磁偶极子梯度张量的几何不变量及其应用

磁梯度张量系统姿态的变化将影响梯度场测量和数据解释的精度,使得具有坐标变换不变性特点的张量不变量成为磁梯度张量数据解释的研究热点.本文在对磁偶极子产生的磁梯度张量进行特征值分析的基础上得到了:测量点与磁偶极子位置形成的位置矢量、磁偶极子磁矩矢量与绝对值最小的特征值对应的特征向量垂直;位置矢量和磁矩矢量与最大及最小特征值对应的特征向量共面,且两矢量间的夹角可由磁梯度张量矩阵的特征值表示.最后,将本文所得磁偶极子梯度张量的几何不变量用于磁性目标的跟踪中,取得了较好的实时跟踪效果.     

Motion of the north magnetic pole within the scope of the dynamic model of the main geomagnetic field sources

The dipole model of the main geomagnetic field sources has been developed by the authors for several years. At present, the model includes 13 sources that existed and continuously developed during the 20th century. It has been assumed that the main dipole motion can be related to the motion of the Earth’s axis of inertia. At the same time, the known sharp changes in the direction of this motion, the so-called “wanderings” of the axis of inertia coincide in time with a change in the coordinates of the exit point of the main dipole magnetic moment vector on the Earth’s surface, dependent mostly on changes in the vector inclination. The motion of the north magnetic pole has been studied based on the model. It has been obtained that the dynamics of the main dipole parameters and, mainly, a stable variation in the inclination of the magnetic moment vector are responsible for the westward pole motion. At the same time, the observed rapid northward motion of the pole is related to the time variations in the parameters of 12 sources approximating the so-called nondipole part of the main field.     

EXTRACTING FEATURES OF ALLUVIAL FAN AND DISCUSSING LANDFORMS EVOLUTION BASED ON HIGH-RESOLUTION TOPOGRAPHY DATA: TAKING ALLUVIAL FAN OF LAOHUSHAN ALONG HAIYUAN FAULT ZONE AS AN INSTANCE

Range-front alluvial fan deposition in arid and semiarid environments records vast amounts of climatic and tectonic information. Differentiating and characterizing alluvial fan morphology is an important part in Quaternary alluvial fan research. Traditional method such as field observations is a most important part of deciphering and mapping the alluvial fan. Large-scale automatically mapping of alluvial fan stratigraphy before traditional field observations could provide guidance for mapping alluvial fan morphology, thus improving subsequent field work efficiency. In this research, high-resolution topographic data were used to quantify relief and roughness of alluvial fan within the Laohushan. These data suggest that mean surface roughness plotted against the size of the moving window is characterized by an initial increase in surface roughness with increased window size, but it shows no longer increase as a function of windows size. These data also suggest that alluvial fans in this study site smooth out with time until a threshold is crossed where roughness increases at greater wavelength with age as a result of surface runoff and headward tributary incision into the oldest surfaces which suggests the evolution process of alluvial fan. Researchers usually differentiate alluvial morphology by mapping characteristics of fan surface in the field by describing surface clast size, rock varnish accumulation, and desert pavement development and analysis of aerial photographs or satellite imagery. Recently, the emergence of high-resolution topographic data has renewed interest in the quantitative characterization of alluvial and colluvium landforms. Surface morphology that fan surface initially tends to become smoother with increasing age due to the formation of desert pavement and the degradation of bar-and-swale topography and subsequently, landforms become more dissected due to tectonics and climatic change induced increased erosion and channelization of the surface with time is widely used to distinguish alluvial fan types. Those characteristics would reflect various kinds of morphology metrics extracted from high-resolution topographic data. In the arid and semiarid regions of northwestern China, plenty of alluvial fans are preserved completely for lack of artificial reforming, and there exists sparse surface vegetation. In the meantime, range-front alluvial fan displaced by a number of active faults formed a series of dislocated landforms with different offsets which is a major reference mark in fault activity research. In this research, six map units(Qf₆-Qf₁), youngest to oldest, were observed in the study area by mapping performed by identifying geomorphic features in the field that are spatially discernible using hill-shade and digital orthophoto map. Alluvial fan relief and roughness were computed across multiple observation scales(2m×2m to 100m×100m)based on the topographic parameters of altitude difference and standard deviation of slope, curvature and aspect. In this research, mean relief keeps increasing with increased window size while mean surface roughness is characterized by a rapid increase over wavelengths of 6~15m, representing the typical length scale of bar-and-swale topography. At longer wavelengths, surface roughness values increase by only minor amounts, suggesting the topographic saturation length is 6~15m for those fan surfaces in which saturation length of standard deviation of curvature is less than 8m. Box and whisker plot of surface roughness averaged over 8m² for each alluvial fan unit in the study area suggests that the pattern of surfaces smoothing out with age and then starting to become rougher again as age increases further beyond Qf₄ or Qf₃ unit. The younger alluvial fan is characterized by prominent bar-and-swale while the older alluvial fan is characterized by tributaries headward incision. Cumulative frequency distributions of relief and surface roughness in Figure 8 are determined in an 8m by 8m moving window for the comparison of six alluvial fan units in the northeast piedmont of Laohushan. From these distributions we know that Qf₆ and Qf₁ reflect the prominent relief which is related to bar-and-swale and tributaries headward incision respectively, while Qf₄ and Qf₃ reflect the moderate relief which is related to subdued topography. Surface roughness, in addition to facilitating the characterization of individual fan units, lends insight to alluvial landform development. We summarize an alluvial landform evolutionary scheme which evolves four stages depending on characteristics of alluvial fan morphology development and features of relief and roughness. The initial stage in this study site is defined as the active alluvial fan channels with bars of coarse cobbles and boulders and swales consisting of finer-grained pebbles and sand which could be reflected by high mean relief and mean roughness values. As time goes, bar-and-swale topography is still present, but an immature pavement, composed of finer grained clasts, has started to form. In the third stage, the bar-and-swale topography on the fan surface is subdued, yet still observable, with clasts ranging from pebbles to cobbles in size and there exists obvious headward tributary incision. Eventually, tributary channels form from erosion by surface runoff. Headward incision of these tributaries wears down the steep walls of channels that are incised through the stable, planar surface, transforming the oldest alluvial landforms into convex hillslopes, leaving only small remnants of the planar surface intact. Those evolutionary character suggests that alluvial fans in this area smooth out with time, however, relief or roughness would be translated to increase at greater wavelength with age until a threshold is crossed. This research suggests that relief and roughness calculated from high-resolution topographic data of this study site could reflect alluvial fan morphology development and provide constraint data to differentiate alluvial fan unit.     

Mitigating systematic error in topographic models for geomorphic change detection: accuracy,precision and considerations beyond off-nadir imagery

Unmanned aerial vehicles (UAVs) and structure-from-motion photogrammetry enable detailed quantification of geomorphic change. However, rigorous precision-based change detection can be compromised by survey accuracy problems producing systematic topographic error (e.g. ‘doming’), with error magnitudes greatly exceeding precision estimates. Here, we assess survey sensitivity to systematic error, directly correcting topographic data so that error magnitudes align more closely with precision estimates. By simulating conventional grid-style photogrammetric aerial surveys, we quantify the underlying relationships between survey accuracy, camera model parameters, camera inclination, tie point matching precision and topographic relief, and demonstrate a relative insensitivity to image overlap. We show that a current doming-mitigation strategy of using a gently inclined (<15°) camera can reduce accuracy by promoting a previously unconsidered correlation between decentring camera lens distortion parameters and the radial terms known to be responsible for systematic topographic error. This issue is particularly relevant for the wide-angle cameras often integrated into current-generation, accessible UAV systems, frequently used in geomorphic research. Such systems usually perform on-board image pre-processing, including applying generic lens distortion corrections, that subsequently alter parameter interrelationships in photogrammetric processing (e.g. partially correcting radial distortion, which increases the relative importance of decentring distortion in output images). Surveys from two proglacial forefields (Arolla region, Switzerland) showed that results from lower-relief topography with a 10°-inclined camera developed vertical systematic doming errors > 0·3 m, representing accuracy issues an order of magnitude greater than precision-based error estimates. For higher-relief topography, and for nadir-imaging surveys of the lower-relief topography, systematic error was < 0·09 m. Modelling and subtracting the systematic error directly from the topographic data successfully reduced error magnitudes to values consistent with twice the estimated precision. Thus, topographic correction can provide a more robust approach to uncertainty-based detection of event-scale geomorphic change than designing surveys with small off-nadir camera inclinations and, furthermore, can substantially reduce ground control requirements. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd     

