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Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix 非对称刚度矩阵粘弹性波的表示定理
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2021-02-01 DOI: 10.1007/s11200-020-0158-2
Luděk Klimeš

In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In this paper, we thus derive the representation theorem for viscoelastic waves in a medium with a non-symmetric stiffness matrix. The representation theorem expresses the wave field at a receiver, situated inside a subset of the definition volume of the viscoelastodynamic equation, in terms of the volume integral over the subset and the surface integral over the boundary of the subset. For the given medium, we define the complementary medium corresponding to the transposed stiffness matrix. We define the frequency-domain complementary Green function as the frequency-domain Green function in the complementary medium. We then derive the provisional representation theorem as the relation between the frequency-domain wave field in the given medium and the frequency-domain complementary Green function. This provisional representation theorem yields the reciprocity relation between the frequency-domain Green function and the frequency-domain complementary Green function. The final version of the representation theorem is then obtained by inserting the reciprocity relation into the provisional representation theorem.

在弹性介质中,证明了刚度张量相对于第一对指标和第二对指标的交换是对称的,但该证明不适用于粘弹性介质。因此,我们导出了非对称刚度矩阵介质中粘弹性波的表示定理。表示定理表示位于粘弹性动力学方程定义体积子集内的接收器处的波场,表示为该子集上的体积积分和子集边界上的表面积分。对于给定的介质,我们定义了与转置刚度矩阵相对应的互补介质。我们将频域互补格林函数定义为互补介质中的频域格林函数。在此基础上,导出了给定介质中频域波场与频域互补格林函数之间关系的临时表示定理。这个临时表示定理给出了频域格林函数与频域互补格林函数之间的互易关系。然后将互易关系插入到临时表示定理中,得到了最终版本的表示定理。
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引用次数: 1
A data-driven method for time-varying wavelet extraction based on the local frequency spectrum 一种基于局域频谱的时变小波提取方法
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2021-02-01 DOI: 10.1007/s11200-020-1251-2
Yumeng Jiang, Siyuan Cao, Siyuan Chen, Duo Zheng

Seismic wavelet extraction always plays a central role in high-resolution seismic processing. Conventional methods assume that seismic data are stationary when a constant wavelet is considered, which ignores the time-varying characteristics of seismic wavelets. In reality, seismic data are nonstationary because of attenuation, scattering, and other physical processes during propagation, which means that the frequency spectrum of seismic signal changes from shallow to deep formations. We have developed a time-varying wavelet extraction method by using a highly energy-concentrated time-frequency representation technique. Time-varying wavelets are generated according to the local frequency spectrum at every instant. In addition, because the estimations of parameters for wavelet extraction are fully data-driven, the results of the proposed method are more accurate and suitable for the nonstationary nature of actual seismic data. Synthetic tests indicate the reliability and robustness of the proposed method, even under noise contamination. By applying the time-varying wavelet extracted using the proposed method to seismic inversion on a field data example, we obtain the deconvolution result with improved resolution and a better fit to the well-log reflectivity compared to that by using conventional wavelet extraction methods.

地震小波提取一直是高分辨率地震处理的核心。传统方法在考虑恒定小波时假定地震数据是平稳的,忽略了地震小波的时变特性。实际上,地震数据在传播过程中会受到衰减、散射等物理过程的影响,是非平稳的,这意味着地震信号的频谱会从浅层到深层发生变化。利用能量高度集中的时频表示技术,提出了一种时变小波提取方法。根据每一时刻的局域频谱产生时变小波。此外,由于小波提取的参数估计完全是数据驱动的,因此该方法的结果更准确,更适合实际地震资料的非平稳性质。综合实验表明,即使在噪声污染下,该方法也具有良好的可靠性和鲁棒性。将该方法提取的时变小波应用于现场地震反演实例,得到的反褶积结果与常规小波提取方法相比,分辨率提高,与测井反射率的拟合效果更好。
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引用次数: 2
Recent Macaronesian kinematics from GNSS ground displacement analysis 基于GNSS地面位移分析的Macaronesian运动学
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2021-01-08 DOI: 10.1007/s11200-020-1122-x
Ignacio Barbero, Cristina Torrecillas, Raúl Páez, Gonçalo Prates, Manuel Berrocoso

Macaronesia is a complex oceanic region spanning three tectonic plates in the northeast Atlantic ocean. It is composed of four archipelagos, widely distributed and limited to the east by the Iberian Peninsula and north-western coast of Africa. This study aims to clarify recent Macaronesian kinematics from 19 GNSS stations located on the four archipelagos and the Iberian and African coastlines. The analysis is based on nearly 15 years of common data acquisition and aimed to detect new effects of intraplate tectonics or similar local/regional events consistent with calculated ground displacements. Evaluating the GNSS stations residual velocities relative to those expected from the NNR-MORVEL56 model, higher residuals were found at continental coastal stations (Africa) than at oceanic ones (Canaries and Madeira). From the computed strain rate map, the possible existence of a shear zone connecting the Gloria and Transmoroccan fault systems, already mentioned by other authors, was depicted. Cluster statistical analysis of the horizontal residual velocities helped to identify tectonic boundaries in Macaronesia and four groups of analogous intraplate residual velocities within this region. Three of four groups were identified in the Azores, highlighting the African-Nubian-Eurasian diffuse plate boundary in this region. Furthermore, in the Canary Islands, two distinct kinematic behaviours were detected, possibly due to the activity along a previously detected tectonic fault between Tenerife and Gran Canaria, where some stations have similar intraplate residuals to those at Madeira and Cape Verde stations, while others have similar intraplate residuals to those of continental stations. Finally, all stations on oceanic crust, except Cape Verde, present recent ground subsidence which may be attributed to isostatic adjustment.

马卡罗尼西亚是大西洋东北部一个横跨三个构造板块的复杂海洋区域。它由四个群岛组成,分布广泛,东部受伊比利亚半岛和非洲西北海岸的限制。本研究旨在从位于四个群岛和伊比利亚和非洲海岸线的19个GNSS站澄清最近的马卡罗尼西亚运动学。该分析基于近15年的普通数据采集,旨在检测与计算出的地面位移相一致的板内构造或类似的局部/区域事件的新影响。相对于NNR-MORVEL56模式的预期,评估GNSS站的剩余速度,发现大陆沿海站(非洲)的剩余比海洋站(加那利岛和马德拉岛)的剩余要高。从计算的应变率图中,描绘了其他作者已经提到的连接格洛里亚和跨摩洛哥断裂系统的剪切带的可能存在。水平残余速度的聚类统计分析有助于确定马卡罗尼西亚的构造边界和该地区四组类似的板内残余速度。在亚速尔群岛发现了4个群中的3个,突出了该地区的非洲-努比亚-欧亚扩散板块边界。此外,在加那利群岛,检测到两种不同的运动行为,可能是由于先前在特内里费岛和大加那利岛之间检测到的构造断层的活动,其中一些台站具有与马德拉和佛得角台站相似的板内残余,而其他台站具有与大陆台站相似的板内残余。最后,除佛得角外,海洋地壳上的所有台站最近都出现地面沉降,这可能归因于均衡调整。
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引用次数: 1
Mantle deformation and seismic anisotropy beneath Northeast India inferred from SKKS birefringence 由SKKS双折射推断的印度东北部地幔形变和地震各向异性
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2021-01-08 DOI: 10.1007/s11200-020-1121-y
Poulommi Mondal, Debasis D. Mohanty

The present study produces very new SKKS splitting measurements from the Northeast India, suggesting the region as tectonically more heterogeneous and complex in nature. It fills the gap of anisotropic parameters from an epicentral range of 140°–180° in order to understand the lithospheric deformation patterns of the terrain in a better way. The splitting parameters namely polarisation direction of fast waves (?) and delay time are the manifestation of anisotropic effects of a medium. The present SKKS splitting measurements from nine broadband seismic stations in Northeast India incorporate new understandings of deformation patterns for this region. At the Himalayan collision zone and sub-Himalayan region, the deformation pattern showing a perfect alignment of the ? parallel to the collisional arc (Main Boundary Thrust, Main Central Thrust), suggests that a localized strain derived from N-S Indo-Eurasian collision is the major source behind its complex tectonics. The SKKS splitting measurements at Assam foredeep region streamline the effect of Kopili fault in controlling the deformation patterns in a NW-SE direction. There is a significant difference in anisotropic behaviour of stations at the northern Shillong plateau compared to the stations at its southern proximity. The absolute plate motion (APM) parallel to ? in northern fringe of the plateau strictly indicates the influence of asthenospheric flow, which in turn is driven by APM of Indian plate in a no net rotation reference frame. On the other hand, major regional structures like the Dauki and Dapsi faults control the anisotropic pattern at the southern extremity of this plateau.

目前的研究产生了来自印度东北部的非常新的SKKS分裂测量,表明该地区在构造上更加不均匀和复杂。它填补了震中140°~ 180°范围内各向异性参数的空白,以便更好地了解地形的岩石圈变形模式。分裂参数即快波极化方向和延迟时间是介质各向异性效应的表现。目前来自印度东北部9个宽带地震台站的SKKS分裂测量结果结合了对该地区变形模式的新认识。在喜马拉雅碰撞带和亚喜马拉雅地区,变形模式呈现出完美的?平行于碰撞弧(主边界冲断、主中央冲断),表明源自南北向印度-欧亚碰撞的局部应变是其复杂构造背后的主要来源。阿萨姆前深地区SKKS分裂测量结果表明,Kopili断裂控制北西-东南方向的变形模式。西隆高原北部台站的各向异性与靠近西隆高原南部台站的各向异性有显著差异。平行于?的绝对板块运动(APM)在高原北部边缘,严格地表示软流圈流的影响,而软流圈流又受到无净旋转参考系下印度板块APM的驱动。另一方面,主要的区域构造,如道基断裂和大寺断裂控制了高原南端的各向异性格局。
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引用次数: 5
A new univariate deformation analysis approach considering displacements as model errors 一种考虑位移作为模型误差的单变量变形分析新方法
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2021-01-08 DOI: 10.1007/s11200-020-1024-y
Bahattin Erdogan, Serif Hekimoglu, Utkan Mustafa Durdag

In Conventional Deformation Analysis (CDA), at least two different epochs are adjusted by using the Least Squares Estimation (LSE) method and compared statistically. The effect of the geometry of the network is an essential part of the adjustment model and the LSE method smears the effects of the displaced point over the other nondisplaced points. In this study, to remove these spoiling effects and to increase the reliability of the deformation analysis, a new approach is introduced. This approach depends on the analysis of the differences between observations of the two epochs, and also considers the principles of the model error approach. All possible combinations of the differences of the observations are considered as model errors in Gauss-Markov model and the estimated model error for the combination, that has the smallest variance, is compared with a critical value to answer the question whether it is significant or not. To compare the results of the new approach with the CDA, the Monte Carlo simulation technique and mean success rate are used in a leveling network. As a consequence, according to the simulation results, the new approach is better than the CDA by 7.6% and 9.7% for one and two displaced points, respectively, when the deformation network is designed as a subnetwork.

在传统的形变分析(CDA)中,采用最小二乘估计(LSE)方法至少调整两个不同的时期,并进行统计比较。网络几何的影响是平差模型的重要组成部分,LSE方法将位移点的影响涂抹在其他非位移点上。在本研究中,为了消除这些破坏影响,提高变形分析的可靠性,引入了一种新的方法。该方法依赖于对两个时期观测值差异的分析,并考虑了模型误差方法的原理。在高斯-马尔可夫模型中,将观测值差异的所有可能组合视为模型误差,并将方差最小的组合的估计模型误差与临界值进行比较,以回答是否显著的问题。为了将新方法的结果与CDA方法进行比较,将蒙特卡罗模拟技术和平均成功率应用于一个水准网。仿真结果表明,当变形网络作为子网络设计时,对于一个位移点和两个位移点,新方法分别比CDA方法好7.6%和9.7%。
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引用次数: 1
Rate of seismic deformation in the Gulf of Aqaba inferred from moment-tensor summation 由矩张量求和推断的亚喀巴湾地震变形速率
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2020-11-09 DOI: 10.1007/s11200-020-1028-7
Sattam Almadani

This study aims to quantify the rate of coseismic deformation in the Gulf of Aqaba. Earthquake catalogue, Gutenberg-Richter relationship and fault plane solutions were integrated to measure the size and shape of deformation using the moment-tensor summation technique. First, the Gutenberg-Richter relationship was established using seismicity data from the period of 1964–2019. Then, the moment-tensor summation based on 44 focal mechanism solutions was used to calculate the shape of deformation. The eigenvalues of moment-tensor reflect the diversity of focal mechanism solutions that alternate from normal to strike-slip fault styles in the deformation zone. The analysis reveals a dominant shear deformation in the Gulf of Aqaba that extends in a direction of N42.2°E at a rate of 2.6 ± 0.04 mm yr?1and shortens in the direction of N305.2°E at a rate of 2.0 ± 0.02 mm yr?1. These results suggest that the active deformation occurring in the Gulf of Aqaba is due to the relative tectonic movements between the Arabian and African plates, as well as Sinai subplate.

本研究旨在量化亚喀巴湾同震形变的速率。结合地震目录、古腾堡-里希特关系和断层平面解,利用矩张量求和技术测量变形的大小和形状。首先,利用1964-2019年的地震活动数据建立了古腾堡-里希特关系。然后,采用基于44个焦点机构解的矩张量求和来计算变形形状。矩张量特征值反映了震源机制解的多样性,震源机制解在变形带正断层和走滑断层之间交替存在。分析表明,亚喀巴湾的主要剪切变形以2.6±0.04 mm /年的速率向N42.2°E方向延伸。沿N305.2°E方向以2.0±0.02 mm / yr的速率缩短。这些结果表明,亚喀巴湾的活动变形是由于阿拉伯板块和非洲板块以及西奈板块之间的相对构造运动造成的。
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引用次数: 1
Exact line search method for using the L1-norm misfit function in full waveform inversion 利用l1范数失拟函数进行全波形反演的精确线搜索方法
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2020-11-09 DOI: 10.1007/s11200-020-0904-5
Xiaona Ma, Guanghe Liang, Shanhui Xu, Zhiyuan Li, Haixin Feng

Full waveform inversion (FWI) is a non-linear inverse problem that can be sensitive to noise. The tolerance of the noise-interference characteristics depends on the types of misfit functions. To date, different misfit functions, such as the least-squares norm (L2), the least-absolute-value norm (L1), and combinations of the two (e.g., the Huber and hybrid criteria), have been applied to FWI. The L2 norm is highly sensitive to non-Gaussian errors in the data and gives rise to high-amplitude artifacts in reconstructed models. For non-Gaussian noise data, the L1 norm and the Huber and hybrid criteria always reliably reconstruct models. However, the Huber and hybrid criteria require tedious error investigations to estimate their threshold criterion. Thus, the L1 norm is adopted here to improve the anti-noise ability of the FWI. The step length is closely related to the misfit function, and an optimal step-length estimation method can rapidly make the FWI algorithm reach the global minimum, with a reduced number of iterations and fewer extra forward modeling simulations during each iteration. The step length can usually be obtained using the exact or inexact line search method. Generally, the exact line search method is faster than the inexact one. Therefore, we derived an exact line search method for the L1 norm in the FWI process. Its effectiveness was tested using noise-free data from Overthrust and the SEG/EAGE salt models. The results demonstrate that this method can recover high-resolution velocity models with low computational costs. Numerical tests using the synthetic Overthrust model contaminated by strong noise were used to further validate the robustness of this exact line search method.

全波形反演(FWI)是一个对噪声敏感的非线性反演问题。噪声干扰特性的容限取决于失配函数的类型。迄今为止,不同的失配函数,如最小二乘范数(L2)、最小绝对值范数(L1),以及两者的组合(如Huber和hybrid准则),已被应用于FWI。L2范数对数据中的非高斯误差高度敏感,并在重建模型中产生高振幅伪影。对于非高斯噪声数据,L1范数和Huber及混合准则总是可靠地重建模型。然而,Huber准则和混合准则需要繁琐的误差调查来估计它们的阈值准则。因此,这里采用L1范数来提高FWI的抗噪声能力。步长与失拟函数密切相关,最优步长估计方法可以快速使FWI算法达到全局最小值,减少迭代次数,减少每次迭代时额外的正演模拟次数。步长通常可以用精确或不精确的直线搜索方法得到。一般来说,精确线搜索方法比不精确线搜索方法要快。因此,我们推导出了FWI过程中L1范数的精确直线搜索方法。使用来自Overthrust和SEG/EAGE盐模型的无噪声数据测试了其有效性。结果表明,该方法能够以较低的计算成本恢复高分辨率速度模型。利用强噪声污染下的逆冲综合模型进行了数值试验,进一步验证了该精确线搜索方法的鲁棒性。
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引用次数: 1
Effect of a high-resolution global crustal model on gravimetric geoid determination: a case study in a mountainous region 高分辨率全球地壳模型对重力大地水准面确定的影响:以山区为例
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2020-10-27 DOI: 10.1007/s11200-020-1023-z
Ramazan Alpay Abbak

A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m?3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.

在假定大地水准面之上没有地形的情况下,利用Stokes公式确定了精确的重力大地水准面模型。然后,通过考虑地壳密度为2670 kg m?3为地形质量。事实上,地形质量的实际密度与恒定值相差约±20%。最近,加拿大新不伦瑞克大学发布了一个30″分辨率的全球地壳密度模型。本文研究了在土耳其某山区使用该模型对重力大地水准面精度的影响。数值结果表明,该模型对大地水准面高度的影响可达几分米,这在1厘米大地水准面精确建模中是不可忽视的。因此,该模型中包含的地形密度变化的影响是显著的,在精确确定大地水准面时应予以考虑,特别是在山区。
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引用次数: 6
Modeling 3D acoustic-wave propagation using modified cuboid-based staggered-grid finite-difference methods with temporal and spatial high-order accuracy 基于改进长方体交错网格的时空高阶精度有限差分方法模拟三维声波传播
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2020-10-27 DOI: 10.1007/s11200-020-1013-1
Shigang Xu, Yang Liu

To improve the modeling accuracy and adaptability of traditional temporal second-order staggered-grid finite-difference (SFD) methods for 3D acoustic-wave modeling, we propose a modified time-space-domain temporal and spatial high-order SFD stencil on a cuboid grid. The grid nodes on a double-pyramid stencil and the standard orthogonality stencil are used to approximate temporal and spatial derivatives. This stencil can adopt different grid spacing in each spatial axis, and thus it is more flexible than the existing one with the same grid spacing. Based on the time-space-domain dispersion relation, the high-order FD coefficients are generated by using Taylor expansion and least squares. Numerical analyses and modeling examples demonstrate that our proposed schemes have higher accuracy and better stability than other conventional schemes, and thus larger time steps can be used to improve the computational efficiency in 3D case.

为了提高传统时间二阶交错网格有限差分(SFD)方法在三维声波建模中的精度和适应性,提出了一种改进的长方体网格时空高阶交错网格模型。利用双金字塔模板和标准正交模板上的网格节点来近似时空导数。该模板可以在每个空间轴上采用不同的网格间距,因此比现有的相同网格间距的模板更具灵活性。基于时间-空间色散关系,采用泰勒展开和最小二乘法生成高阶FD系数。数值分析和建模实例表明,本文提出的格式比其他传统格式具有更高的精度和更好的稳定性,因此可以使用更大的时间步长来提高三维情况下的计算效率。
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引用次数: 0
Gravity sparse inversion using the interior-point method and a general model weighting function 利用内点法和一般模型加权函数进行重力稀疏反演
IF 0.9 4区 地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2020-10-24 DOI: 10.1007/s11200-020-0831-5
Wenwu Zhu, Junhuan Peng, Sanming Luo, Xiangang Meng, Jinzhao Liu, Chuandong Zhu

This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds.

本文提出了一种优化的重力稀疏反演方法。该方法使用边界约束的内点法和由密度模型的深度、紧度和核加权函数组成的一般加权函数来最小化全局目标函数。对于紧致度加权函数,实际实验表明,随着相对指数因子β值的增大,恢复模型变得更加紧致。但是,如果不采用合适的边界约束方法,则需要将β设为较大的值以获得紧凑的反演结果时,反演结果无法控制在指定的约束范围内。内点法允许在不违反边界约束的情况下使用较大的β来获得更紧凑的反演结果。此外,使用该方法可以更清晰地识别接近的模型。为了提高计算效率和获得更精确的正则化参数,还采用了预条件共轭梯度和l曲线或直线搜索方法。将该方法应用于3个综合算例:利用无噪声重力异常资料反演两个相邻的不同深度正体、利用无噪声或污染重力异常资料反演三个不同深度正或负体、利用污染重力异常资料反演具有一定倾角特征的三个正或负体。该方法还应用于巴西帕拉州Rio Maria地区Woodlawn硫化物体、Missouri铁矿体和花岗岩类岩体的反演。在所有6个测试用例中,使用较大的β值,并且在指定边界内恢复的密度模型具有更清晰的边界。
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引用次数: 1
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