

Mantle discontinuities beneath Izu-Bonin and the implications

The detailed structure of the Earths interior is a major field of geophysics study and the existence and the properties of mantle discontinuities are its important content. Since the lateral heterogeneity was discovered with the seismic tomography method,…     

A test problem for structural systems with discontinuities

The direct integration method for structural systems having force and/or stiffness discontinuities is known to present considerable numerical difficulties. A non-linear one-degree-of-freedom test problem having these characteristics is developed and its exact oscillation period determined. The effects on amplitude and phase of small perturbations of the switching point, such as are caused by fixed-step integration, have been studied. Artificial energy changes introduced at discontinuities by fixed-step explicit and implicit methods are investigated. For a number of commonly used algorithms orders of convergence in fixed-step integration of the test problem degrade from design value before, toO(h) after, the first discontinuity traversal.O(h) convergence is maintained for any number of discontinuity traversals thereafter, but design order can be recovered by locating the switching point sufficiently precisely.     

Influence of geostatic stresses on permeability of jointed rock masses

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Surface waves on MHD tangential discontinuities: case for moderate to low plasma-β values

Variation of phase speed of the magnetoacoustic surface waves on a magnetohydrodynamic (MHD), tangential discontinuity (TD) is examined against the variation of Alfvén speeds on opposite sides of the discontinuity with the acoustic speeds remaining constant. The discontinuous thermal profile of the plasma is employed to classify various surface wavemodes. The existence conditions for the surface waves manifest themselves through the appearance of critical values for various parameters restricting the propagation of such waves on the TD. The limiting situation of extremely low-β plasmas is studied to improve upon earlier results based on simplified calculations. Theoretical understanding of the basic structure of surface waves is then applied to specific observations of discontinuities in the interplanetary magnetic field (IMF) to arrive at simple estimates of phase speed of the surface waves on such discontinuities that may be tested in further observations.     

Generation of SH-type waves due to shearing stress discontinuity in a sandy layer overlying an isotropic and inhomogeneous elastic half-space

The generation of SH-type waves due to sudden application of a stress discontinuity which moves after creation at the sandy layer of finite thickness overlying an isotropic and inhomogeneous elastic half-space is considered. The displacements are obtained in exact form by the method due to Cagniard modified by De Hoop. The numerical calculations are obtained. Two cases of shearing stress discontinuities are considered for different sandiness parameters. The graphs are drawn to show the effect of sandiness in the displacement components.     

The upper mantle discontinuities in western Canada fromPs conversions

We have investigated variations in the travel times ofPs converted phases from the upper mantle 410 and 660 km discontinuities recorded on the western stations of the Canadian National Seismograph Network using a variant of the technique introduced byVinnik (1977). Clear and unambiguous signals for both discontinuities are observed at 8 of the 11 stations considered and exhibit variations which correlate well with regional tectonic setting. Stations located in regions which are currently tectonically active are characterized by largerPs arrival times relative to directP than those situated on the North American craton. In addition the difference in arrival times between the 410 and 660Ps phases suggest that most of the variation is the result of structure above the transition zone but below the Moho. Stations located in the Cascadia subduction zone generally exhibit poorer signal quality than those elsewhere, a feature that may result from upper mantle velocity heterogeneity, discontinuity topography or a combination of both. A detailed investigation of possible lateral variations in discontinuity topography associated with subduction awaits the compilation of a more comprehensive data set which will permit the monitoring of an azimuthal dependence in signal.     

牡丹江和海拉尔台下方地幔间断面结构及推论

利用牡丹江(MDJ)和海拉尔(HIA)台1988-2000年的宽频带三分量数字地震记录,通过地幔间断面产生的P-SV转换波,研究台站下方地幔间断面的分布以及日本海俯冲带对660km间断面的影响.为了提高所得结果的可靠性,采用了线性-偏振滤波方法和修正的N次根倾斜叠加方法来提取P-SV转换波.前一方法通过实验选取适当的光滑平均和提出立体角的约束;对后一方法进行了震源深度校正和间断面倾斜的修正.结果表明,在MDJ和HIA台下方,除在660,410,220和520km深度附近均存有间断面外,在140,350,570,740和1080km深度附近也存在间断面,显示了地幔中径向分层的复杂性;另外,MDJ台下方660-840km之间的间断面结果比HIA台下方的复杂,似有分层结构,可能反映了俯冲带的影响.     

Stationary strong magnetohydrodynamic discontinuities and pressure balanced structures in the solar wind stream

Strong disturbances of magnetic clouds in the solar wind stream are considered when solar MHD shock waves from the surrounding plasma collide with these inhomogeneities. The boundaries of the considered plasma inhomogeneities are presented as stationary tangential discontinuities. The collision of solar fast shock waves with the back and front boundaries is studied as a decomposition of an arbitrary discontinuity. It is asserted that secondary waves of rarefaction and reverse shock waves arise depending on the initial conditions. It is pointed out that a change occurs in the configuration of the plasma inhomogeneity under study, which is caused by the incoming perturbation repeatedly observed by spacecrafts.     

基于三重震相方法探测日本海俯冲区地幔转换带的速度结构

本文基于中国数字地震台网记录的发生于日本北海道地区的一次中源地震的三重震相资料研究了日本海俯冲区地幔转换带的速度结构．结果表明,该区域P波速度结构与S波速度结构的一致性整体上较强．冷的西太平洋俯冲板块导致410 km间断面出现了10 km的抬升,660 km间断面出现了25 km的下沉;410 km和660 km间断面之上均存在与俯冲板块相关的高速层;660 km间断面下方存在厚度为65 km的低速异常．纵横波波速比vP/vS值在210—400 km深度范围内偏低,约为1.827,体现出海洋板块低泊松比的特征;在560—685 km深度范围内,该值偏高,约为1.831,可能预示地幔转换带底部含有一定量的水．      

Array Triplication Data Constraining Seismic Structure and Composition in the Mantle

Seismic data recorded in the upper mantle triplication distance range between 10° and 30° are generated by wave propagation through complex upper mantle structure. They can be used to place constraints on seismic velocity structures in the upper mantle, key seismic features near the major discontinuities, and anisotropic structure varying with depth. In this paper, we review wave propagation of the upper mantle triplicated phases, how different key seismic features can be studied using upper mantle triplicated data, and the importance of those seismic features to the understanding of mantle temperature and composition. We present two examples of using array triplicated phases to constrain upper mantle velocity structures and detailed features of a certain discontinuity, with one for a shallow event and the other for deep events. For the shallow event, we present examples of how the array triplication data can be used to constrain several key properties of the upper mantle: existence of a lithospheric lid, existence of a low velocity zone beneath the lithospheric lid, and P/S velocity ratio as a function of depth. For deep events, we show examples of how array triplication data can be used to constrain the detailed structures of a certain discontinuity: velocity gradients above and below the discontinuity, velocity jumps across the discontinuity and depth extents of different velocity gradients. We discuss challenges of the upper mantle triplication study, its connection to other approaches, and its potential for further studying some other important features of the mantle: the existence of double 660-km discontinuities, existence of low-velocity channels near major discontinuities and anisotropy varying with depth.     

Receiver functions in northeast China - implications for slab penetration into the lower mantle in northwest Pacific subduction zone

Seismic studies of the subducting lithosphere and the upper mantle discontinuities in the northwest Pacific subduction zone beneath Japan and northeast China have suggested contrary subduction scenarios. There was little consensus on the issue whether the subducting slab penetrates the upper mantle discontinuities into the lower mantle or it is deflected atop of the 660-km discontinuity over several hundred kilometers. We calculate receiver functions from a recent seismic broadband station network located in northeast China and find topographic variations of the upper mantle discontinuities. A deeper-than-normal 660-km discontinuity is observed over an area of 400 km and it coincides with the stagnant slab imaged by seismic tomography. The 660-km discontinuity is locally depressed by more than 35 km and the transition zone is thickened by more than 20 km in the east of the region where it encounters the slab. These observations provide evidence of the slab accumulating in the mantle transition zone and locally penetrating into the lower mantle.     

长白山-镜泊湖火山区上地幔间断面接收函数研究

利用布设在长白山地区的19个PASSCAL宽频带流动地震台站近一年的远震记录和布设在镜泊湖火山区14个宽频带轻便数字地震仪三个月的远震记录,共得到高质量的423个接收函数,通过对这些接收函数的共转换点叠加得到研究区的间断面的分布及形态.研究结果表明,研究区存在410、520km和660km间断面.410km和660km间断面较为连续且具有正相关性质,410km间断面在长白山天池火山下局部上隆,660km间断面具有复杂的多界面性质.410km和660km之间的过渡带厚约250km,接近全球平均水平.珲春深震区下660km界面下陷,其上还有多组震相,这些震相在珲春深震区东西两侧不连续,推测西太平洋板块至少已经俯冲到欧亚大陆下的上地幔过渡带中.410km间断面在长白山火山区下局部上隆,660km间断面具有的复杂结构和珲春深源地震的发生均与俯冲板块在过渡带中的活动有关. 俯冲板块在受到660km间断面的强大阻力后,在660km间断面之上变为近水平扩张.推测在欧亚大陆下西太平洋板块的最前端可能已经不是一个完整的整体,或许是由几个有一定联系的板块残片组成.     

Tangential discontinuities and the optical analogy for stationary fields. v. formal integration of the force-free field equations

Abstract

This paper demonstrates the appearance of tangential discontinuities in deformed force-free fields by direct integration of the field equation ? x B = αB. To keep the mathematics tractable the initial field is chosen to be a layer of linear force-free field B_x = + B ₀cosqz, B_y = — B ₀sinqz, B_z = 0, anchored at the distant cylindrical surface ? = (x ² + y ²)^1/2 = R and deformed by application of a local pressure maximum of scale l centered on the origin x = y = 0. In the limit of large R/l the deformed field remains linear, with α = q[1 + O(l ²/R ²)]. The field equations can be integrated over ? = R showing a discontinuity extending along the lines of force crossing the pessure maximum. On the other hand, examination of the continuous solutions to the field equations shows that specification of the normal component on the enclosing boundary ? = R completely determines the connectivity throughout the region, in a form unlike the straight across connections of the initial field. The field can escape this restriction only by developing internal discontinuities.

Casting the field equation in a form that the connectivity can be specified explicitly, reduces the field equation to the eikonal equation, describing the optical analogy, treated in papers II and III of this series. This demonstrates the ubiquitous nature of the tangential discontinuity in a force-free field subject to any local deformation.     

GEOELECTRICAL SURVEYS OF DIPPING STRUCTURES1

Among resistivity methods, models containing two dipping discontinuity surfaces with a conductive medium between them have been considered in this study. The theoretical apparent resistivity curves obtained for such models were calculated using Alfano's integral equation for various dip angles of planes at different array distances from the contacts. The results obtained showed that it is possible to achieve the dip values of the discontinuities under particular conditions, but ambiguities cannot be ruled out.