Some Insights into Topographic,Elastic and Self-gravitation Interaction in Modelling Ground Deformation and Gravity Changes in Active Volcanic Areas

Surface displacements and gravity changes due to volcanic sources are influenced by medium properties. We investigate topographic, elastic and self-gravitation interaction in order to outline the major factors that are significant in data modelling. While elastic-gravitational models can provide a suitable approximation to problems of volcanic loading in areas where topographic relief is negligible, for prominent volcanoes the rough topography could affect deformation and gravity changes to a greater extent than self-gravitation. This fact requires the selection, depending on local relief, of a suitable model for use in the interpretation of surface precursors of volcanic activity. We use the three-dimensional Indirect Boundary Element Method to examine the effects of topography on deformation and gravity changes in models of magma chamber inflation/deflation. Topography has a significant effect on predicted surface deformation and gravity changes. Both the magnitude and pattern of the geodetic signals are significantly different compared to half-space solutions. Thus, failure to account for topographic effects in areas of prominent relief can bias the estimate of volcanic source parameters, since the magnitude and pattern of deformation and gravity changes depend on such effects.     

Research Note: A proposed procedure for ameliorating edge effects in magnetic data transformations

Reduction to pole and other transformations of total field magnetic intensity data are often challenging to perform at low magnetic latitudes, when remanent magnetization exists, and when large topographic relief exists. Several studies have suggested the use of inversion-based equivalent source methods for performing such transformations under those complicating factors. However, there has been little assessment of the importance of erroneous edge effects that occur when fundamental assumptions underlying the transformation procedures are broken. In this work we propose a transformation procedure that utilizes magnetization vector inversion, inversion-based regional field separation and equivalent source inversion on unstructured meshes. We investigated whether edge effects in transformations could be reduced by performing a regional separation procedure prior to equivalent source inversion. We applied our proposed procedure to the transformation of total field magnetic intensity to all three Cartesian magnetic field components using a complicated synthetic example based on a real geological scenario from mineral exploration. While the procedure performed acceptably on this test example, the results could be improved. We pose many questions regarding the various choices and control parameters used throughout the procedure, but we leave the investigation of those questions to future work.     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

3D magnetotelluric modelling including surface topography

An edge finite‐element method has been applied to compute magnetotelluric (MT) responses to three‐dimensional (3D) earth topography. The finite‐element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D‐2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal‐hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two‐dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode.     

用云南下关测点的水压致裂结果分析地形起伏对应力测值的影响

本文以云南下关黄草坝的水压致裂应力测量结果为例,讨论了地形起伏对云南区应力测值的影响。结果表明,地形起伏对应力测值的绝对影响随深度的增加衰减缓慢,相对影响急剧减小。100米以内深度的应力测量,地形影响可能给测值带来10%以上的误差。云南区的水压致裂应力测量深达500米,是可以排除掉地形起伏的影响的。     

起伏地形下大地电磁L-BFGS三维反演方法

为推进大地电磁三维反演的实用化,本文实现了基于L-BFGS算法的带地形大地电磁三维反演.首先推导了大地电磁法三维反演的Tikhonov正则化目标函数以及Hessian矩阵逆矩阵近似表达式和计算方法,然后设计了一种既能保证空气电阻率固定不变又能保证模型平滑约束的协方差矩阵统一表达式,解决带地形反演问题.在反演算法中采用正则化因子冷却法以及基于Wolf条件的步长搜索策略,提升了反演的稳定性.利用开发的算法对多个带地形地电模型（山峰地形下的单个异常模型、峰-谷地形下的棋盘模型）的合成数据进行了三维反演,并与已有大地电磁三维反演程序（ModEM）进行对比,验证了本文开发的三维反演算法的正确性和可靠性.最后,利用该算法反演了华南某山区大地电磁实测数据,得到该区三维电性结构,揭示了研究区以高阻介质为基底,中间以低阻不整合面和相对低阻介质连续分布,浅部覆盖高阻介质的电性结构特征,进一步验证了本文算法的实用性.     

Magnetic variation generated by a tangential magnetic dipole located in the Earth's core

Summary The harmonically variable magnetic field, generated by a tangential magnetic dipole (TMD), located eccentrically at the surface of the Earth's core, is investigated for various periods of time variations and for a three-layer conductivity model of the Earth. Numerical computations have shown that the field is inductively damped for variation periods of less than 500 years as compared to the field of a static TMD. It is proved that the field appropriate to the TMD, has a more complicated distribution of the Earth's surface than the field of a radial magnetic dipole. Comparison with maps of the non-dipole part of the geomagnetic field shows that the TMD is not as suitable for interpreting the observed non-dipole field and its variations as the eccentric radial magnetic dipole.     

关于东亚大陆磁场的研究

本文利用近三十年来的地面测量资料和东亚地区11个地磁台的资料,以及1965.0、1975.0国际地磁参考场等资料,对东亚大陆磁场的时、空变化特征进行了研究。内容包括:东亚大陆磁场的空间分布特征及场源深度的估算,东亚大陆磁场的中心位置及其磁场强度、磁场方向,近三十年来东亚大陆磁场的长期变化特征等。得到的主要结果是:1.东亚大陆磁场的中心位置近三十年来没有西向漂移的迹象,从而推断它的长期变化主要由场源强度的变化所引起,而不是主要由非偶场的西向漂移所引起;2.东亚大陆磁场的中心与它的长期变化的中心不相一致,同时,在青藏高原的东部还可能存在一弱中心。     

鲁甸地震的滑坡物质运移规律与地形特征

长期、缓慢的地貌演化具有阶段性的特点,构造抬升与侵蚀相互作用引起山坡物质运移,使地貌单元具有向相对稳定状态转变的趋势.滑坡作为山坡物质运移的一种主要方式,在地貌演化过程中起到了重要作用.2014年鲁甸MS6.5地震诱发了异常多的滑坡,可以看作是该区地貌物质在短时间内发生的集中调整过程.这些滑坡主要沿河流分布,表明河流侵...     

Numerical calculations of the perturbation of normal heat flow by topographic and local conductivity structure

A numerical method is used to investigate the effect of topographic and local thermal conductivity anomalies on near-surface heat flow for two-dimensional models. Heat flow associated with a sloping topographic structure is calculated. Also, the effects of a fault structure associated with the sloping topography are considered. Vertical and horizontal heat flow components are calculated alone; the surface of the earth as well as throughout the whole region of interest. The results indicate that surface heat flow is substantially affected by topographic relief and the horizontal heat flow component associated with topographic features can be large. Also, regional heat flow is greatly perturbed by local thermal conductivity anomalies and the effect of topographic features may be considerably modified by the subsurface structure.     

1690～2000年地磁场能量的三维分布及其长期变化

利用Bloxham & Jackson 地磁场模型和国际参考地磁场模型(IGRF),研究了1690～2000年地磁总能量及其北向、东向和垂直向分量的能量以及非偶极子磁场的能量在地球内部的分布及长期变化.结果表明,地表和地核以外地磁场总能量及其北向和垂直向的能量是持续衰减的,垂直向的磁场能量占总能量的64％以上,对总能量的贡献起主要作用;东向分量的能量随时间的变化以增加为主.地磁场的能量变化率存在56年的周期,主要是由偶极子磁场产生的.地表以外的非偶极子磁能从减小到增大转折出现在1770年,比地核以外滞后40年.地球内部磁能随时间的变化显示,偶极子磁能逐渐减小,非偶极子磁能增加,越靠近核幔边界增加越快;偶极子和非偶极子磁能的变化量相等的分界面在距地心3780km处.从核幔边界到地表,磁能变化的衰减非偶极子比偶极子快,表明偶极子磁场比非偶极子磁场有更深的场源.     

