煤层厚度地震槽波层析成像分辨率分析

透射法地震槽波勘探技术依据不同煤厚槽波频散特征差异,利用敏感频率下槽波走时层析成像算法反演得到煤层槽波速度,进而预测煤层厚度分布.层析反演结果的准确性直接影响煤厚探测的精度,反演得到小异常体常被错误地当作高精细度的体现.槽波层析反演分辨率是衡量反演结果精细程度的重要指标,决定了反演结果的可靠程度,但对于槽波分辨率的估算缺乏有效的技术手段.通过对比分析理论模型、棋盘格模型、射线密度和统计分辨率等方法,探讨这些分辨率分析方法的优缺点.根据义马11061工作面层析成像结果以及后期实际煤厚揭露数据,验证了槽波勘探方法的合理性和准确,认为采用巷帮煤厚作为约束条件,可提高层析成像分辨率,采用统计分辨率方法对反演结果分析较为实用.     

不同电极阵列联合反演在古墓探测中的应用

电阻率层析成像是一种广泛应用在水文、考古和地质等浅地表勘探领域的地球物理方法。为了增强电阻率层析成像的分辨率、应对复杂的地质问题,本文提出基于雅可比矩阵的不同电极阵列直流电阻率数据的加权联合反演算法,并以温纳和偶极-偶极电极阵列数据为例,在理论模型和古墓探测的野外实例中测试该算法的有效性。结果表明,加权联合反演结果的横向和纵向分辨率都优于单一电极阵列的反演结果,并在实例中缓解“U形”电极阵列的固有缺陷、减少反演模糊性、更好地约束墓室宽度的反演结果。      

菲涅耳体地震层析成像分辨率研究

层析成像分辨率的研究,不仅可以帮助分析层析方法的反演能力,评价层析反演的效果,还可以帮助指导层析参数设置,优化观测系统设计等.本文对比研究了前人提出的两种菲涅耳体层析成像分辨率的计算方法,并针对其存在的问题进行了优化.文中通过对二维理论模型的定量计算,总结了菲涅耳体地震层析成像分辨率的一些规律,并将其与射线层析的分辨率...     

Lg波衰减模型中建模误差的定量评估

对Lg波衰减模型中建模误差的统计特征进行了系统研究,并建立了地壳二维Lg波衰减模型。由于Lg波振幅可能受到几何扩散函数的强烈影响,合理评估反演过程的误差对于能否使用最小二乘意义下的反演非常重要。通过在川滇及其邻近地区收集的建模误差样本,使用K-S数值检验方法、Q-Q图和正态分布图形检验方法对Lg波衰减层析成像反演的输入数据中建模误差的分布特征进行了统计分析。采用奇异值分解（SVD）和反投影方法,分别获得了川滇地区的Q_Lg模型,定量计算模型的协方差矩阵和分辨率矩阵,定量评估了Q_Lg模型中每个格点的分辨率和误差。结果表明:在一阶近似条件下建模误差服从正态分布;通过开发的数据筛选程序,可以产生一个接近完美正态分布的数据集;与反投影方法相比,利用SVD方法获得的地壳Q值的分辨率更高;在射线覆盖较好的区域,Q_Lg模型的分辨率达到100 km,相对误差小于3%。      

贝叶斯同化重力反演方法构建龙门山地壳密度模型

重力异常对地壳横向密度变化敏感,而无约束重力反演得到的密度模型其垂向分辨能力往往不理想.为了改善反演结果的垂向分辨率,本文参考已有先验分层模型,基于贝叶斯原理,提出了一种重震联合反演的新策略,可实现多种参考模型和复杂加权参数条件下的最大后验概率估计.理论模型测试结果表明,对于深度加权、多参考模型约束等多种问题,本文提出的新方法都可以稳健地获得最优化的模型参数.本文同时以中国地震科学台阵在龙门山地区及周边的一维接收函数分层模型和地震层析成像结果为参考,通过此方法对该区的重力异常进行反演,获得了该区的高精度三维密度结构,其水平分辨率优于10 km,垂直分辨率优于5 km.结合四条通过汶川和芦山地震震中的剖面进行分析后发现,反演得到的密度结构模型在过强震震源区位置横向变形显著,其揭示的分层地壳结构和变形模式与地表已知断裂构造具有相关性.本文提出的重震联合反演新策略,可为研究潜在强震风险源区的地壳结构和物性特征提供有效的科技方法支撑.     

不同观测方式下基于伴随矩阵的2.5D全通道电阻率反演研究

全通道电阻率层析成像是采用除去2个供电电极其余接地电极全部采集数据并参与反演计算的一种电阻率成像方法.相比较传统的对称四极测深、斯伦贝谢、偶极-偶极、单极-偶极、单极-单极等勘探方式来说,全通道采集得到的数据可以更好地覆盖目标地质体因此可以更准确地确定介质的电阻率.本文基于有限差分方法求解二维静电场方程和基于伴随方法计算非线性灵敏度矩阵,并利用牛顿共轭梯度反演方法实现全通道电阻率层析成像.理论模型的正演和反演表明了算法的可靠性.与常规四极电阻率法采集方式相比,全通道电阻率法具有更好的分辨率及更灵活的布极方式.在此基础上,着重分析了各种观测装置的有效勘探范围和成像分辨率.本文的研究可以有效指导电阻率法勘探观测装置形式的设计与选取,更好的解决实际工程地质问题.     

