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An elevation mask modeling method based on azimuth rounding for monitoring building deformation 基于方位角舍入的建筑变形监测高程掩模建模方法
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-06-27 DOI: 10.1007/s40328-023-00413-y
Han Junqiang, Tu Rui, Lu Xiaochun, Xiao Xia, Zhang Rui, Fan Lihong, Zhang Pengfei, Wang Siyao

With the rapid growth of the construction industry, precise and efficient monitoring of building deformation has become a crucial factor in ensuring their secure construction and stable operation. The frequent occurrence of occlusion and diffraction errors in satellite signals caused by high-rise buildings has emerged as a primary challenge that constrains the accuracy of positioning in deformation monitoring by BeiDou Navigation Satellite (BDS). To solve the problems, this study proposes an elevation mask angle modeling method of satellite signal occlusion based on azimuth rounding and applies it to real-time BDS building deformation monitoring and positioning algorithm. The proposed approach involves defining a particular subset of integer azimuth and elevation angles, followed by utilizing the minimum elevation angle from this subset to develop a model for the azimuth-dependent elevation mask angle. We aimed to develop an elevation angle mask model using a conventional approach, and the model can be utilized to focus on non-line-of-sight (NLOS) and multipath signals and attenuate their impact on positioning accuracy by reducing their weight. The experimental results show that the elevation angle mask model can be easily completed by using the observation data of BDS satellites in a single day, and its use can make the number of effective satellites involved in the calculation of real-time deformation monitoring of BDS more accurate and reliable. The root mean square (RMS) of positioning results including float solutions was increased respectively by 91.1%, 93.3%, and 72.7% in the direction of East-North-Up (ENU), and the RMS of results with fixed ambiguity was increased by 6.9%, 10.0%, and 29.5%, respectively. Therefore, it can be concluded that the elevation mask angle modeling algorithm is convenient to realize and can significantly improve the performance of deformation monitoring results by BDS.

随着建筑业的快速发展,对建筑物变形进行精确、高效的监测已成为保证其安全施工和稳定运行的关键因素。高层建筑引起的卫星信号频繁出现遮挡和衍射误差,已成为制约北斗卫星变形监测定位精度的主要挑战。针对这一问题,本研究提出了一种基于方位角舍入的卫星信号遮挡仰角建模方法,并将其应用于BDS建筑变形实时监测与定位算法。所提出的方法包括定义整数方位角和仰角的特定子集,然后利用该子集中的最小仰角来开发与方位角相关的仰角掩模角模型。我们的目标是使用传统方法开发仰角掩模模型,该模型可用于聚焦非视距(NLOS)和多径信号,并通过降低其权重来减弱其对定位精度的影响。实验结果表明,仰角掩模模型可以很容易地利用BDS卫星在一天内的观测数据完成,它的使用可以使参与BDS实时变形监测计算的有效卫星数量更加准确和可靠。含浮子溶液的定位结果在东北朝上(ENU)方向的均方根(RMS)分别提高了91.1%、93.3%和72.7%,固定模糊定位结果的均方根(RMS)分别提高了6.9%、10.0%和29.5%。由此可见,仰角掩模建模算法实现方便,能显著提高北斗系统变形监测结果的性能。
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引用次数: 0
Inversion of self-potential data by a hybrid DE/PSO algorithm 基于混合DE/PSO算法的自势数据反演
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-06-21 DOI: 10.1007/s40328-023-00414-x
Sanam Hosseinzadeh, Gökhan Göktürkler, Seçil Turan-Karaoğlan

The aim of this work is to investigate whether retrieving the model parameters of self-potential (SP) anomalies using a combination of differential evolution (DE) and particle swarm optimization (PSO) is possible. This approach hybridizes DE and PSO in a parallel way. Each algorithm is self-contained and obtains a [premature] solution after a user-defined generation number. This hybrid algorithm (DE/PSO) selects the best individual in DE and PSO populations and carries it to the next iteration. Cooperation of DE and PSO can significantly improve the results. Simulations through noise-free synthetic anomalies show that the DE/PSO hybrid algorithm is successful in providing more accurate solutions than those obtained using each single metaheuristic. The algorithm also speeds up the rate of convergence to get the optimum solution. We implemented the algorithm in R programming environment using available metaheuristics packages. Then, the reliability of the code was investigated using some mathematical test functions having two and higher dimensions (unknowns). The performance of the hybrid to invert SP anomalies was tested by synthetic and field data sets. The true model parameters were well-recovered from synthetic data sets including noise-free and noisy data. In the tests with field data, SP anomalies over a shallow ore deposit in Süleymanköy (Türkiye), a deep ore deposit in Arizona (USA), and multiple sources of graphite deposits in KTB borehole site (Germany) were inverted. Low misfit values between the observed and calculated SP anomalies were obtained during the test studies.

这项工作的目的是研究是否可能使用差分进化(DE)和粒子群优化(PSO)的组合来检索自势(SP)异常的模型参数。这种方法以并行的方式将DE和PSO杂交。每个算法都是自包含的,在用户定义的生成数之后得到一个[早产儿]解。这种混合算法(DE/PSO)在DE和PSO种群中选择最优个体,并将其携带到下一次迭代中。DE和PSO的配合可以显著提高结果。通过无噪声合成异常的仿真表明,DE/PSO混合算法比单个元启发式算法提供了更精确的解。该算法还加快了收敛速度以获得最优解。我们使用可用的元启发式包在R编程环境中实现了该算法。然后,利用二维及高维(未知)的数学测试函数对代码的可靠性进行了研究。通过综合数据集和现场数据集测试了该混合方法反演SP异常的性能。从合成数据集(包括无噪声数据和有噪声数据)中很好地恢复了真实的模型参数。在现场数据测试中,反演了Süleymanköy (t rkiye)浅层矿床、美国亚利桑那州深部矿床和德国KTB钻孔多点石墨矿床的SP异常。在试验研究中,观测到的SP异常与计算得到的SP异常之间的不拟合值很低。
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引用次数: 1
3D geological model and geotechnical data for Bucharest: necessary input for assessing local seismic hazard of a densely populated area 布加勒斯特的三维地质模型和岩土数据:评估人口稠密地区当地地震危险的必要投入
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-06-02 DOI: 10.1007/s40328-023-00412-z
Andrei Bala, Dragos Toma-Danila, Viorica Ciugudean-Toma

Especially after the March 4, 1977 disastrous Vrancea earthquake (Mw 7.4), the necessity for a detailed local seismic hazard map for Bucharest, the capital city of Romania, was recognized. The distribution of earthquake effects as well as subsequent earthquake recordings throughout the city revealed a high variability of seismic ground motion, not only due to source effects but also due to local site effects. The geophysical methods employed in recent years allowed only limited results, so that there are no general geological models of the city applicable to a city-wide analysis. By using a recently compiled geological database, which relies mostly on several hundreds of borehole measurements performed for the subway in Bucharest and a recent DEM for the area, this study establishes the positions of the main seven Quaternary layers beneath the city. A 3D geological model is obtained by interpolation using the GIS kriging method. The 3D geologic model covers most of the city area, reflecting the confidence boundaries. This study also discusses geotechnical data availability and the influence of hydrogeology on the analysis of microzonation of the Bucharest city area.

特别是在1977年3月4日灾难性的弗朗西亚地震(Mw 7.4)之后,人们认识到为罗马尼亚首都布加勒斯特绘制详细的当地地震危险地图的必要性。地震效应的分布以及随后在整个城市的地震记录表明,地震地面运动的高度变异性不仅是由于震源效应,而且是由于局部场地效应。近年来采用的地球物理方法只能得到有限的结果,因此没有适用于全市分析的一般城市地质模型。通过使用最近编制的地质数据库,该数据库主要依赖于对布加勒斯特地铁进行的数百个钻孔测量和该地区最近的DEM,本研究确定了城市下方主要的七个第四纪层的位置。利用GIS克里格法插值得到三维地质模型。三维地质模型覆盖了大部分城市区域,反映了置信边界。本研究还讨论了岩土资料的可获得性和水文地质对布加勒斯特城区微区带分析的影响。
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引用次数: 0
A frequency domain approach to evaluate 2D seismic site response: application to the real case 一种评估二维地震场地反应的频域方法:在实际案例中的应用
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-04-28 DOI: 10.1007/s40328-023-00411-0
Navid Soltani, Mohammad Hossein Bagheripour

The seismic response obtained at the ground level can be quite different in terms of load characteristics compared with incident wave applied to the bedrock. These changes may be due to soil conditions and topography of the area. In this study, a practical approach is proposed in the frequency-domain to evaluate two-dimensional seismic ground response using transfer functions. To use the formulation of the proposed approach, a program was written called “2DTF”. The linear 2DTF software is promoted to equivalent linear program, and then two real cases of the Adames region during September 7th, 1999 earthquake are adopted for further study. These case studies have different characteristics, including free fields and areas where topography has a direct effect of changing the nature of the incident seismic waves. The superiority of the proposed two-dimensional over the conventional one-dimensional methods (despite its simplicity and practicality) is its capability to simulate different soil layering conditions and surface irregularity with high speed and accuracy. Numerical case studies show that using the 2DTF program provides reasonable and consistent results with local observations as well as verified research.

与基岩上的入射波相比,在地面上得到的地震反应在荷载特征方面可能有很大的不同。这些变化可能是由于该地区的土壤条件和地形。在本研究中,提出了一种在频域使用传递函数来评估二维地震地面反应的实用方法。为了使用所提出的方法的公式,编写了一个名为“2DTF”的程序。将线性2DTF软件提升为等效线性程序,并采用1999年9月7日阿达姆斯地区地震的两个实际案例进行进一步研究。这些案例研究具有不同的特征,包括自由场和地形对改变入射地震波性质有直接影响的区域。所提出的二维方法相对于传统的一维方法的优势(尽管它简单实用)是它能够以高速度和精度模拟不同的土壤分层条件和表面不规则性。数值算例研究表明,采用2DTF程序得到的结果与当地观测结果和已验证的研究结果合理且一致。
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引用次数: 0
Active tectonics of the Circum-Pannonian region in the light of updated GNSS network data 基于最新GNSS网络数据的环潘诺尼亚地区活动构造
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-04-05 DOI: 10.1007/s40328-023-00409-8
Kristóf Porkoláb, Taco Broerse, Ambrus Kenyeres, Eszter Békési, Sándor Tóth, Bálint Magyar, Viktor Wesztergom

The Pannonian basin is an extensional back-arc basin that has undergone neotectonic inversion and is currently shortening. The understanding and quantification of present-day deformation processes during this inversion are still incomplete. To this end, we investigate the active deformation of the Circum-Pannonian region via the interpolation of GNSS-derived velocity field and the derivation of the strain rate fields. For the interpolation of the velocity field, we use ordinary kriging, a strochastic interpolation method. Our results show that estimating a strain rate field that is virtually free of short-wavelength noise requires the scaling of the velocity uncertainties, i.e. assuming a minimum standard deviation of 1 mm/yr in our case. The deformation of the Circum-Pannonian region is defined by the 2–3 mm/yr, NNE-directed motion of the Dinarides, and by the 0.5–1.5 mm/yr, WSW to SSW directed motion of the eastern areas (European foreland, East Carpathians, South Carpathians, Transylvanian basin). These opposite-sense motions define a large-scale, on average NE-SW shortening and transpression-type deformation in the Dinarides as well as in the Pannonian basin, while the East and South Carpathians undergo regional N–S extension. Neotectonic structures generally show good agreement with the strain rate field, for example in the Dinarides, Eastern Alps, or in the western Pannonian basin. However, the presence of fault-parallel shortening or biaxial shortening along sinistral neotectonic structures in the central and eastern Pannonian basin show some discrepancy between current geodetic and observed neotectonic deformation. The vertical velocity field shows dominantly 100 and 1000 km wavelength signals, the former is probably related to the response of the Pannonian lithosphere-asthenosphere system to neotectonic basin inversion, while latter can possibly be explained by far-field subsidence patterns induced by the mantle response to melting of the Fennoscandian ice sheet during the current interglacial period.

潘诺尼亚盆地是一个经历了新构造反转并正在缩短的伸展弧后盆地。对这一反演过程中现今变形过程的理解和量化仍然不完整。为此,我们通过插值gnss导出的速度场和推导应变率场来研究环潘诺尼亚区域的主动变形。对于速度场的插值,我们使用普通克里格插值法,这是一种随机插值方法。我们的结果表明,估计一个几乎没有短波噪声的应变率场需要对速度不确定性进行缩放,即假设在我们的情况下,最小标准偏差为1毫米/年。环潘诺尼亚地区的变形由第纳里季的2-3 mm/yr的北北东向运动和东部地区(欧洲前陆、东喀尔巴阡山脉、南喀尔巴阡山脉、特兰西瓦尼亚盆地)的0.5-1.5 mm/yr的WSW - SSW运动决定。这些反向运动决定了第纳里季和潘诺尼亚盆地的大规模、平均为NE-SW的缩短和挤压型变形,而东喀尔巴阡山脉和南喀尔巴阡山脉则经历了区域性的N-S伸展。新构造构造通常与应变速率场具有较好的一致性,例如在迪纳里德斯、东阿尔卑斯或潘诺尼亚盆地西部。然而,潘诺尼亚盆地中东部沿左旋新构造断层平行缩短或双轴缩短的存在,表明当前大地测量与观测到的新构造变形存在一定的差异。垂直速度场以100 km和1000 km波长信号为主,前者可能与潘诺尼亚期岩石圈-软流圈系统对新构造盆地反转的响应有关,后者可能与当前间冰期地幔对芬诺斯坎德冰盖融化的响应引起的远场沉降模式有关。
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引用次数: 2
Effects of thermal shock and aging on natural stones: an experimental and statistical study 热冲击和老化对天然石材的影响:实验和统计研究
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-04-04 DOI: 10.1007/s40328-023-00410-1
Engin Özdemir, Didem Eren Sarıcı

Natural stones are exposed to sudden and slow-developing thermal cycles, affecting their physico-mechanical and surface properties. In this study, changes in the physico-mechanical properties of natural stones in response to sudden (thermal shock) and slow-developing (thermal aging) thermal cycles were investigated on natural stone samples with various compositions (magmatic, sedimentary, metamorphic). Both the thermal shock and thermal aging cycles were simulated by first heating the specimens to 105 °C for 18 h. In case of the thermal shock cycles, the heating phase was followed by placing the samples in purred water for 6 h. To simulate the thermal aging cycles, specimens were allowed to cool at room temperature (23 °C) for 6 h. At the end of the cycles, a selection of physico-mechanical properties was evaluated and compared with the initial values. Results indicate that thermal treatments have a significant negative effect on the strength of the natural stone samples. Regression models were developed to estimate uniaxial compressive strength, point load strength, Brazilian tensile strength from non-destructive test parameters (Schmidt hardness, P wave velocity, porosity) of natural and treated samples. Results show that there are strong correlations between mechanical properties and non-destructive test parameters (R2 > 0.96, MAPE values between 2 and 5%).

天然石材暴露在突然和缓慢发展的热循环中,影响其物理力学和表面性能。本研究以岩浆岩、沉积岩、变质岩等不同成分的天然石材为研究对象,研究了突发性(热冲击)和缓慢发育性(热老化)热循环对天然石材物理力学性能的影响。热冲击和热老化周期模拟首先加热标本为18 h。105°C的热冲击循环,加热阶段之后,将样品放置在里面水6 h。模拟热老化周期,标本被允许冷却室温(23°C) 6 h。最后的周期,选择物理力学性质均与初始值。结果表明,热处理对天然石材的强度有显著的负影响。建立回归模型,根据无损测试参数(施密特硬度、P波速、孔隙率)估计天然和处理样品的单轴抗压强度、点载荷强度、巴西抗拉强度。结果表明,力学性能与无损检测参数之间存在较强的相关性(R2 > 0.96, MAPE值在2 ~ 5%之间)。
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引用次数: 0
Seismic site characterization using multichannel analysis of surface waves in the Singhbhum region of Jharkhand, India: a case study 利用多通道表面波分析印度贾坎德邦Singhbhum地区的地震现场特征:一个案例研究
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-04-01 DOI: 10.1007/s40328-023-00408-9
Ashhad Imam, Keshav K. Sharma, Virendra Kumar

The present study carries out subsurface exploration of Jamshedpur region using Active Multichannel Analysis of Surface Waves techniques that provide information on the different lithological characteristics. Four different sites (MASW-1 to MASW-4) were chosen in proximity to river basin to obtain a probable shear wave velocity profile. To record the raw wave field traces produced by a 10 kg sledgehammer, a linear array of 24 numbers of 4.5 Hz geophones was employed. The effects of data acquisition parameters, like sampling frequency (500 Hz, 1000 Hz, and 2000 Hz) and offset distance (1 m, 6 m, 8 m, and 20 m), were used to obtain a high-resolution dispersion image. Due to the variables selected as data acquisition parameters, the optimal set of data parameters was found, providing the best resolution of dispersion images for all the selected sites. The results indicate that the best resolution of the dispersion image was produced at an offset distance range of 6–8 m at sampling frequencies range of 500–1000 Hz at 1 m geophone spacing with five stacking, indicating a strong signal to noise ratio in a range of 80–90%. Up to a depth of ~ 3 m, stiff silty clay soil was discovered, and at depths of 30 m or more, medium- to very-dense weathered mica schist was discovered. At sites MASW-1 and MASW-3, respectively, slag fillings were found in the top layer at depths of 1.2 and 2.3 m. Greater depths of hard rock layers have also been found at site MASW-3. Locations along the river generally fall into National Earthquake Hazards Reduction Program (NEHRP) categories C or D.

本研究利用主动多通道表面波分析技术对Jamshedpur地区进行了地下勘探,提供了不同岩性特征的信息。选取了靠近流域的4个不同测点(MASW-1至MASW-4),获得了可能的横波速度剖面。为了记录一个10公斤重的大锤产生的原始波场轨迹,采用了一个由24个4.5 Hz检波器组成的线性阵列。利用采样频率(500 Hz、1000 Hz和2000 Hz)和偏移距离(1 m、6 m、8 m和20 m)等数据采集参数的影响,获得高分辨率色散图像。根据所选择的数据采集参数变量,找到最优的数据参数集,为所有选定的站点提供最佳的色散图像分辨率。结果表明,在偏移距离为6 ~ 8 m、检波器间隔为1 m、采样频率为500 ~ 1000 Hz、5次叠加的情况下,色散图像分辨率最高,信噪比达到80 ~ 90%。3 m以下为坚硬的粉质粘土,30 m以上为中至极致密的风化云母片岩。MASW-1和MASW-3分别在1.2 m和2.3 m的顶部层中发现了矿渣充填体。在MASW-3遗址也发现了更深的硬岩层。沿江地区一般属于国家减少地震灾害规划(NEHRP)的C类或D类。
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引用次数: 0
Using geophysical log data to predict the fracture density in a claystone host rock for storing high-level nuclear waste 利用地球物理测井资料预测存放高放核废料的粘土岩宿主岩的裂缝密度
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-03-02 DOI: 10.1007/s40328-023-00407-w
Emese Tóth, Ervin Hrabovszki, Tivadar M. Tóth

Previously drilled boreholes of a host rock for a potential nuclear waste repository in Hungary revealed a highly fractured claystone rock body. A crucial step for characterizing the hydrodynamic behavior of such a fractured reservoir is fracture identification and accurate calculation of the fracture density. Although acoustic borehole televiewers provide a reliable base for determining the fracture density, older boreholes usually lack such data. However, conventional borehole geophysical measurements are often accessible in such cases. The aim of this study was to identify any correlations between well log data and fracture density. Multiple linear regression analysis was performed on data from two boreholes penetrating the Boda Claystone Formation in southwest Hungary. The upper section of the BAF-4 borehole was used for training, where the fracture density was estimated with a fit of R2 = 0.767. The computed regression function predicted the fracture density with high accuracy in both boreholes for all intervals with typical lithological features. However, in some sections where anomalous well log data indicated changes in the lithology, the prediction accuracy decreased. For example, the function underestimated the fracture density in sandy intervals.

先前在匈牙利一个潜在的核废料储存库的宿主岩石上钻孔发现了一个高度断裂的粘土岩体。裂缝识别和裂缝密度的准确计算是表征此类裂缝性储层水动力特性的关键步骤。尽管声波井眼电视为确定裂缝密度提供了可靠的基础,但较老的井眼通常缺乏此类数据。然而,在这种情况下,通常可以使用常规的钻孔地球物理测量方法。这项研究的目的是确定测井数据与裂缝密度之间的相关性。对穿透匈牙利西南部Boda粘土岩组的两个钻孔数据进行了多元线性回归分析。BAF-4井眼上部用于训练,裂缝密度估计拟合R2 = 0.767。计算出的回归函数对具有典型岩性特征的所有井段的裂缝密度均有较高的预测精度。然而,在一些异常测井数据显示岩性变化的路段,预测精度下降。例如,该函数低估了砂质层段的裂缝密度。
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引用次数: 0
Delineation of hydrothermal alteration zones associated with mineral deposits, using remote sensing and airborne geophysics data. A case study: El-Bakriya area, Central Eastern Desert, Egypt 利用遥感和航空地球物理数据圈定与矿床有关的热液蚀变带。案例研究:埃及中东部沙漠El-Bakriya地区
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-02-27 DOI: 10.1007/s40328-023-00405-y
Reda Abdu Yousef El-Qassas, Atef Mohamed Abu-Donia, Ali Elsayed Ali Omar

El-Bakriya area is situated in the Central Eastern Desert of Egypt. It includes several mineral occurrences and/or deposits. Data from remote sensing and airborne geophysics (gamma-ray and magnetic) were combined to identify the hydrothermal alteration zones and structures related to these occurrences. Various processing of ASTER satellite images revealed fifteen zones of high probability for metallic mineralizations. Airborne gamma-ray spectrometric data clarify K-enrichment zones, which are correlated geologically with the distribution of calc-alkaline, alkali feldspar granites (Younger granites), and calc-alkaline quartzdiorites to granodiorites (Older granites), as well as basement metavolcanics and metasediments. An integrated hydrothermal alteration map was constructed, based on both ASTER remote sensing and airborne gamma-ray spectrometric data. This map delineates some metallic mineral occurrences and/or deposits, which are located in the detected hydrothermal alteration zones. Besides, it displays new potential zones for mineralization, such as: Gabal (G.) El-Shalul, G. El-Bakriya, G. Siwat El-Arsha and G. Umm Bisilla. The geologic and airborne magnetic maps demonstrate five structural lineament trends of E–W, ENE–WSW, NE–SW, NW–SE, and NNW–SSE directions, which might act as pathways to transport the hydrothermal solutions in the study area.

El-Bakriya地区位于埃及的中东部沙漠。它包括几个矿产地和/或矿床。结合遥感和航空地球物理(伽马射线和磁)数据,确定了与这些产状有关的热液蚀变带和构造。对ASTER卫星图像的各种处理揭示了15个高概率金属矿化带。机载伽玛能谱数据明确了钾富集带,与钙碱性、碱长石花岗岩(较年轻花岗岩)、钙碱性石英闪长岩-花岗闪长岩(较老花岗岩)以及基底变质火山和变质沉积岩的分布具有地质相关性。基于ASTER遥感和机载伽玛能谱数据,构建了综合热液蚀变图。这张地图描绘了位于已探测到的热液蚀变带的一些金属矿点和/或矿床。此外,还发现了新的成矿潜力带,如:Gabal (G.)El-Shalul, G. El-Bakriya, G. Siwat El-Arsha和G. Umm Bisilla。地质和航空磁图显示了E-W、ENE-WSW、NE-SW、NW-SE和NNW-SSE五个方向的构造线向,可能是研究区热液运移的通道。
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引用次数: 2
Transformation from a global spherical to an adjusted local rectangular harmonic model 从全局球面模型到调整局部矩形调和模型的转换
IF 1.4 4区 地球科学 Q2 Earth and Planetary Sciences Pub Date : 2023-02-21 DOI: 10.1007/s40328-023-00406-x
Georgios Panou, Romylos Korakitis

This work presents a technique to transform a global spherical to an adjusted local rectangular harmonic model. First, the mathematical form of a global spherical harmonic model is presented. Second, the necessary conversion from global (geocentric) into local rectangular coordinates is given. Third, Laplace’s equation is solved by the method of separation of variables in local rectangular coordinates and its solutions in different functional forms are presented. Then, the estimation of the coefficients of these mathematical models by a least squares’ adjustment process is described, using as data the values of the disturbing potential of the Earth’s gravity field. The strategy for the selection of the best mathematical model for a successful transformation is described and validated in different case studies. These refer to areas in Greece, China and Germany and include comparisons with other models or methods. The results show the applicability of the presented transformation and confirm its advantages.

本文提出了一种将全局球面模型转换为调整后的局部矩形调和模型的方法。首先,给出了全局球谐模型的数学形式。其次,给出了从全局(地心)坐标到局部直角坐标的必要转换。第三,在局部直角坐标系下用分离变量法求解拉普拉斯方程,给出了不同函数形式下的拉普拉斯方程解。然后,以地球重力场扰动势值为数据,用最小二乘平差法对这些数学模型的系数进行估计。在不同的案例研究中描述并验证了为成功的转换选择最佳数学模型的策略。这些是指希腊、中国和德国的地区,包括与其他模型或方法的比较。结果表明了所提出的改造方法的适用性和优越性。
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引用次数: 1
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Acta Geodaetica et Geophysica
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