Numerical Investigations in the Analytical and Semi-Analytical Computation of Gravimetric Terrain Effects

A recently proposed method for the computation of the gravitational effect due to the topographic masses defined by a Digital Elevation Model (DEM) involves the representation of the surface relief by means of parts of bilinear surfaces. The so-called bilinear method delivers eventually the mathematical model for the gravitational attraction of a right rectangular prism, whose top is modeled by a bilinear surface. Scope of the paper is to assess the new method by conducting numerical tests using both real and synthetic data. The performance of the bilinear method is evaluated in terms of its computational efficiency as well as its precision by comparing it with other analytical methods available for the practical evaluation of gravitational terrain effects. The techniques considered for the assessment of the bilinear approximation are the vastly applied right rectangular prism method and the polyhedral modeling, a less popular but extremely flexible approach based on the closed expression for the gravity field of an arbitrarily shaped mass distribution defined by planar faces. The different geometric modeling of the topographic relief produces discrepancies to the gravitational attraction of up to several mGal. Thus the choice for the geometric representation of the terrain plays a fundamental role to the numerical computation of potential field quantities especially in the critical region surrounding the computation point.     

Transient electromagnetic surveys with unimodal transverse magnetic field: ideas and results

The theory behind transient electromagnetic surveys can be well described in terms of transverse magnetic and transverse electric modes. Soundings using transverse magnetic and transverse electric modes require different source configurations. In this study, we consider an alternating transverse magnetic field excitation by a circular electric dipole. The circular electric dipole transmitter is a horizontal analogue of the vertical electric dipole. Offshore surveys using circular electric dipole might represent an alternative to the conventional marine controlled‐source electromagnetic method at shallow sea and/or for exploring relatively small targets. Field acquisition is carried out by recording either electric or magnetic responses. Electric responses bear information on the 1D structure of a layered earth and successfully resolve high‐resistivity targets in marine surveys. Land‐based circular electric dipole soundings are affected by induced polarisation. On the contrary, magnetic responses are absent on the surface of a 1D earth, and as a result, they are very sensitive to any and even very small 3D conductivity perturbations. In addition, they are sensitive to induced polarisation or some other polarisation effects in the subsurface. At present, circular electric dipole transmitters and magnetic receivers are successfully used in on‐land mineral and petroleum exploration.     

海原断裂带中东段地貌差异及其成因探讨

以定量化地形因子为切入点的构造地貌学方法已成为活动构造研究的有效手段,被广泛用于定性或半定量解析地貌对新构造运动的响应及其演化过程。针对海原断裂带中东段现今地貌差异,以SRTM 90m分辨率DEM为基础,利用ArcGIS软件和Matlab程序脚本,提取了海原断裂带中东段高程、坡度、地形起伏、地形侵蚀以及河流陡峭系数等地形因子。从空间分布上看,上述各项地形因子沿断裂走向均呈现 “西高东低”的整体分布特征。西段海拔高、坡度陡、起伏大、侵蚀强、抬升快,中段和东段海拔低、坡度缓、起伏小、侵蚀弱、抬升慢,此外,在断裂带的东南尾端呈略微增加趋势,达到小范围内的峰值。在此基础上,通过对比分析地形因子与年降水量、基岩岩性,初步探讨了构造与降水、岩性等因素对地形地貌的控制作用,认为不同降水条件对地貌后期改造起显著作用,基岩岩性与现今地貌之间并无显著关系,该区域地貌类型主要受构造抬升差异所控制。沿断裂带走向上的现今地貌差异表明,西段处于相对快速的构造隆升和强挤压造山构造背景,中段由于受到黄河下切及河流冲积作用影响,地貌参数记录的抬升特征并不显著,而东段则反映出大型断裂带尾端挤压调整效应。     

CSAMT勘探中场区、记录规则、阴影及场源复印效应的解析研究

由矢量位导出均匀大地表面上水平接地谐变电偶极子地下电磁场的闭合表达式, 将地层波和地面波显式地区分开来, 据此定义了与远区场和近区场对应的地面波区和地层波区. 对长期困扰CSAMT勘探工作者的记录点问题、阴影和场源复印效应问题给出了物理解释. 由地层波与地面波之比给出了定量划分场区的方法, 每一场分量最佳记录规则下的条件和判断是产生阴影和场源复印效应的前提. 山西沁水盆地CSAMT勘探覆盖点的推断结果表明, 阴影和场源复印效应是由地层波所携带的源与观测点之间、源下方真实地质情况的信息决定, 是可以利用的.     

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.