地震层析成像反演中解的定量评价及其作用

对地震层析成像非线性问题线性化处理之后,各种反演算法归纳成为对不适定方程的求解。地震层析成像反演算法的解的物理意义是给出地质结构,因此对于解的可信度产生怀疑。本研究根据解估计的分辨率矩阵的原理,提出ＬＳＱＲ（Ｌｅａｓｔ Ｓｑｕａｒｅ ＱＲ）算法解协方差矩阵的评价算法,用相关分析可以为那些求解过程中得不到分辨率矩阵的反演方法提供解的定量评价。并用本文提出的解的定量评价方法试评了一个实际地壳模型的地震     

基于模型空间压缩的大地电磁三维反演研究

本文提出了一种基于模型空间压缩技术的大地电磁三维反演方法.该方法在传统大地电磁三维反演理论的基础上,通过小波变换将待反演的空间域模型参数映射到小波域进行反演,获得小波域更新模型后再通过小波逆变换得到空间域反演模型.由于小波变换具有压缩特性和多尺度分辨能力,本文反演方法可在一定程度上提高反演分辨率.为了提高反演效率,我们针对基于L_1范数的模型约束求解不易收敛的反演问题,提出了一种基于模型粗糙度的简单有效的预条件处理技术.为验证本文算法的有效性,本文首先对经典的"棋盘"模型进行三维反演测试.反演结果表明本文算法的反演效率与传统方法相当,但对于深部异常体具有更好的分辨能力.最后,我们通过对实测数据反演进一步验证本文算法的有效性.     

二维时间空间域弹性波全波形反演-理论模型数值试验

本文使用炮并行和区域分解(物理上分割模型,使用基于MPI的分布式存储架构的计算集群,节约单个CPU内核的内存使用量,快速进行正演数值模拟)两种并行算法.该方法的每一步迭代都能确保近似海森矩阵的正定,因此,算法稳健.将时间正向传播的炮波场和反向逆时间传播的残差波场(伴随波场)进行零延迟互相关计算,得到误差泛函的梯度,然后对梯度乘以一个预条件算子,从而加快反演的收敛速度.通过抛物线搜索方法而估计步长,使用L-BFGS算法(限定内存的BFGS算法)求解模型的更新量,进行二维时间空间域弹性波全波形反演.将该反演方法应用到Marmousi2弹性波理论模型,分别反演Marmousi2理论模型的纵波速度、横波速度以及密度等三个参数.我们分别使用截止频率为2 Hz、5 Hz、10 Hz和20 Hz四个阶段的低通巴特沃斯滤波器,采用多尺度的策略,从理论模型数据的低频分量开始反演,将低频分量的反演结果作为高频分量反演时的初始模型,然后依次反演数据的高频分量.理论模型数值试验反演所得到的结果证实:二维时间空间域弹性波全波形反演计算灵活,适用于各种观测系统,能够方便地对地震数据进行加时窗;二维时间空间域弹性波全波形反演所得纵波速度模型的分辨率最高,横波速度模型的分辨率次之,密度模型的分辨率稍微差些.     

地震层析成像反演中解的定量评价及其应用

对地震层析成像非线性问题线性化处理之后,各种反演算法归纳成为对不适定方 程的求解．地震层析成像反演算法的解的物理意义是给出地质结构,因此对于解的可靠性及 分辨率研究非常重要．然而许多反演算法不能给出解的评价方法,因而对解的可信度产生怀 疑．本研究根据解估计的分辨率矩阵的原理,提出ＬＳＱＲ（Ｌｅａｓｔ Ｓｑｕａｒｅ ＱＲ）算法解协方差矩 阵的评价算法,用相关分析可以为那些在求解过程中得不到分辨率矩阵的反演方法提供解的 定量评价．并用本文提出的解的定量评价方法试评了一个实际地壳模型的地震层析成像的 速度重建结果．     

A Trade-Off Solution between Model Resolution and Covariance in Surface-Wave Inversion

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data.     

航空电磁拟三维模型空间约束反演

为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题,通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外,同时还考虑了垂直测线方向测点在空间上的相互约束.为此,首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案,然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵,并使用L-BFGS算法使目标函数最小化,获得最优拟三维模型空间反演解.基于理论模型和实测数据反演,对单点反演与两种空间约束反演方案的有效性进行比较,证明本文空间约束反演算法对于噪声的压制效果好,反演的界面连续光滑,同时内存需求和反演时间少,是一种快速有效的反演策略.     

Non-linear inversion of resistivity profiling data for some regular geometrical bodies1

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting. We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.     

Appraisal problem in the 3D least squares Fourier seismic data reconstruction

Least squares Fourier reconstruction is basically a solution to a discrete linear inverse problem that attempts to recover the Fourier spectrum of the seismic wavefield from irregularly sampled data along the spatial coordinates. The estimated Fourier coefficients are then used to reconstruct the data in a regular grid via a standard inverse Fourier transform (inverse discrete Fourier transform or inverse fast Fourier transform). Unfortunately, this kind of inverse problem is usually under‐determined and ill‐conditioned. For this reason, the least squares Fourier reconstruction with minimum norm adopts a damped least squares inversion to retrieve a unique and stable solution. In this work, we show how the damping can introduce artefacts on the reconstructed 3D data. To quantitatively describe this issue, we introduce the concept of “extended” model resolution matrix, and we formulate the reconstruction problem as an appraisal problem. Through the simultaneous analysis of the extended model resolution matrix and of the noise term, we discuss the limits of the Fourier reconstruction with minimum norm reconstruction and assess the validity of the reconstructed data and the possible bias introduced by the inversion process. Also, we can guide the parameterization of the forward problem to minimize the occurrence of unwanted artefacts. A simple synthetic example and real data from a 3D marine common shot gather are used to discuss our approach and to show the results of Fourier reconstruction with minimum norm reconstruction.     

Two‐dimensional joint inversions of cross‐hole resistivity data and resolution analysis of combined arrays

In this study, a new two‐dimensional inversion algorithm was developed for the inversion of cross‐hole direct current resistivity measurements. In the last decades, various array optimisation methods were suggested for resistivity tomography. However, researchers have still collected data by using classical electrode arrays in most cross‐hole applications. Therefore, we investigated the accuracy of both the individual and the joint inversion of the classical cross‐hole arrays by using both synthetic and field data with the developed algorithm. We showed that the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole electrode arrays gives inverse solutions that are closer to the real model than the individual inversions of the electrode array datasets for the synthetic data inversion. The model resolution matrix of the suggested arrays was used to analyse the inversion results. This model resolution analysis also showed the advantage of the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole arrays. We also used sensitivity sections from each of the arrays and their superpositions to explain why joint inversion gives better resolution than the any individual inversion result.     

Conditionality of inverse solutions to discretised integral equations in geoid modelling from local gravity data

The eigenvalue decomposition technique is used for analysis of conditionality of two alternative solutions for a determination of the geoid from local gravity data. The first solution is based on the standard two-step approach utilising the inverse of the Abel-Poisson integral equation (downward continuation) and consequently the Stokes/Hotine integration (gravity inversion). The second solution is based on a single integral that combines the downward continuation and the gravity inversion in one integral equation. Extreme eigenvalues and corresponding condition numbers of matrix operators are investigated to compare the stability of inverse problems of the above-mentioned computational models. To preserve a dominantly diagonal structure of the matrices for inverse solutions, the horizontal positions of the parameterised solution on the geoid and of data points are identical. The numerical experiments using real data reveal that the direct gravity inversion is numerically more stable than the downward continuation procedure in the two-step approach.     

On the limits of linear moment-tensor inversion of teleseismic body wave spectra

The limits of linear moment-tensor inversions from long-period teleseismic body waves are analysed in detail, using inverse methods. We focus our attention on single-station and few-stations methods. Information on the feasibility of full or deviatoric moment-tensor determinations prior to inversion are deduced from the system conditioning. The resolution and correlation of the momenttensor components are analysed using the resolution matrix. Conclusions on the importance and independence of the data are drawn from the information matrix. The single--station case and its implications are discussed in greater detail, as well as possible constraints on the inversion.     

Comparison of Frequency-Selection Strategies for 2D Frequency-Domain Acoustic Waveform Inversion

Several frequency-selection strategies have been used to obtain global minimum solutions in waveform inversion. One strategy, called the discretization method, is to discretize frequencies with a large sampling interval to minimize redundancy in wavenumber information. Another method, the grouping method, groups frequencies with redundancy in wavenumber information. The grouping method can be carried out in two ways. With the first method, the minimum frequency is fixed and the maximum frequency is gradually extended upward (i.e., the overlap-grouping method). Under the second method, frequencies are not overlapped across the groups and waveform inversion proceeds from lower to higher frequency groups (i.e., the individual-grouping method). In this study, we compare these three frequency-selection strategies using both synthetic and real data examples based on logarithmic waveform inversion. Numerical examples for synthetic and real field data demonstrate that the three frequency-selection methods provide solutions closer to the global minimum compared to solutions resulting from simultaneously performed waveform inversion, and that the individual-grouping method yields slightly better resolution for the velocity models than the other methods, particularly for the deeper part. These results may imply that using either too small or too large data sets at every stage slightly deteriorates inversion results, and that grouping data in appropriately sized aggregations improves inversion results.     

Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (≥2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data.     

Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields

In this paper, we present a methodology to perform geophysical inversion of large‐scale linear systems via a covariance‐free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore–Penrose pseudo‐inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two‐dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo‐inverse outperforms the classical least‐squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root‐mean‐square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non‐linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non‐linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill‐conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations.