Estimating Field Source Parameters of Gravity Change in North China Based on the Euler Deconvolution Method

Based on the absolute and relative gravity observations in North China from 2009 to 2014, spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theoretical model to get the best estimates of parameters. Gravity field change caused by the depth and distribution in North China is calculated by back analysis. The results show the structural index that equals 1 is suitable for inversion of the gravity variation data. The inversion results indicate that the depths of anomaly field sources are spread over the Hetao fault. The research method of this paper can be used in the quantitative study on the field source and may shed new light on the interpretations of gravity change, and also provide quantitative basis for earthquake prediction index criterions based on the gravity change.     

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.     

A new approach for separating mixed model parameters:application to simultaneous inversion of earthquake source parameters

A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.     

Damage detection on framed structures: modal curvature evaluation using Stockwell Transform under seismic excitation

The key parameters for damage detection and localization are eigenfrequencies, related equivalent viscous damping factors and mode shapes. The classical approach is based on the evaluation of these structural parameters before and after a seismic event, but by using a modern approach based on time-frequency transformations it is possible to quantify these parameters throughout the ground shaking phase. In particular with the use of the S-Transform, it is possible to follow the temporal evolution of the structural dynamics parameters before, during and after an earthquake. In this paper, a methodology for damage localization on framed structures subjected to strong motion earthquakes is proposed based on monitoring the modal curvature variation in the natural frequency of a structure. Two examples of application are described to illustrate the technique: Computer simulation of the nonlinear response of a model, and several laboratory(shaking table) tests performed at the University of Basilicata(Italy). Damage detected using the proposed approach and damage revealed via visual inspections in the tests are compared.     

Fast and accurate earthquake location within complex medium using a hybrid globallocal inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine,plus an examination of the root mean squares(RMS) error distribution.The method exploits the advantages of network ray tracing and robust formulation of the Fréchet derivatives to simultaneously update all possible initial source parameters around most local minima(including the global minimum) in the solution space,and finally to determine the likely global solution.Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method.This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters,but also offers the attractive features of global optimal searching in the RMS travel time error distribution.Unlike the traditional global search method,for example,the Monte Carlo approach,where millions of tests have to be done to find the final global solution,the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution.The search is aided by inspection of the RMS error distribution.Benchmark tests against two popular approaches,the direct grid search method and the oct-tree important sampling method,indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data,but more importantly it offers two-order of magnitude speed-up in computational effort.Such an improvement,combined with high accuracy,make it a promising hypocenter determination scheme in earthquake early warning,tsunami early warning,rapid hazard assessment and emergency response after strong earthquake occurrence.     

Information flow and controlling in regularization inversion of quantitative remote sensing

In order to minimize uncertainty of the inversed parameters to the largest extent by making full use of the limited information in remote sensing data, it is necessary to understand what the information flow in quantitative remote sensing model inversion is, thus control the information flow. Aiming at this, the paper takes the linear kernel-driven model inversion as an example. At first, the information flow in different inversion methods is calculated and analyzed, then the effect of information flow controlled by multi-stage inversion strategy is studied, finally, an information matrix based on USM is defined to control information flow in inversion. It shows that using Shannon entropy decrease of the inversed parameters can express information flow more properly. Changing the weight of a priori knowledge in inversion or fixing parameters and partitioning datasets in multi-stage inversion strategy can control information flow. In regularization inversion of remote sensing, information matrix based on     

Synthetic tidal parameters for gravity over China and its neighbor area

The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are con- structed with Earth’s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravime- ters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravim- etric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric obser- vations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.     

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.     

华北时变重力场离散小波多尺度分解

On the basis of the absolute and relative gravity observations in North China, spatial dynamic variation of regional gravity fields is obtained. A multi-scale decomposition technique is used to separate anomalies at different depths, and give some explanation to gravity variation at different time space scales. Gravity variation trends in North China are improved. Based on this result and the analysis of wavelet power spectrum, the images of the depth of wavelet approximation and detail are obtained. The results obtained are of scientific significance for the deep understanding of potential seismic risk in North China from gravity variations in different time space scales.     

Atmospheric correction of remote sensing imagery based on the surface spectrum’s vector space

Due to the atmosphere effect,the qualities of images decrease conspicuously,practically in the visible bands,in the processing of earth observation by the satellite-borne sensors.Thus,removing the atmosphere effects has become a key step to improve the qualities of images and to retrieve the actual reflectivity of surface features.An atmospheric correction approach,called ACVSS(Atmospheric Correction based Vector Space of Spectrum),is proposed here based on the vector space of the features’ spectrum.The reflectance image of each band is retrieved first according to the radiative transfer equation,then the spectrum’s vector space is constructed using the infrared bands,and finally the residual errors of the reflectance images in the visible bands are corrected based on the pixel position in the spectrum’s vector space.The proposed methodology is verified through atmospheric correction on Landsat-7 ETM+ imagery.The experimental results show that our method is more accurate and the corrected image is more distinct,compared with those offered by current popular atmospheric correction software.     

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized, we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.     

Grey wolf optimizer: a new strategy to invert geophysical data sets

There is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self‐potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise‐free and noise‐corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise‐corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self‐potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.     

基于密度模型稀疏表征的重力反演方法

重力反演是恢复地下密度空间分布的有效工具,而选择合理的密度模型约束方法是提升重力反演分辨率和可靠性的关键.常规约束方法大多是从剖分网格空间中的密度模型出发,通过调整光滑或稀疏约束权重来匹配反演目标,但当地质体类型多样、异常分离不准确及网格剖分方案不合理时,模型约束的合理性与灵活性难以得到有效保证.为此,本文提出了一种基于密度模型稀疏表征的重力反演方法.首先假设待反演的密度模型表征为模型特征矩阵和稀疏分解系数的线性组合,之后重新推导了重力反演目标函数,并给出了分解系数的稀疏求解过程.相比现有重力反演方法,用于构建模型特征矩阵的特征模型可包含不同类型地质体的先验几何信息,分解系数的稀疏性保证了待反演目标来自于最典型的地质模式组合.最后,通过模型试验及实际资料验证了基于密度模型稀疏表征的重力反演方法的有效性.     

大地电磁的人工鱼群最优化约束反演

大地电磁的反演问题是非线性,如果采用线性反演方法容易陷入局部极小,使得反演结果非唯一性严重.本文将人工鱼群算法引入到地球物理反演之中,提出了非线性的大地电磁人工鱼群最优化反演.该方法不需要进行偏导数的求取,可以对反演的范围进行约束,以减小反演结果的非唯一性.同时我们对搜索步长进行了改进,给出适用于大地电磁反演的人工鱼群参数.大量的理论数据试算表明,人工鱼群反演算法能够较好地寻找到全局最优解.实测数据的处理结果表明,该方法可以用来处理实际资料,并且能够取得很好的应用效果.     

网格剖分方式对大地电磁数据反演的影响

随着计算机技术的飞速发展,大地电磁测深数据的各种反演方法得到空前发展。对于反演过程中的网格剖分问题,前人研究有限。本文就此进行研究,确定影响网格剖分方式的因素,找到一种合适的网格剖分方法。为此,设计一个复杂模型,对正演模拟得到的数据加入随机噪声作为反演的输入数据,选择不同的网格剖分方式,使用DASOCC与NLCG反演方法,以相同参数分别进行反演,对所得结果进行对比分析。结果显示,在设定的模型及参数条件下,针对DASOCC反演方法,纵向及横向网格均不加密,反演效果比较理想,即横向采用一个测点对应一个网格的剖分方式,纵向采用表层加密,100 m以下后一网格为前一网格厚度1.1倍的剖分方式;针对NLCG反演方法,纵向与DASOCC反演方法相同,采用不加密网格的剖分方式得到的结果较好,而横向则建议采用一个测点对应一个网格,并在2个测点之间插入一个网格的剖分方式。     

基于地质体空间位置优化约束的航空重力梯度数据三维物性反演

重力数据的物性反演面临着严重的多解性问题,降低多解性的有效手段是加入约束条件.而边界识别、深度估计及成像方法可获取地质体的水平位置、深度范围等几何参数信息,本文将基于数据本身挖掘的地质体几何参数信息约束到物性反演中,以降低反演的多解性.通过引入基于深度信息的深度加权函数及基于水平位置的水平梯度加权函数建立优化约束条件,有效地提高了反演结果的横向及纵向分辨率.重力梯度数据包含更多的地质体空间特征信息,将优化约束反演方法应用到全张量数据的反演中,模型试验表明本文方法反演结果与理论模型更加吻合.最后对美国路易斯安那州文顿盐丘实测航空重力梯度数据的应用表明,本文方法在其他地球物理、地质资料不足的情况下获得更可靠的反演结果.     

基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演

随着重力和重力梯度测量技术的日趋成熟,基于重力和重力梯度数据的反演技术得到了广泛关注.针对反演多解性严重、计算效率低和内存消耗大等难点问题,本文开展了三维重力和重力梯度数据的联合反演研究,该方法结合重力和重力梯度两种数据,将L0范数正则化项加入到目标函数中,并在数据空间下采用改进的共轭梯度算法求解反演最优化问题.同时,本文摒弃了依赖先验信息的深度加权函数,引入了自适应模型积分灵敏度矩阵,用来克服因重力和重力梯度数据核函数随深度增加而衰减引起的趋肤效应问题.为了提高反演计算效率,本文又推导出基于规则网格化的重力和重力梯度快速正演计算方法.模拟试算表明,改进的共轭梯度法可以降低反演的迭代次数,提高反演的收敛速度;自适应模型积分灵敏度矩阵,可以有效解决趋肤效应,提高反演纵向分辨能力;数据空间和改进的共轭梯度算法结合,可以更好地降低反演求解方程的维度,避免存储灵敏度矩阵,有效地降低反演计算时间和内存消耗量.野外实例表明,该算法可以在普通计算机下快速地获得地下密度分布模型,表现出较强的稳定性和适用性.     

Focusing iterative migration of gravity gradiometry data acquired in the Nordkapp Basin,Barents Sea

Geological interpretation based on gravity gradiometry data constitutes a very challenging problem. Rigorous 3D inversion is the main technique used in quantitative interpretation of the gravity gradiometry data. An alternative approach to the quantitative analysis of the gravity gradiometry data is based on 3D smooth potential field migration. This rapid imaging approach, however, has the shortcomings of providing smooth images since it is based on direct integral transformation of the observed gravity tensor data. Another limitation of migration transformation is related to the fact that, in a general case, the gravity data generated by the migration image do not fit the observed data well. In this paper, we describe a new approach to rapid imaging that allows us to produce the density distribution which adequately describes the observed data and, at the same time, images the structures with anomalous densities having sharp boundaries. This approach is based on the basic theory of potential field migration with a focusing stabilizer in the framework of regularized scheme, which iteratively transfers the observed gravity tensor field into an image of the density distribution in the subsurface formations. The results of gravity migration can also be considered as an a priori model for conventional inversion subsequently. We demonstrate the practical application of migration imaging using both synthetic and real gravity gradiometry data sets acquired for the Nordkapp Basin in the Barents Sea.     

Depth and morphology of reflectors from the non-linear inversion of arrival-time and waveform semblance data. Part I: method and applications to synthetic data

We propose a two-dimensional, non-linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source-to-receiver acquisition lay-out. This method uses a scheme of non-linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite-difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best-fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities.