Interpretation of general geophysical patterns in Iran based on GRACE gradient component analysis

Only with satellites it is possible to cover the entire Earth densely with gravity field related measurements of uniform quality within a short period of time. However, due to the altitude of the satellite orbits, the signals of individual local masses are strongly damped. Based on the approach of Petrovskaya and Vershkov we determine the gravity gradient tensor directly from the spherical harmonic coefficients of the recent EIGEN-GL04C combined model of the GRACE satellite mission. Satellite gradiometry can be used as a complementary tool to gravity and geoid information in interpreting the general geophysical and geodynamical features of the Earth. Due to the high altitude of the satellite, the effects of the topography and the internal masses of the Earth are strongly damped. However, the gradiometer data, which are nothing else than the second order spatial derivatives of the gravity potential, efficiently counteract signal attenuation at the low and medium frequencies. In this article we review the procedure for estimating the gravity gradient components directly from spherical harmonics coefficients. Then we apply this method as a case study for the interpretation of possible geophysical or geodynamical patterns in Iran. We found strong correlations between the cross-components of the gravity gradient tensor and the components of the deflection of vertical, and we show that this result agrees with theory. Also, strong correlations of the gravity anomaly, geoid model and a digital elevation model were found with the diagonal elements of the gradient tensor.     

天山及邻区Vening Meinesz均衡重力异常特征及其动力学意义

本文基于Vening Meinesz区域均衡模型,通过试验不同参数计算Vening Meinesz均衡补偿深度,将其与CRUST1.0模型给出的莫霍面深度进行拟合,得到适应于天山及邻区的平均补偿深度、"地区性指标"以及区域补偿半径.结合地球重力场模型EIGEN-6C4与地形数据,利用球冠体积分方法进行地形效应、沉积层效应计算和均衡校正,得到了研究区的Vening Meinesz均衡重力异常.结果显示天山及邻区的均衡重力异常幅值在-110~120 mGal之间,表明了天山及周边盆地岩石圈所处于的均衡状态,同时揭示了研究区的壳幔密度分布特征.天山、塔里木盆地、准噶尔盆地等块体的地壳垂向形变可能部分地由均衡调整引起,且均衡调整趋势与地面形变测量结果相契合.通过对均衡重力异常成因的解释,从地壳均衡角度分析了该地区复杂的构造背景及其新生代以来的演化历程.     

基于实测重力异常和地形数据确定重力梯度的研究

本文利用澳大利亚北领地West Arnhem Land 地区实测重力异常数据并联合DEM(9")和SRTM3(3")地形高程数据,使用移去-恢复技术和Stokes积分方法计算了该地区两条剖面的重力梯度及其功率谱密度,使用FFT方法解算了整个地区的重力梯度值,结果证明了联合重力异常数据和高分辨率地形高程数据能有效地提高重力梯度的解算精度;功率谱密度的计算结果与国外成熟的重力梯度功率谱密度模型相吻合,表明高于0.3 Hz频率范围的功率谱密度可看做噪声,为重力梯度数据处理中噪声的辨别和剔除提供了借鉴,另外对重力梯度辅助导航基准图的构建以及重力梯度测量系统的标定提供了有益的探索.     

基于Lp范数正则化的V字型密度界面重力反演

V字型密度界面是一类常见的密度界面,如海沟、半地堑以及俯冲带之下的莫霍面,利用重力数据刻画此类密度界面形态对于区域构造研究、油气勘探以及物理海洋学等都具有重要意义.本文首先建立了L_p-范数形式的模型约束函数,并利用正则化原理将其与重力数据误差函数和已知深度约束函数结合形成V字型密度界面反演的目标函数,推导了目标函数的梯度表达式,并以非线性共轭梯度法为核心给出了反演流程.二维简单模型试算结果表明p=5时该方法能准确地刻画V字型密度界面起伏特征,且亦能准确地应用于二维复杂密度界面和三维界面的反演.最后将反演方法应用于挑战者深渊及邻区的实际资料处理之中,利用研究区海底地形数据和沉积层厚度数据对自由空间重力异常逐层剥离而得到莫霍面引起的重力异常,用本文方法对此重力异常进行反演,结果呈现了板块俯冲作用引起的V字型莫霍面起伏特征.     

大地电磁全信息资料三维共轭梯度反演研究(英文)

在对张量阻抗数据、倾子数据和共轭梯度算法深入分析的基础上,我们实现了大地电磁全信息资料三维共轭梯度反演算法。基于全信息资料的三维共轭梯度反演研究,探讨了同时利用五个电磁场分量整理得到的大地电磁资料进行三维反演定量解释的方法以及全信息数据在三维反演中的作用。理论模型合成数据的反演结果表明,在三维反演中使用张量阻抗和倾子数据结合的全信息数据的反演结果优于只使用张量阻抗数据(或只使用倾子数据)的反演结果,提高了反演结果的分辨率和可信度。合成数据的反演算例也验证了所实现的大地电磁全信息资料三维共轭梯度反演算法的正确性和稳定性。     

Noise filtering of full-gravity gradient tensor data

In oil and mineral exploration, gravity gradient tensor data include higher-frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry (FTG) data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high-frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.     

How long is a hillslope?

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope–area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope–area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length–relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end‐member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length–relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

卫星重力梯度测量与地球引力场的精度研究

本文根据地球引力位的球谐函数展开式,利用重力梯度张量各分量导出了位系数模型的精度估计公式.从三方面进行了研究:假定卫星重力梯度仪测量精度,探讨用重力梯度数据确定地球重力场模型的精度;求出位系数模型和大气阻力引起的重力梯度卫星的轨道误差;最后,反求轨道误差和位系数误差对重力梯度测量值的影响.数值计算表明,与地面技术和常规卫星方法相比,卫星梯度测量可使重力场模型的精度至少提高3-5倍;利用重力梯度张量全分量求得的重力值精度比单用径向分量V_rr的结果提高40％以上;若仅顾及位系数模型和大气阻力误差,则轨道误差对梯度测量值的影响△V_i3（i=3,2,1）至少可分别在1/4和1/3弧圈内达到△V_i3≤σ（仪器精度）.     

Three-dimensional inversion of full magnetic gradient tensor data based on hybrid regularization method

Rapid developments in SQUID-based technology make it possible for geophysical exploration to direct measure, inverse and interpret magnetic gradient tensor data. This contribution introduces a novel three-dimensional hybrid regularization method for inversion of magnetic gradient tensor data, which is based on the minimum support functional and total variation functional. Compared to the existing stabilizers, for example, the minimum support stabilizer, the minimum gradient support stabilizer or the total variation stabilizer, our proposed hybrid stabilizer, in association with boundary penalization, improves the revision result greatly, including higher spatial and depth resolution, more clear boundaries, more highlighted images and more evident structure depiction. Moreover, suitable selection of model parameter λ will further improve the image quality of the recovered model. We verify our proposed hybrid method with various synthetic magnetic models. Experiment results prove that this method gives more accurate results, exhibiting advantages of less computational costs even when less prior information of magnetic sources are provided. Comparison of results with different types of magnetic data with and without remanence indicates that our inversion algorithm can obtain more detailed information on the source structure based on rational estimation of total magnetization direction. Finally, we present a case study for inverting SQUID-based magnetic tensor data acquired at Da Hinggan Mountains area, inner Mongolia, China. The result also certifies that the method is reliable and efficient for real cases.     

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.     

孕震过程中重力位、重力、重力梯度变化的数值模拟研究

简要介绍了为探索和解释地震前后重力变化的各种孕震模式,推导了由孕震引起的密度变化和位移与地面重力位、重力、重力梯度之间的变化关系。摸拟计算了孕震位移和密度变化引起的重力位、重力、重力梯度变化的空间分布并分析了重力位、重力、重力梯度变化的空间分布特征。与此同时,采用广义司托克斯云积分和有限差分方法对云南丽江7. 0级地震前重力位、重力、重力水平梯度进行了计算。结果表明,强震前重力位、重力、重力梯度有其自身的变化特征,这对预测强震有实际意义。     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

基于共轭梯度算法的重力梯度数据三维聚焦反演研究

重力梯度数据相对于传统重力数据,能够更细致、准确地描述地球浅部构造和研究矿产资源分布等信息.本文采用共轭梯度算法,在加权密度域求解重力梯度数据三维聚焦反演最优化问题,以恢复地下三维密度分布,目标函数包括数据不拟合函数和最小支撑稳定函数.首先,在推导目标函数对加权密度的一阶导数时,为了得到更合理的计算公式,我们考虑变加权函数中含有密度变量;此外,本文通过密度上下限约束,改善了传统聚焦反演中聚焦因子选取困难的问题.新算法获得的反演结果,对聚焦因子的选择约束较少,相比传统聚焦算法,能够更容易的获得理想结果.将方法应用于理论模型验证其有效性和正确性,并应用本文方法处理文顿盐丘地区的航空全张量重力梯度数据,得到了与已知地质信息匹配的密度分布,表明本文方法具有处理实际数据的能力.     

近地表密度估计的重力贝叶斯分析方法及在云南地区的应用

基于布格重力异常相对于地形起伏光滑分布的约束条件,从一维自由空气重力异常数据出发,采用贝叶斯方法估算近地表岩石密度,同时采用三次B样条函数拟合布格重力异常,获取光滑分布的布格重力异常.数据拟合和光滑约束之间的权重采用Akaike贝叶斯准则(ABIC准则)自动确定.均匀剖分模型和不均匀剖分模型数据试验都验证了该方法的有效性.相关参数评价表明,足够多的样条系数可以提高估计结果的准确性,样条系数的个数接近测点数时可获得较稳定的估计结果.增大异常的噪声水平时,ABIC准则可有效地自动增大先验光滑约束的权重.云南地区两条重力剖面应用结果表明,剖面沿线的近地表密度值起伏变化明显(达2.45~2.8g·cm^-3),前寒武纪和古生代地层密度相对较高(主要为2.53~2.75g·cm^-3),而中生代密度较低(2.45~2.73g·cm^-3);本文估计的近地表密度结果与区域物性资料及地表地质特征较吻合;估计的剖面布格重力异常具有光滑性;红河断裂两侧近地表密度差异较大,可达0.4g·cm^-3.本文获得的两条剖面近地表密度结构和布格重力异常为该区深部结构与构造研究提供更可靠的重力基础数据.     

Inverse modelling of elastic thickness by convolution method - the eastern Alps as a case example

An unconventional scheme is used to estimate the flexural rigidity, or equivalently the elastic thickness of the lithosphere, given the topography and gravity data. The flexural rigidity is the parameter that governs the flexural response of the lithosphere in the frame of the thin plate flexure model. The scheme is an alternative to the widely used calculation of admittance of topography (sea-floor or continental topography) and gravity, bearing some advantages which are explained in the paper. The scheme involves the inversion of the gravity data in order to formulate a model of the crust-mantle interface (CMI) undulations. In a second step the flexure parameter is then evaluated from the relation between topography and CMI variations. Instead of calculating the admittance function using a spectral analysis, a set of point-load response functions are used in order to retrieve the optimal flexure parameter. This has two main advantages: instabilities of the numerical admittance evaluation at wavenumbers with low spectral energy in the topography are overcome and the analysis can be made over an area which is not necessarily rectangular, as required for the spectral analysis. The proposed method allows a higher space resolution of elastic thickness than any spectral method. For validation, the numerical strategy is applied to the situation of a realistic synthetic model, where all inputs and outputs are known a priori. Finally the spatial variations of the elastic thickness are studied in an area across the Eastern Alps.     

基于地形精化的金星重力场模型VGM2013

高精度金星重力场的获取,是金星探测的重要内容.本文利用最新的金星地形和重力模型,通过高通滤波后的残差地形（RTM）并在考虑均衡改正的情况下改进了重力的短波成分,最终提出了一个新的金星重力模型VGM2013,该模型赤道分辨率达10 km量级,大大高于现有的金星重力场模型,最终结果是金星表面重力加速度和重力扰动.研究中同时发现金星在Airy-Heiskanen均衡模型下的全球最优补偿深度为30 km,金星地壳的密度可能小于当前认为的2700~2900 kg·m^-3.VGM2013模型的结果可为将来的金星探测器定轨和着陆导航提供参考,作为重力计算的先验模型.但由于该模型没有包含短波重力观测信息,不建议直接用于更小尺度的地质和地球物理解释.     

Investigation of topographic reductions and aliasing effects on gravity and the geoid over Greece based on various digital terrain models

The reduction of gravity-field related quantities (e.g., gravity anomalies, geoid heights) due to the topography plays a crucial role in both geodetic and geophysical applications, since in the former it is an intermediate step towards geoid prediction and in the latter it reveals lateral as well as radial density contrasts and infers the geology of the area under study. The computations are usually carried out by employing a DTM and/or a DBM, which describe the topography and bathymetry, respectively. Errors in these DTMs/DBMs will introduce errors in the computed topographic effects, while poor spatial resolution of the topography and bathymetry models will result in aliasing effects to both gravity anomalies and geoid heights, both influencing the accuracy of the estimated solutions. The scope of this work is twofold. First, a validation and accuracy assessment of the SRTM 3″ (90 m) DTM over Greece is performed through comparisons with existing global models as well as with the Greek 450 m national DTMs. Whenever a misrepresentation of the topography is identified in the SRTM data, it is “corrected” using the local 450 m DTM. This process resulted in an improved SRTM DTM called SRTMGr, which was then used to determine terrain effects to gravity field quantities. From the fine-resolution SRTMGr DTMs, coarser models of 15″, 30″, 1′, 2′ and 5′ have been determined in order to investigate aliasing effects on both gravity anomalies and geoid heights by computing terrain effects at variable spatial resolutions. From the results acquired in two test areas, it was concluded that SRTMGr provides similar results to the local DTM making the use of other older global DTMs obsolete. The study for terrain aliasing effects proved that when high-resolution and accuracy gravity and geoid models are needed, then the highest possible resolution DTM should be employed to compute the respective terrain effects. Based on the results acquired from two the test areas a corrected SRTMGr DTM has been compiled for the entire Greek territory towards the development of a new gravimetric geoid model. Results from that analysis are presented based on the well-known remove-compute-restore method, employing land and marine gravity data, EGM08 as a reference geopotential model and the SRTMGr DTM for the computation of the RTM effects.     

Discussion of Mean Gravity Along the Plumbline

According to the definition of the orthometric height, the mean value of gravity along the plumbline between the Earth's surface and the geoid is defined in an integral sense. In Helmert's (1890) definition of the orthometric height, a linear change of the gravity with depth is assumed. The mean gravity is determined so that the observed gravity at the Earth's surface is reduced to the approximate mid-point of the plumbline using Poincaré-Prey's gravity gradient. Niethammer (1932) and later Mader (1954) took into account the mean value of the gravimetric terrain correction within the topography considering the constant topographical density distribution along the plumbline (for more details see Heiskanen and Moritz, 1967). Vaníek et al. (1995) included the effect of the lateral variation of the topographical density into the definition of Helmert's orthometric height. Recently, Hwang and Hsiao (2003) discussed the influence of the vertical gradient of disturbing gravity on the orthometric heights. In this paper, the mean integral value of gravity along the plumbline within the topography is defined so that the actual topographical density distribution and the change of the disturbing gravity with depth are taken into account. Based on the definition of the mean gravity, the relation between the orthometric and normal heights is discussed.     

三维起伏地形条件下航空瞬变电磁响应特征研究

航空瞬变电磁法以其速度快、成本低、通行性好等的优势能够有效的应用于地质地形条件复杂的地区.目前对于航空瞬变电磁法的研究主要基于平坦地形的理想情况,对于地形效应的研究相对较少,然而实际应用中地形不可避免,若忽略地形影响将对资料解释造成较大的误差,从而制约航空电磁方法的进一步发展.本文基于交错网格的时域有限差分方法对三维起伏地形条件下航空瞬变电磁进行正演模拟,在保证算法准确性的前提下给出大量模型算例.以经典地形模型为例,利用所给方法计算三维正演响应,结果显示起伏对于航空瞬变电磁数据有着显著的影响且影响主要集中在早期.而后,以实际地质资料为基础,构建起伏地形条件下包含多个异常体的三维复杂模型,计算了复杂模型的航空瞬变电磁响应,并给出三维全域视电阻率曲线,从而对地形效应的影响有了更加直观的认知.最后,通过大量模型讨论了地形的尺寸参数、电性参数、飞行轨迹与飞行高度等因素变化对于航空瞬变电磁数据的影响情况,并得出有价值的结论.     

Gravity for Lithosphere Architecture Determination and Analysis: the Central Eastern Mediterranean case study

The Central-Eastern Mediterranean region is known to be a complex area due to the interaction of four tectonic plates, namely Arabia, Africa, Anatolia and Eurasia, and by the presence of an ancient oceanic crust in the Herodotus and Ionian Basins. The analysis of the available literature highlights that the distribution of the freely available geophysical data (i.e. seismic, gravity and magnetic observations) is quite disparate. In this framework, high-resolution global gravity field models, such as XGM2019e, mainly based (offshore) on satellite data, can be profitably used as a uniform dataset to study, in a coherent way, large regions. In the current work, we exploit the XGM2019e model, together with a set of a priori information, derived mainly from geophysical data retrieved from the literature, to study the structure of the crust in the Central-Eastern Mediterranean area. The study is organized in three different phases: in the first one, we enhanced the map of geological crustal provinces by means of an automatic Bayesian classification algorithm applied to the second radial derivatives of the gravitational potential. In the second phase, using as observation a grid of gravity anomalies, we applied a full three-dimensional inversion procedure (always based on a Bayesian paradigm) to estimate the mass density variations and the geometries of the main geological units in the whole study area. Finally, in the third phase, we performed a refined three-dimensional local inversion on the Cyprus area to improve the modelling of the shallowest layers. The main results of this study, carried out in the framework of the European Space Agency GIADA project, are freely available, upon request, at https://www.g-red.eu/geophysics/ .