共查询到20条相似文献，搜索用时 15 毫秒
1.
为推进大地电磁三维反演的实用化,本文实现了基于L-BFGS算法的带地形大地电磁三维反演.首先推导了大地电磁法三维反演的Tikhonov正则化目标函数以及Hessian矩阵逆矩阵近似表达式和计算方法,然后设计了一种既能保证空气电阻率固定不变又能保证模型平滑约束的协方差矩阵统一表达式,解决带地形反演问题.在反演算法中采用正则化因子冷却法以及基于Wolf条件的步长搜索策略,提升了反演的稳定性.利用开发的算法对多个带地形地电模型（山峰地形下的单个异常模型、峰-谷地形下的棋盘模型）的合成数据进行了三维反演,并与已有大地电磁三维反演程序（ModEM）进行对比,验证了本文开发的三维反演算法的正确性和可靠性.最后,利用该算法反演了华南某山区大地电磁实测数据,得到该区三维电性结构,揭示了研究区以高阻介质为基底,中间以低阻不整合面和相对低阻介质连续分布,浅部覆盖高阻介质的电性结构特征,进一步验证了本文算法的实用性. 相似文献
2.
研究了基于矢量有限元方法的大地电磁带地形三维反演算法并开发了三维反演计算程序代码.在大地电磁场正演数值模拟方面,采用并行直接稀疏求解器PARDISO且无需进行散度校正的快速正演方案,对典型地形模型,在中等规模计算条件下,与双共轭梯度法(BICG)计算结果比较,发现PARDISO比BICG快10倍以上;通过理论模型试算,并与前人的有限元法计算结果对比,验证了带地形三维正演计算程序的正确性.在反演方面,本研究基于共轭梯度方法编写了大地电磁带地形三维反演代码,为了避免直接求取雅可比矩阵,将反演中的雅可比矩阵计算问题转为求解两次“拟正演”问题,进而将PARDISO的快速正演方案应用于“拟正演”问题的求解,以提高反演计算效率.利用开发的反演算法对多个带地形地电模型的合成数据进行了三维反演,反演结果能很好地重现理论模型的电性结构,验证了本文开发的三维反演算法的正确性和可靠性.最后,利用该算法反演了某矿区大地电磁实测数据,反演得到的三维电性结构清晰地反映了研究区的地电特征,将反演结果与该区已有地质资料结合进行解释,应用效果明显,进一步验证了本文算法的有效性. 相似文献
3.
N.G. Papadopoulos P. Tsourlos C. Papazachos G.N. Tsokas A. Sarris J.H. Kim 《Geophysical Prospecting》2011,59(3):557-575
In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data. 相似文献
4.
M.H. Loke N. Papadopoulos P.B. Wilkinson D. Oikonomou K. Simyrdanis D.F. Rucker 《Geophysical Prospecting》2020,68(8):2579-2597
New developments in mobile resistivity meter instrumentation have made it possible to survey large areas with dense data coverage. The mobile system usually has a limited number of electrodes attached to a cable that is pulled along behind an operator so that a large area can be covered within a short time. Such surveys can produce three-dimensional datasets with hundreds of thousands of electrodes positions and data points. Similarly, the inverse model used to interpret the data can have several hundred thousand cells. It is impractical to model such large datasets within a reasonable time on microcomputers used by many small companies employing standard inversion techniques. We describe a model segmentation technique that subdivides the finite-element mesh used to calculate the apparent resistivity and Jacobian matrix values into a number of smaller meshes. A fast technique that optimizes the calculation of the Jacobian matrix values for multi-channel systems was also developed. A one-dimensional wavelet transform method was then used to compress the storage of the Jacobian matrix, in turn reducing the computer time and memory required to solve the least-squares optimization equation to determine the inverse model resistivity values. The new techniques reduce the calculation time and memory required by more than 80% while producing models that differ by less than 1% from that obtained using the standard inversion technique with a single mesh. We present results using a synthetic model and a field dataset that illustrates the effectiveness of the proposed techniques. 相似文献
5.
A two‐and‐half dimensional model‐based inversion algorithm for the reconstruction of geometry and conductivity of unknown regions using marine controlled‐source electromagnetic (CSEM) data is presented. In the model‐based inversion, the inversion domain is described by the so‐called regional conductivity model and both geometry and material parameters associated with this model are reconstructed in the inversion process. This method has the advantage of using a priori information such as the background conductivity distribution, structural information extracted from seismic and/or gravity measurements, and/or inversion results a priori derived from a pixel‐based inversion method. By incorporating this a priori information, the number of unknown parameters to be retrieved becomes significantly reduced. The inversion method is the regularized Gauss‐Newton minimization scheme. The robustness of the inversion is enhanced by adopting nonlinear constraints and applying a quadratic line search algorithm to the optimization process. We also introduce the adjoint formulation to calculate the Jacobian matrix with respect to the geometrical parameters. The model‐based inversion method is validated by using several numerical examples including the inversion of the Troll field data. These results show that the model‐based inversion method can quantitatively reconstruct the shapes and conductivities of reservoirs. 相似文献
6.
2D data modelling by electrical resistivity tomography for complex subsurface geology 总被引：3，自引：1，他引：3
A new tool for two‐dimensional apparent‐resistivity data modelling and inversion is presented. The study is developed according to the idea that the best way to deal with ill‐posedness of geoelectrical inverse problems lies in constructing algorithms which allow a flexible control of the physical and mathematical elements involved in the resolution. The forward problem is solved through a finite‐difference algorithm, whose main features are a versatile user‐defined discretization of the domain and a new approach to the solution of the inverse Fourier transform. The inversion procedure is based on an iterative smoothness‐constrained least‐squares algorithm. As mentioned, the code is constructed to ensure flexibility in resolution. This is first achieved by starting the inversion from an arbitrarily defined model. In our approach, a Jacobian matrix is calculated at each iteration, using a generalization of Cohn's network sensitivity theorem. Another versatile feature is the issue of introducing a priori information about the solution. Regions of the domain can be constrained to vary between two limits (the lower and upper bounds) by using inequality constraints. A second possibility is to include the starting model in the objective function used to determine an improved estimate of the unknown parameters and to constrain the solution to the above model. Furthermore, the possibility either of defining a discretization of the domain that exactly fits the underground structures or of refining the mesh of the grid certainly leads to more accurate solutions. Control on the mathematical elements in the inversion algorithm is also allowed. The smoothness matrix can be modified in order to penalize roughness in any one direction. An empirical way of assigning the regularization parameter (damping) is defined, but the user can also decide to assign it manually at each iteration. An appropriate tool was constructed with the purpose of handling the inversion results, for example to correct reconstructed models and to check the effects of such changes on the calculated apparent resistivity. Tests on synthetic and real data, in particular in handling indeterminate cases, show that the flexible approach is a good way to build a detailed picture of the prospected area. 相似文献
7.
大地电磁法三维共轭梯度反演研究 总被引：12，自引：4，他引：8
Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified. 相似文献
8.
Mattia Aleardi 《Geophysical Prospecting》2020,68(9):2738-2761
Markov chain Monte Carlo algorithms are commonly employed for accurate uncertainty appraisals in non-linear inverse problems. The downside of these algorithms is the considerable number of samples needed to achieve reliable posterior estimations, especially in high-dimensional model spaces. To overcome this issue, the Hamiltonian Monte Carlo algorithm has recently been introduced to solve geophysical inversions. Different from classical Markov chain Monte Carlo algorithms, this approach exploits the derivative information of the target posterior probability density to guide the sampling of the model space. However, its main downside is the computational cost for the derivative computation (i.e. the computation of the Jacobian matrix around each sampled model). Possible strategies to mitigate this issue are the reduction of the dimensionality of the model space and/or the use of efficient methods to compute the gradient of the target density. Here we focus the attention to the estimation of elastic properties (P-, S-wave velocities and density) from pre-stack data through a non-linear amplitude versus angle inversion in which the Hamiltonian Monte Carlo algorithm is used to sample the posterior probability. To decrease the computational cost of the inversion procedure, we employ the discrete cosine transform to reparametrize the model space, and we train a convolutional neural network to predict the Jacobian matrix around each sampled model. The training data set for the network is also parametrized in the discrete cosine transform space, thus allowing for a reduction of the number of parameters to be optimized during the learning phase. Once trained the network can be used to compute the Jacobian matrix associated with each sampled model in real time. The outcomes of the proposed approach are compared and validated with the predictions of Hamiltonian Monte Carlo inversions in which a quite computationally expensive, but accurate finite-difference scheme is used to compute the Jacobian matrix and with those obtained by replacing the Jacobian with a matrix operator derived from a linear approximation of the Zoeppritz equations. Synthetic and field inversion experiments demonstrate that the proposed approach dramatically reduces the cost of the Hamiltonian Monte Carlo inversion while preserving an accurate and efficient sampling of the posterior probability. 相似文献
9.
A three‐dimensional (3D) electrical resistivity modelling code is developed to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh, allowing the estimation of the potential everywhere without the need to interpolate between nodes. Modelling generates a huge matrix, made up of Green's functions, which is stored by using the method of pyramidal compression. The potential is compared with the analytical and the numerical solutions obtained by finite‐difference codes for two models: the two‐layer case and the vertical contact case. The integral method is more accurate around the source point and at the limits of the domain for the potential calculation using a pole‐pole array. A technique is proposed to calculate the sensitivity (Jacobian) and Hessian matrices in 3D. The sensitivity is based on the derivative with respect to the block conductivity of the potential computed using the integral equation; it is only necessary to compute the electrical field at the source location. A direct extension of this technique allows the determination of the second derivatives. The technique is compared with the analytical solutions and with the calculation of the sensitivity according to the method using the inner product of the current densities calculated at the source and receiver points. Results are very accurate when the Green's function that includes the source image is used. The calculation of the three components of the electric field on the interfaces of the mesh is carried out simultaneously and quickly, using matrix compression. 相似文献
10.
提出了一种计算体积分方程的方法－改进型局域非线性迭代（MLNI），并用其对三维井间电磁场进行反演计算，该方法将井间大尺度散射体分为近场和远场区域两部分，它们的位置和尺寸均随场点位置的变化而改变，采用局域非线性近似计算近场区域的影响，将远场区域的影响作为外部激励源，采用迭代方法计算，该方法具有计算速度快，所需内存量少，收敛性好的优点，在反演中采用基于MLNI的非线性反演方法，利用这种方法可以将成像区域集中于一定范围内而不是整个三维空间，该反演方法由于考虑到了雅可比矩阵元素的非线性项，因而与传统的Born迭代反演方法相比更为精确和稳定，考虑到信息量和计算机内存的限制，第1次成像采用双重体元分割法进行较粗略的成像，然后缩小成像范围进行第2次较精确的成像，数值计算结果表明，MLNI是一种有效的计算井间大尺度异常体散射场的方法，将该方法用于反演过程能够得到较高分辨率的三维井间电导率图像。 相似文献
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利用共轭梯度法的电阻率三维反演研究 总被引：72，自引：22，他引：50
利用共轭梯度（ＣＧ）迭代技术,实现了直流电阻率测量数据的三维最小构造反演。 首先,运用共轭梯度迭代算法解反问题的线性方程组,只需求Ｊａｃｏｂｉａｎ矩阵Ｇ与任一向量ｘ的 乘积Ｇｘ及ＧＴ与任何一向量ｙ的乘积ＧＴｙ,再引入Ｇ的Ｒｏｄｉ算法,则Ｇｘ及ＧＴｙ均可在每次反 演迭代中的一次正演计算后一并求得．因此,每次反演迭代仅需一次正演计算,大大加快了 计算速度;而且避免了直接求 Ｇ以及 ＧＴＧ的逆矩阵,也避免了存储 Ｇ和 ＧＴＧ所需庞大的存储 量。另外,由于反演参数太多,求模型光滑约束的最小构造反演能够有效地消除多余构造信 息,得到可靠的反演结果。将这３种方法和技术融合于三维反演中,取得了好的反演效果．为 改进传统最小构造反演收敛慢的问题,还提出了一种新的反演迭代技术,仅需１０次左右甚至 更少迭代即可收敛。 相似文献
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We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation. 相似文献
15.
Application of Large‐Scale Inversion Algorithms to Hydraulic Tomography in an Alluvial Aquifer 
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下载免费PDF全文 P. Fischer A. Jardani A. Soueid Ahmed M. Abbas X. Wang H. Jourde N. Lecoq 《Ground water》2017,55(2):208-218
Large‐scale inversion methods have been recently developed and permitted now to considerably reduce the computation time and memory needed for inversions of models with a large amount of parameters and data. In this work, we have applied a deterministic geostatistical inversion algorithm to a hydraulic tomography investigation conducted in an experimental field site situated within an alluvial aquifer in Southern France. This application aims to achieve a 2‐D large‐scale modeling of the spatial transmissivity distribution of the site. The inversion algorithm uses a quasi‐Newton iterative process based on a Bayesian approach. We compared the results obtained by using three different methodologies for sensitivity analysis: an adjoint‐state method, a finite‐difference method, and a principal component geostatistical approach (PCGA). The PCGA is a large‐scale adapted method which was developed for inversions with a large number of parameters by using an approximation of the covariance matrix, and by avoiding the calculation of the full Jacobian sensitivity matrix. We reconstructed high‐resolution transmissivity fields (composed of up to 25,600 cells) which generated good correlations between the measured and computed hydraulic heads. In particular, we show that, by combining the PCGA inversion method and the hydraulic tomography method, we are able to substantially reduce the computation time of the inversions, while still producing high‐quality inversion results as those obtained from the other sensitivity analysis methodologies. 相似文献
16.
对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差. 相似文献
17.
Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine. 相似文献
18.
目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型... 相似文献
19.
To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical. 相似文献
20.
瞬变电磁法的严格三维反演计算复杂、占用资源多,在普通计算机上难以实现.本文引入瞬变电磁矩变换的概念,提出一种快速三维反演方法.该方法基于阻性限制(resistive limit)特性,建立包含异常体的三维大地的一阶矩响应正演算法,根据不同约束条件,选择优化的最速下降法实现瞬变电磁快速三维反演.文中通过含异常体的三维大地正演一阶矩与仿真数据一阶矩的对比,验证了快速三维正演算法的有效性,之后在不同约束条件下,利用优化的最速下降法实现了对含噪声的仿真瞬变电磁数据的快速三维反演.结果表明,该方法能够在普通计算机上短时间内较为准确地反演出地下异常体的体积和位置,在瞬变电磁数据的实时解释工作中具有良好的应用前景. 相似文献