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瞬变电磁法正演计算进展 总被引：4，自引：1，他引：3
详细介绍了瞬变电磁法正演计算的方法、现状和发展趋势.瞬变电磁法一维正演计算需要将电磁场从频率域转换至时间域,转换方法有三种,分别是Gaver-Stehfest算法、余弦变换和Guptasarma算法.在这三种方法中,使用较多的是Gaver-Stehfest算法和余弦变换,Gaver-Stehfest算法速度较快,但精度不及余弦变换.瞬变电磁法的数值模拟主要集中于2.5维和三维,使用的数值计算方法有积分方程法、有限差分法、有限单元法和SLDM法.积分方程法主要在三维数值模拟中使用,现已很少使用;有限差分法和有限单元法是目前瞬变电磁法2.5维和三维数值模拟的主要方法;SLDM法主要应用于三维数值模拟.我国瞬变电磁法正演计算成果主要集中在回线源激发的瞬变电磁场一维数值计算和利用有限单元法进行2.5维和三维数值模拟.瞬变电磁法正演计算的发展趋势有:数值算法的改进、提高计算效率和研究地形对瞬变电磁场的影响规律. 相似文献
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《地球物理学进展》2016,(1)
本文对瞬变电磁法2.5维有限元正演进行了研究.从频率域麦克斯韦方程组出发,经过傅里叶变换推导出了走向y方向频率域电磁场响应的变分问题,然后运用频率域和时间域的转换公式求解出时间域瞬变电磁场的解.在求解频率域电磁场响应时为提高精度采用了基于二次插值的高阶有限元的算法,即单元网格插值为二次函数,同时推导出了经有限元离散后的泛函问题;在求解时间域电磁响应采用了正余弦变换的数字滤波算法.通过基本模型的正演,验证了算法的可行性.同时,也对比了基于G-S变换的线性有限元算法的数值结果,结果表明,本文采用的算法精度更高,层状模型最大延迟采样时间提高到了100 ms以上. 相似文献
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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
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《应用地球物理》2015,(4)
针对地面场源在地层介质中所产生瞬变电磁场的数值计算方法和响应分析问题,本文展开研究.解法方面,传统离散镜像法多采用复数运算、数字滤波等方法计算量大,针对这些问题,提出一种改进的离散镜像方法:基于Gaver-Stehfest概率变换算法将电磁场解式实数化,选用Prony方法对目标核函数进行指数级数逼近,根据离散镜像原理和近似系数闭合式求解瞬变电磁场.通过试算均质模型中瞬变电磁场并对比汉克尔变换的数字滤波法所得结果,证明该方法有效且具有较好的精度和适用性.继而基于该方法计算地表磁偶源在典型地电模型中产生的瞬变电磁场,对"地面激发-地层中测量"方式所得感应磁场水平分量响应进行分析并得出结论瞬变场水平分量响应与地电结构、观测时间、空间位置等因素有关,感应磁场水平分量响应反映出涡流场分布及其垂向梯度变化情况,在探测异常体的工作中应尽量选取零偏移距、较大偏移距位置钻孔或用较大观测延时以减小背景场对勘测结果的影响。文中所用离散镜像方法与正演计算结论可为相关研究工作提供参考依据。 相似文献
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《应用地球物理》2017,(1)
本文对地-井瞬变电磁法多分量响应进行计算分析。规则局部体瞬变场响应的计算方法与解释模型对于实际导电围岩模型的适用性较差,针对该问题,本文提出了一种基于地下瞬态电磁场数值模拟的计算分析方法。瞬变电磁场模拟方面,本文以时域有限差分法实现正演模拟,引入采用Gaver-Stehfest逆拉氏变换与Prony法的离散镜像法求解初始电磁场,应用透射边界条件保证迭代计算精度。通过均质半空间模型算例,证明该套方法可行。响应分析方面,设定含井旁目标体和导电围岩的地电模型,以上述方法对地下瞬态电场进行正演,以多分量观测装置为例换算感应电动势。通过对比各条件下瞬态电场与多分量响应,得出结论:地-井瞬变电磁多分量感应电动势响应反映了地下瞬态电场沿水平、垂直方向的梯度变化;响应特征取决于地层中瞬变场在不同条件下的"扩散、衰减、畸变"过程和观测位置的电磁场状态。本文的计算分析方法兼顾围岩背景场与局部体异常场,较之传统局部体瞬变场原理能够更全面的反映地质信息。 相似文献
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本文从瞬变电磁均匀半空间二次磁场响应公式出发,提出了一种基于神经网络的视电阻率快速计算方法.以中心回线为例,根据瞬变响应公式的特点,简化网络结构,选用三层BP神经网络和误差训练算法,用均匀半空间样本数据进行训练,确定了收敛快、误差小的一步正割法和隐含单元数,得到基于不同采样时窗的一组网络参数.用本文方法与二分法、牛顿迭代法做模型计算比较,及最后的实验计算,说明算法的快速,准确.本文方法不依赖初始模型,避开了复杂的电磁场数值计算,实现了视电阻率的快速计算,对瞬变电磁法资料的快速解释有一定的参考价值. 相似文献
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在波场的正变换中,保证瞬变电磁场的计算精度的同时,应用两步最优化算法,成功地控制和减少了积分系数个数和离散数字积分的采样点个数,解决了在波场反变换式中,由于积分系数过多而产生的欠定方程组的问题,同时改善了第一类算子方程的不适定性.在波场反变换中,将正则化算法用于逆变换过程的计算中,通过采用偏差原理和Newton迭代格式选出最优的正则化参数,使得反变换所得到的波场稳定、可靠.通过对数值计算结果与已知波场函数对比,证明了该方法的有效性和实用性. 相似文献
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Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks. 相似文献
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In most previous studies on the dynamic response of a long cylindrical cavity subjected to internal transient dynamic loads, the porous medium was usually assumed to be completely saturated by ground water. In practice, however, the full saturation condition does not always exist. In this paper the surrounding soil and the lining of the cavity are respectively treated as a nearly saturated porous medium and an elastic material, and the governing equations for the dynamic problem are derived. A set of exact solutions are obtained in the Laplace transform domain for three types of transient loads, i.e. suddenly applied constant load, gradually applied step load and triangular pulse load. By utilizing a reliable numerical method of inverse Laplace transforms, the time-domain solutions are then presented. The influence of the degree of saturation of the surrounding soil on the dynamic response of the lined cavity is examined for numerical examples. 相似文献
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A Laplace-transform analytic element method (LT-AEM) is described for the solution of transient flow problems in porous media. Following Laplace transformation of the original flow problem, the analytic element method (AEM) is used to solve the resultant time-independent modified Helmholtz equation, and the solution is inverted numerically back into the time domain. The solution is entirely general, retaining the mathematical elegance and computational efficiency of the AEM while being amenable to parallel computation. It is especially well suited for problems in which a solution is required at a limited number of points in space–time, and for problems involving materials with sharply contrasting hydraulic properties. We illustrate the LT-AEM on transient flow through a uniform confined aquifer with a circular inclusion of contrasting hydraulic conductivity and specific storage. Our results compare well with published analytical solutions in the special case of radial flow. 相似文献
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Transient response of a beam on viscoelastic foundation under an impact load during nondestructive testing 总被引：1，自引：1，他引：0
Beam responses under an impact NDT load are studied using the Fourier and Laplace transforms. Numerical computation is performed for a parametric study of beam and load parameters. It is shown that under an impact load, the time duration for displacement to vanish is ten times longer than that for velocity and acceleration. The maximum response is achieved first in acceleration, followed by velocity, and finally displacement, all of which occur before the impact load is removed. At the moment that the impact load is removed from the beam, there is a discontinuity in the velocity and acceleration responses, but not in displacement response. The effect of K and ph on beam response is much less significant than that of El and C, which have similar effect on beam response. As El increases, peak values of displacement, velocity and acceleration response decrease. The effect of K on beam response only becomes appreciable after the impact load is removed. While the peak of displacement remain almost unchanged as K increases, the displacement response decays to zero faster for large K values than for small K values. 相似文献
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An analysis of a recent modified frequency-domain procedure for computing the response of linear systems using the fast Fourier transform (FFT) algorithm is described. This modified procedure eliminates the appended free-vibration interval that is used in the standard approach. The duration of the period of computation still needs to be longer than that of the response interval of interest, but only slightly. Reducing the period of computation lowers the number of frequencies at which the transfer function needs to be defined. The major drawback of the method is a high sensitivity to errors in the computed values of the transfer function, which reduces the role of interpolation in the transfer function definition. The modified method is related to the discrete Laplace transform. 相似文献
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We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets. 相似文献
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We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized: the real number of the electromagnetic field solution based on the Gaver–Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the “ground excitation–stratum measurement” method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drillhole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research. 相似文献
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一、引言 在研究椭圆形裂纹扩展问题中,如果不考虑破裂的终止,则常常假定震源的滑移函数为 相似文献
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Numerical inversion is required when Laplace transform cannot be inverted analytically by manipulating tabled formulas of special cases. However, the numerical inverse Laplace transform is generally an ill-posed problem, and there is no universal method which works well for all problems. In this study, we selected seven commonly used numerical inverse Laplace transform methods to evaluate their performance for dealing with solute transport in the subsurface under uniform or radial flow condition. Such seven methods included the Stehfest, the de Hoog, the Honig–Hirdes, the Talbot, the Weeks, the Simon and the Zakian methods. We specifically investigated the optimal free parameters of each method, including the number of terms used in the summation and the numerical tolerance. This study revealed that some commonly recommended values of the free parameters in previous studies did not work very well, especially for the advection-dominated problems. Instead, we recommended new values of the free parameters for some methods after testing their robustness. For the radial dispersion, the de Hoog, the Talbot, and the Simon methods worked very well, regardless of the dispersion-dominated or advection-dominated situations. The Weeks method can be used to solve the dispersion-dominated problems, but not the advection-dominated problems. The Stehfest, the Honig–Hirdes, and the Zakian methods were recommended for the dispersion-dominated problems. The Zakian method was efficient, while the de Hoog method was time-consuming under radial flow condition. Under the uniform flow condition, all the methods could present somewhat similar results when the free parameters were given proper values for dispersion-dominated problems; while only the Simon method, the Weeks method, and the de Hoog method worked well for advection-dominated problems. 相似文献