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Gradient-based joint inversion of point-source moment-tensor and station-specific time shifts 基于梯度的点源力矩张量和特定站点时移联合反演
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-31 DOI: 10.1093/gji/ggae188
Thanh-Son Phạm
Summary The misalignment of the observation and predicted waveforms in regional moment tensor inversion is mainly due to seismic models’ incomplete representation of the Earth's heterogeneities. Current moment tensor inversion techniques, allowing station-specific time shifts to account for the model error, are computationally expensive. Here, we propose a gradient-based method to jointly invert moment-tensor parameters, centroid depth, and unknown station-specific time shifts utilizing the modern functionalities in deep learning frameworks. A $L_2^2$ misfit function between predicted synthetic and time-shifted observed seismograms is defined in the spectral domain, which is differentiable to all unknowns. The inverse problem is solved by minimizing the misfit function with a gradient descent algorithm. The method's feasibility, robustness, and scalability are demonstrated using synthetic experiments and real earthquake data in the Long Valley Caldera, California. This work presents an example of fresh opportunities to apply advanced computational infrastructures developed in deep learning to geophysical problems.
摘要 区域矩张量反演中观测波形与预测波形不一致的主要原因是地震模型对地球异质性的表述不完整。目前的矩张量反演技术允许特定台站的时间偏移来考虑模型误差,但计算成本高昂。在此,我们提出了一种基于梯度的方法,利用深度学习框架的现代功能,联合反演矩张量参数、中心点深度和未知的特定站点时间偏移。在频谱域定义了预测合成地震图与时移观测地震图之间的 $L_2^2$ misfit 函数,该函数对所有未知数都是可微分的。通过梯度下降算法最小化误拟合函数来解决逆问题。该方法的可行性、稳健性和可扩展性通过加利福尼亚州长谷破火山口的合成实验和真实地震数据得到了验证。这项工作提供了一个实例,说明将深度学习中开发的先进计算基础设施应用于地球物理问题的新机遇。
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引用次数: 0
Evaluating and Validating 3D Simulated MASW and SPAC In-Situ Tests in Argostoli, Greece 评估和验证希腊阿尔戈斯托利的三维模拟 MASW 和 SPAC 现场试验
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-31 DOI: 10.1093/gji/ggae187
Andrea C Riaño, Fernando Lopez-Caballero, Fabrice Hollender
Summary Geophysics and Geotechnical Engineering commonly use one-dimensional (1D) wave propagation analysis, simplifying complex scenarios by assuming flat and homogeneous soil layers, vertical seismic wave propagation, and negligible pore water pressure effects (total stress analysis). These assumptions are commonly used in practice, providing the basis for applications like analyzing site responses to earthquakes and characterizing soil properties through inversion processes. These processes involve various in-situ tests to estimate the subsurface soil’s material profile, providing insights into its behavior during seismic events. This study seeks to address the limitations inherent to 1D analyses by using three-dimensional (3D) physics-based simulations to replicate in-situ tests performed in the Argostoli basin, Greece. Active and passive source surveys are simulated, and their results are used to determine material properties at specific locations, employing standard geophysical methods. Our findings underscore the potential of 3D simulations to explore different scenarios, considering different survey configurations, source types, and array sets.
摘要 地球物理学和岩土工程通常使用一维(1D)波传播分析,通过假设土层平坦且均匀、地震波垂直传播以及孔隙水压力效应可忽略不计(总应力分析)来简化复杂情况。这些假设在实践中很常用,为分析场地对地震的响应以及通过反演过程确定土壤特性等应用提供了基础。这些过程涉及各种原位测试,以估算地下土壤的材料剖面,从而深入了解其在地震事件中的行为。本研究试图通过使用基于物理的三维(3D)模拟来复制在希腊阿尔戈斯托利盆地进行的原位测试,从而解决 1D 分析固有的局限性。我们模拟了主动源和被动源勘测,并采用标准地球物理方法将其结果用于确定特定位置的材料属性。我们的研究结果强调了三维模拟在探索不同方案、考虑不同勘测配置、源类型和阵列集方面的潜力。
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引用次数: 0
Including geological orientation information into geophysical inversions with unstructured tetrahedral meshes 利用非结构化四面体网格在地球物理反演中加入地质方位信息
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-30 DOI: 10.1093/gji/ggae186
Mitra Kangazian, Colin G Farquharson
Summary Minimum-structure, or Occam’s style of, inversion introduces a regularization function into the underdetermined geophysical inverse problems to stabilize the inverse problem and mitigate its non-uniqueness. The regularization function is typically designed such that it can incorporate a priori information into the inversion framework, thus constructing models that have more plausible representations of the true Earth’s subsurface structure. One type of a priori information is geological orientation information such as strike, dip, and tilt angles of the subsurface structure. This type of information can be incorporated into inverse problems through the roughness operators. Designing such roughness operators for inversion frameworks using unstructured tetrahedral meshes is not as straightforward as for inversion frameworks using structured meshes due to the arbitrary and complex geometry of unstructured meshes. Researchers have developed methods which allow us to incorporate geological orientation information into inversion frameworks with unstructured tetrahedral meshes. The majority of these methods consider each cell in a package with its neighbours, hence, the constructed models are not as sharp as desired if the regularization function is measured using an ℓ1-type measure instead of the ℓ2 norm. To address this issue, we propose a method that calculates the directional derivatives of physical property differences between two adjacent cells normalized by the distance between the cell centroids. This approach is able to both incorporate geological orientation information into the inversion framework and construct models with sharp boundaries for the scenarios in which the regularization term is quantified by an ℓ1-type measure. This method is an integral-based approach, therefore, the roughness operators are scaled appropriately by the cell volumes, which is an important characteristic for the inversions with unstructured meshes. To assess the performance and the capability of the proposed method, it was applied to 3D synthetic gravity and magnetotelluric (MT) examples. The gravity example was also used to investigate the impact of applying the depth weighting function inside and outside the roughness operators for the scenarios that the model objective function is measured by an ℓ1 norm. The examples show that the proposed method is able to construct models with a reasonable representation of the strike and dip directions of the true subsurface model with sharper boundaries if the regularization function is quantified by an ℓ1-type measure. The examples also demonstrate the proposed method behaves numerically well, and has a fast convergence rate.
摘要 最小结构反演或奥卡姆式反演在未确定的地球物理反演问题中引入正则化函数,以稳定反演问题并减轻其非唯一性。正则化函数的设计通常能将先验信息纳入反演框架,从而构建出更可信地反映真实地球地下结构的模型。一种先验信息是地质方位信息,如地下结构的走向、倾角和倾斜角。这类信息可通过粗糙度算子纳入反演问题。由于非结构网格的几何形状随意而复杂,为使用非结构四面体网格的反演框架设计此类粗糙度算子不如使用结构网格的反演框架简单。研究人员已经开发出一些方法,可以将地质方位信息纳入使用非结构化四面体网格的反演框架。这些方法大多将每个单元与其相邻单元打包考虑,因此,如果使用 ℓ1 类型而不是 ℓ2 规范来衡量正则化函数,所构建的模型就不那么清晰。为了解决这个问题,我们提出了一种方法,计算相邻两个单元之间物理特性差异的方向导数,并以单元中心点之间的距离归一化。这种方法既能将地质方位信息纳入反演框架,又能在正则化项被 ℓ1 类型度量量化的情况下构建边界清晰的模型。该方法是一种基于积分的方法,因此粗糙度算子会根据单元体积进行适当缩放,这是非结构网格反演的一个重要特征。为了评估所提出方法的性能和能力,我们将其应用于三维合成重力和磁辐射(MT)示例。重力实例还用于研究在粗糙度算子内部和外部应用深度加权函数对模型目标函数以 ℓ1 准则衡量的影响。实例表明,如果正则化函数采用 ℓ1 类型的度量,则所提出的方法能够构建出合理代表真实地下模型走向和倾角方向的模型,并且边界更加清晰。实例还证明了所提出的方法数值性能良好,收敛速度快。
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引用次数: 0
An integrated method for gravity gradient inversion and gravity gradient depth imaging 重力梯度反演和重力梯度深度成像综合方法
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-18 DOI: 10.1093/gji/ggae173
Yu Tian, Jinzhao Liu, Qing Ye, Lei Shi, Yong Wang, Jörg Ebbing
Summary Gravity gradient data can show the structural features of geological bodies in the shallow lithosphere with higher sensitivity and resolution than conventional gravity data. Gravity gradient inversion can be applied to obtain the lithospheric density structures of geological bodies. However, as with gravity data, gravity gradient data have no inherent depth resolution. The methods of gravity gradient depth imaging and gravity gradient inversion are integrated in this study. The depth imaging method is effective for calculations without prior information and iterative computations. As the parameters in the depth weighting function should be chosen from a set of values used in inversion tests of synthetic data, which brings some uncertainties, the depth imaging results of gravity gradient are introduced into the depth weighting function. Several synthetic models are tested to demonstrate the advantages and features of the effective integrated method. Finally, the integrated method is applied to the interpretation of the GOCE satellite gravity gradient tensors over the northeastern margin of the Qinghai-Tibet Plateau. The results reveal that in the crust of the study area, the distribution of density anomalies is more in line with the mechanism of the crustal flow model, in the upper mantle of the study area, the density anomalies are mainly influenced by the high heat flow environment.
摘要 重力梯度数据可以显示浅岩石圈地质体的结构特征,其灵敏度和分辨率均高于常规重力数据。重力梯度反演可用于获取地质体的岩石圈密度结构。然而,与重力数据一样,重力梯度数据没有固有的深度分辨率。本研究整合了重力梯度深度成像和重力梯度反演方法。深度成像法对于没有先验信息的计算和迭代计算非常有效。由于深度加权函数中的参数应从合成数据反演测试中使用的一组值中选择,这会带来一些不确定性,因此深度加权函数中引入了重力梯度的深度成像结果。对几个合成模型进行了测试,以展示有效集成方法的优势和特点。最后,将该综合方法应用于青藏高原东北缘 GOCE 卫星重力梯度张量的解释。结果表明,在研究区的地壳中,密度异常的分布更符合地壳流动模型的机理;在研究区的上地幔中,密度异常主要受高热流环境的影响。
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引用次数: 0
A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection 球壳雷利-贝纳德对流的广义曲线求解器
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-18 DOI: 10.1093/gji/ggae175
Souvik Naskar, Karu Chongsiripinyo, Siddhant Mishra, Anikesh Pal, Akshay Jananan
Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.
摘要 针对球壳中的布西内斯克对流,开发并实现了一种三维有限差分求解器。该求解器利用雅可比变换将任何复杂的曲线域转换为等效的笛卡尔域,并在后者中求解支配方程。这一功能使求解器能够考虑到行星和恒星对流区域非球形形状的影响。除了使用 MPI 进行并行化之外,还使用管道交替方向隐式方案和用于压力校正的 HYPRE 多网格加速器对粘性项进行隐式处理,从而使求解器能够高效地进行高保真直接数值模拟。我们在两个瑞利数 Ra = 105 和 107 的条件下进行了瑞利-贝纳德对流模拟,同时将普朗特数固定为 1(Pr = 1)。平均径向温度曲线和努塞尔特数在定性和定量方面都与现有文献非常吻合。湍流动能预算的封闭性,除了网格间距相对于局部科尔莫哥罗夫尺度的大小外,还确保了足够的空间分辨率。
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引用次数: 0
Multivariate processing of airborne natural source EM data - application to field data from gobabis (Namibia) 机载自然源电磁数据的多元处理--应用于戈巴比斯(纳米比亚)的实地数据
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-18 DOI: 10.1093/gji/ggae172
A Thiede, M Schiffler, A Junge, M Becken
Summary As deep-seated ore deposits become increasingly relevant for mineral exploration, the demand for time-efficient and powerful deep-sounding exploration methods rises. A suitable method for efficiently sensing ores at great depth is airborne electromagnetics (EM) using natural signal of atmospheric origin. The method relates airborne magnetic field recordings in the audio-frequency range to reference magnetic field recordings measured at a ground-based site and can achieve greater penetration depths when compared to controlled source airborne EM techniques. However, airborne natural source EM data are prone to noise caused by platform vibrations especially deteriorating data quality at low frequencies and thus narrowing the depth of investigation. Motional noise manifests as coherent noise on all airborne magnetic field components demanding for a powerful processing tool to remove such kind of noise. Unlike the bivariate approach, which is widely used in natural source EM, the multivariate approach is capable of detecting and reducing the effect of coherent noise. We introduce a robust multivariate processing for airborne natural source EM data and present the code implementation. The code was applied to a large-scale data set from the Kalahari-Copper-Belt in Namibia covering over 1, 000 km2. We obtained spatially consistent and smooth sounding curves in a frequency range of 10 to 1, 000 Hz including frequencies with prominent motional noise. Transfer functions are in good agreement with other geophysical and geological information.
摘要 随着深层矿藏与矿物勘探的关系日益密切,对省时、强大的深层探测方法的需求也随之增加。利用源自大气的自然信号进行机载电磁学(EM)是有效探测深层矿石的合适方法。这种方法将音频范围内的机载磁场记录与在地面站点测量的参考磁场记录联系起来,与受控源机载电磁技术相比,可以达到更大的穿透深度。然而,机载自然源电磁数据容易受到平台振动造成的噪声影响,特别是低频数据质量下降,从而缩小了调查深度。运动噪声表现为所有机载磁场分量上的相干噪声,需要一种强大的处理工具来去除这类噪声。与在自然源电磁学中广泛使用的二变量方法不同,多变量方法能够检测和减少相干噪声的影响。我们为机载天然源电磁数据引入了一种稳健的多变量处理方法,并介绍了代码实现。该代码应用于纳米比亚卡拉哈里-铜带的大规模数据集,覆盖面积超过 1,000 平方公里。我们获得了空间上一致且平滑的探测曲线,频率范围为 10 至 1,000 Hz,包括运动噪声突出的频率。传递函数与其他地球物理和地质信息十分吻合。
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引用次数: 0
Separation of source, attenuation and site parameters of 2 moderate earthquakes in France: an elastic radiative transfer approach 法国 2 次中度地震的震源、衰减和现场参数分离:弹性辐射传递方法
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-17 DOI: 10.1093/gji/ggae176
G Heller, L Margerin, O Sèbe, J Mayor, M Calvet, P Traversa, S Latour
Summary An accurate magnitude estimation is necessary to properly evaluate seismic hazard, especially in low to moderate seismicity areas such as Metropolitan France. However, magnitudes of small earthquakes are subject to large uncertainties caused by major high-frequency propagation effects which are generally not properly considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. The key feature of our approach is the treatment of attenuation -both scattering and absorption- in a simple but realistic velocity model of the Earth’s lithosphere, including a velocity discontinuity at the Moho. To reach this goal, we developed a 2-step inversion procedure, allowing first to extract attenuation parameters for each source-station path from the whole observed energy envelope using the Levenberg-Marquardt and grid-search algorithms, then to determine site amplification and the source displacement spectrum from which the moment magnitude Mw is extracted. In the first step, we use the forward modeling procedure of Heller et al. (2022) in order to simulate energy envelopes by taking into account the full treatment of wave polarization, the focal mechanism of the source and the scattering anisotropy. The inversion procedure is then applied to the 2019 ML 5.2 Le Teil and 2014 ML 4.5 Lourdes earthquakes which both occurred in southern France. Data from 6 stations are selected for each event. The inversion results confirm a significant variability in the attenuation parameters (scattering and absorption) at regional scale and a strong frequency dependence. Scattering appears to be stronger towards the French Alps and Western Pyrenees. Absorption is stronger as frequency increases. Although not very resolvable, the mechanism of scattering appears to be forward or very forward. By inverting the source spectrum, we determine moment magnitudes Mw of 5.02 ± 0.17 for the Le Teil earthquake and 4.17 ± 0.15 for the Lourdes earthquake.
摘要 要正确评估地震灾害,尤其是在法国大都市等中低地震活动区,必须进行准确的震级估算。然而,小地震的震级受主要高频传播效应的影响,具有很大的不确定性,而这些效应通常没有得到适当考虑。为了解决这个问题,我们开发了一种方法,将震源、衰减和场地参数从地震图全能量包络的弹性辐射传递建模中分离出来。我们的方法的主要特点是在一个简单但现实的地球岩石圈速度模型中处理衰减(包括散射和吸收),包括莫霍面的速度不连续性。为了实现这一目标,我们开发了一种分两步的反演程序,首先使用 Levenberg-Marquardt 和网格搜索算法从整个观测能量包络中提取每个源站路径的衰减参数,然后确定站点放大和源位移谱,并从中提取矩幅 Mw。第一步,我们使用 Heller 等人(2022 年)的前向建模程序,通过全面考虑波的极化、源的聚焦机制和散射各向异性来模拟能量包络。反演程序随后被应用于发生在法国南部的 2019 ML 5.2 Le Teil 地震和 2014 ML 4.5 Lourdes 地震。每次地震都选取了 6 个站点的数据。反演结果证实,区域范围内的衰减参数(散射和吸收)存在显著差异,并且与频率有很大关系。法国阿尔卑斯山和西比利牛斯山脉的散射似乎更强。频率越高,吸收越强。虽然不是很清晰,但散射机制似乎是正向或非常正向的。通过反演震源频谱,我们确定 Le Teil 地震的矩震级 Mw 为 5.02 ± 0.17,卢尔德地震的矩震级 Mw 为 4.17 ± 0.15。
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引用次数: 0
Nonlinear seismic response analysis of slopes considering the coupled effect of slope geometry and soil stratigraphy 考虑斜坡几何形状和土壤地层耦合效应的斜坡非线性地震响应分析
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-17 DOI: 10.1093/gji/ggae174
Yiming Li, Guoxin Wang, Yang Ding
Summary To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2D horizontally layered slope models are constructed. Firstly, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analyzed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear-wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0 ∼ 60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0 ∼ 150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations.
摘要 为研究边坡几何参数和土层性质对地震动地形放大作用的影响,建立了大量二维水平分层边坡模型。首先,比较了斜坡模型的线性和非线性地震响应,结果表明在研究斜坡地形对地面运动的放大效应时,应考虑土壤的非线性特征。然后,从斜坡最大剪切应变、几何和地层对地震响应的影响、最大地形放大指标与坡顶的距离以及坡顶后斜坡地形的影响范围四个方面分析了这些斜坡模型的非线性地震响应。结果表明,边坡地形对地面运动的放大效应随着边坡高度的增加或上覆土层平均剪切波速的减小而增加。此外,地形放大效应随坡度的变化还受到土壤地层性质的显著影响。最大地形放大指标与坡顶之间的距离主要在 0 ~ 60 m 范围内,坡顶后边坡地形的影响范围主要在 0 ~ 150 m 范围内,根据模拟结果的回归分析得出近似关系,可为坡顶后工程结构的抗震设计和抗震改造提供有意义的参考。最后,根据近似关系提供的预测曲线,进一步评估了斜坡几何参数和土壤地层特性对地面运动修正的影响。
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引用次数: 0
Noise source localization using deep learning 利用深度学习进行噪声源定位
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-15 DOI: 10.1093/gji/ggae171
Jie Zhou, B. Mi, Jianghai Xia, Hao Zhang, Ya Liu, Xinhua Chen, Bo Guan, Yu Hong, Yulong Ma
Ambient noise source localization is of great significance for estimating seismic noise source distribution, understanding source mechanisms and imaging subsurface structures. The commonly used methods for source localization, such as the matched field processing and the full-waveform inversion, are time-consuming and not applicable for time-lapse monitoring of the noise source distribution. We propose an efficient alternative of using deep learning for noise source localization. In the neural network, the input data are noise cross-correlation functions and the output are matrices containing the information of noise source distribution. It is assumed that the subsurface structure is a horizontally layered earth model and the model parameters are known. A wavefield superposition method is employed to efficiently simulate ambient noise data with quantities of local noise sources labelled as training datasets. We use a weighted binary cross-entropy loss function to address the prediction inaccuracy caused by a sparse label matrix during training. The proposed deep learning framework is validated by synthetic tests and two field data examples. The successful applications to locate an anthropogenic noise source and a carbon dioxide (CO2) degassing area demonstrate the accuracy and efficiency of the proposed deep learning method for noise source localization, which has great potential for monitoring the changes of the noise source distribution in a survey area.
环境噪声源定位对估计地震噪声源分布、了解震源机制和成像地下结构具有重要意义。常用的震源定位方法,如匹配场处理和全波形反演,耗时较长,不适用于对噪声源分布的延时监测。我们提出了利用深度学习进行噪声源定位的高效替代方法。在神经网络中,输入数据是噪声交叉相关函数,输出是包含噪声源分布信息的矩阵。假设地下结构为水平分层地球模型,且模型参数已知。我们采用波场叠加法来有效模拟环境噪声数据,并将局部噪声源的数量标记为训练数据集。我们使用加权二元交叉熵损失函数来解决训练过程中稀疏标签矩阵造成的预测不准确问题。合成测试和两个现场数据实例验证了所提出的深度学习框架。在定位人为噪声源和二氧化碳(CO2)脱气区方面的成功应用证明了所提出的噪声源定位深度学习方法的准确性和高效性,该方法在监测勘测区域噪声源分布变化方面具有巨大潜力。
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引用次数: 0
Locating clustered seismicity using Distance Geometry Solvers: applications for sparse and single-borehole DAS networks 利用距离几何求解器定位地震群:稀疏和单孔 DAS 网络的应用
IF 2.8 3区 地球科学 Q1 Earth and Planetary Sciences Pub Date : 2024-05-12 DOI: 10.1093/gji/ggae168
Katinka Tuinstra, Francesco Grigoli, Federica Lanza, Antonio Pio Rinaldi, Andreas Fichtner, Stefan Wiemer
Summary The determination of seismic event locations with sparse networks or single-borehole systems remains a significant challenge in observational seismology. Leveraging the advantages of the location approach HADES (eartHquake locAtion via Distance gEometry Solvers), which was initially developed for locating clustered seismicity recorded at two stations, through the solution of a Distance Geometry Problem, we present here an improved version of the methodology: HADES-R (HADES-Relative). Where HADES previously needed a minimum of 4 absolutely located master events, HADES-R solves a least-squares problem to find the relative inter-event distances in the cluster, and uses only a single master event to find the locations of all events, and subsequently applies rotational optimizer to find the cluster orientation. It can leverage iterative station combinations if multiple receivers are available, to describe the cluster shape and orientation uncertainty with a bootstrap approach. The improved method requires P- and S-phase arrival picks, a homogeneous velocity model, a single master event with a known location, and an estimate of the cluster width. The approach is benchmarked on the 2019 Ridgecrest sequence recorded at two stations, and applied to two seismic clusters at the FORGE geothermal test site in Utah, USA, with a microseismic monitoring scenario with a DAS in a vertical borehole. Traditional procedures struggle in these settings due to the ill-posed network configuration. The azimuthal ambiguity in such a scenario is partially overcome by the assumption that all events belong to the same cluster around the master event and a cluster width estimate. We are able to find the cluster shape in both cases, although the orientation remains uncertain. HADES-R contributes to an efficient way to locate multiple events simultaneously with minimal prior information. The method’s ability to constrain the cluster shape and location with only one well-located event offers promising implications, especially for environments where limited or specialised instrumentation is in use.
摘要 确定稀疏台网或单钻孔系统的地震事件位置仍然是观测地震学的一项重大挑战。HADES (通过距离几何求解器确定地震位置) 最初是通过解决距离几何问题来确定两个台站记录的群集地震位置的,利用该定位方法的优势,我们在此介绍该方法的改进版本:HADES-R (HADES-Relative)。HADES 以前需要至少 4 个绝对定位的主事件,而 HADES-R 则通过最小二乘法问题求解群集中事件间的相对距离,并只使用单个主事件来求解所有事件的位置,随后使用旋转优化器求解群集方向。如果有多个接收器,它可以利用迭代台站组合,以自举法描述集群形状和方向的不确定性。改进后的方法需要 P 相和 S 相到达选区、均质速度模型、已知位置的单个主事件以及对星团宽度的估计。该方法以两个台站记录的 2019 年 Ridgecrest 序列为基准,并应用于美国犹他州 FORGE 地热试验场的两个地震群,在垂直钻孔中使用 DAS 进行微震监测。由于网络配置的不确定性,传统程序在这种情况下难以发挥作用。假设所有事件都属于主事件周围的同一个群集,并对群集宽度进行估计,从而部分克服了这种情况下的方位角模糊性。在这两种情况下,我们都能找到集群形状,尽管方位仍不确定。HADES-R 是利用最少的先验信息同时定位多个事件的有效方法。该方法只需一个定位良好的事件就能约束星团的形状和位置,这一点具有广阔的前景,特别是在使用有限或专用仪器的环境中。
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