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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
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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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利用遗传算法进行不考虑近场校正的全场资料CSAMT反演研究.遗传算法属于全局最优化方法,具有对初始模型依赖小,不易陷入局部极值的优点,然而,当未知数较多时,多解性仍是该方法的瓶颈.为了减小多层反演的多解性,在反演中引入最小构造约束,针对CSAMT的遗传算法反演问题定义了最小构造目标函数,经过模型试验找到了其具体表达式,并找到了适合CSAMT资料反演的拉格朗日乘子的最佳取值μ=0.5,实现了基于遗传算法的CSAMT最小构造反演.利用H、A、K、Q和HKH、KHA模型对方法进行了数值试验,在无噪和加入10％噪声情况下,反演结果与模型一致;加入20％噪声后,反演仍取得良好结果,与理论模型基本吻合.将该方法用于水平层状地层和横向变化地层的实测资料反演,结果与地质资料吻合.不同的计算实例表明了该方法的有效性. 相似文献
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《地球物理学进展》2016,(3)
应用CSAMT方法进行标量测量时,一般要求测线沿垂直构造走向的方向布测.在实际测量的时候由于地表条件复杂经常出现无法判断地下构造走向的情况,例如,在长白山地区进行CSAMT测量,由于表面覆盖有玄武岩无法判断地下构造走向,对得到的标量数据进行一维、二维反演处理时无法判断哪种反演方式的结果更准确.鉴于此,建立三维地质模型,应用CSAMT三维正演程序进行数值模拟.研究测线与构造走向平行,呈45°及垂直三种情况下的一维、二维反演,对结果做比较分析.实验结果表明,测线平行构造走向时,一维、二维反演结果近似;测线与构造走向呈45°或垂直时,二维反演结果比一维反演结果对异常体的形状,大小,埋深及电性参数反演的更准确. 相似文献
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地层宏观电性各向异性会对可控源电磁响应产生重要影响.由于海底地层电性结构常表现为电导率各向异性,若仅对海洋可控源电磁(MCSEM)数据进行常规各向同性反演,有可能无法获得准确的反演解释结果,从而削弱MCSEM技术的可靠性.本文实现了电导率垂直各向异性(VTI)条件下频率域海洋可控源电磁数据三维反演算法.其中,三维正演采用基于二次场控制方程的交错网格有限体积法,并利用直接矩阵分解技术来求解离散所得的大型线性方程组,有利于快速计算多场源的响应.反演采用具有近似二次收敛性的高斯牛顿算法对目标函数进行最优化.最后,对具有VTI电性各向异性特征的盐丘构造模型的MCSEM合成数据分别进行了电导率各向同性和垂直各向异性三维反演,结果表明:各向同性三维反演算法无法对受VTI介质影响的MCSEM数据进行正确的反演解释,而垂直各向异性三维反演能够获得更为可靠的地下电阻率结构和异常体分布,展现出对海底电性各向异性结构更为优良的反演解释能力. 相似文献
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速度、密度之间的相互耦合使得密度在多参数全波形反演中较难获得.本文将截断高斯-牛顿法用于声介质速度、密度双参数全波形反演,通过考虑近似Hessian矩阵中反映速度、密度相互作用的非主对角块元素,有效解决了多参数全波形反演中速度、密度之间的耦合问题,在不采用反演策略的情况下,仍能够获得精度较高的速度、密度反演结果.常规的截断牛顿类全波形反演通常利用一阶伴随状态法求取目标函数对模型参数的梯度,利用二阶伴随状态法或有限差分法求解Hessian-向量乘,在每一步内循环迭代过程中需要额外求解两次正演问题,计算量较大.本文基于Born近似,将梯度计算中的核函数-向量乘表示为具有明确物理意义的向量-标量乘的累加运算,同时将Hessian-向量乘转化为两次核函数-向量乘,无需额外求解正演问题,有效降低了计算量.数值实验证明了本文提出的方法的有效性. 相似文献
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CSAMT在山区金属矿勘查中,采用各种滤波和相位积分之类的处理方法,校正因地形起伏和局部电性不均匀引起的静态效应,往往难保奏效,开发消除静态效应的新方法是提高CSAMT资料处理与解释水平和方法应用效果的重要研究课题. 本文以如何消除地形影响为重点,对起伏地形下CSAMT二维大地三维源地电模型,采用加权余弦数值积分法,进行波数域电磁场二维有限单元法正演. 为模拟复杂地形地电模型,选取交叉对称网格三角形剖分法,实现了在国内常用赤道电偶极装置的CSAMT二维正演计算;在二维正演的基础上,开发了基于奥克姆反演法的CSAMT二维反演技术,研制出一套起伏地形下CSAMT二维正反演处理与解释方法技术系统. 通过理论模型试算和实测数据处理证实,本系统能有效地削减起伏地形影响. 在找矿应用中,该系统反演的电阻率断面,极大地消除了起伏地形影响和静态效应,突显出清晰的控矿构造和矿体的异常,取得了重要成效. 相似文献
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运用面向对象思想分析地球物理正演与反演问题,提出了一种基于有限单元正演与正则化非线性最小二乘反演的统一框架结构.该框架采用稀疏线性系统求解作为正演的基础类;分别建立一维、二维、三维的几何模型类,用于完成模型的剖分与有限单元钢度矩阵的生成,其中与单元物质属性相关的计算采用纯虚函数的形式,在具体解问题中实现;以正则化非线性最小二乘最优化算法作为反演基础类,反演中有关模型的正演数据计算及Fréchet矩阵求解等采用纯虚函数的形式,在具体问题中进行计算.框架结构的建立提高了代码的重用性与程序开发速度;对地质单元采用统一的空间剖分,有利于开展联合反演程序设计. 相似文献
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Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm 总被引：1，自引：0，他引：1
Chong Zeng Jianghai Xia Richard D. MillerGeorgios P. Tsoflias 《Journal of Applied Geophysics》2011,75(4):648-655
Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity. 相似文献
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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
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A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole-Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time-domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole-Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two-dimensional resistivity model for each time channel. The time-dependent resistivity of each cell was then interpreted as the response of a homogeneous half-space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half-space Cole-Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany. 相似文献
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The aim of seismic inversion methods is to obtain quantitative information on the subsurface properties from seismic measurements. However, the potential accuracy of such methods depends strongly on the physical correctness of the mathematical equations used to model the propagation of the seismic waves. In general, the most accurate models involve the full non-linear acoustic or elastic wave equations. Inversion algorithms based on these equations are very CPU intensive. The application of such an algorithm on a real marine CMP gather is demonstrated. The earth model is assumed to be laterally invariant and only acoustic wave phenomena are modelled. A complete acoustic earth model (P-wave velocity and reflectivity as functions of vertical traveltime) is estimated. The inversion algorithm assumes that the seismic waves propagate in 2D. Therefore, an exact method for transforming the real data from 3D to 2D is derived and applied to the data. The time function of the source is estimated from a vertical far-field signature and its applicability is demonstrated by comparing synthetic and real water-bottom reflections. The source scaling factor is chosen such that the false reflection coefficient due to the first water-bottom multiple disappears from the inversion result. In order to speed up the convergence of the algorithm, the following inversion strategy is adopted: an initial smooth velocity model (macromodel) is obtained by applying Dix's equation to the result of a classical velocity analysis, followed by a smoothing operation. The initial reflectivity model is then computed using Gardner's empirical relationship between densities and velocities. In a first inversion step, reflectivity is estimated from small-offset data, keeping the velocity model fixed. In a second step, the initial smooth velocity model, and possibly the reflectivity model, is refined by using larger-offset data. This strategy is very efficient. In the first step, only ten iterations with a quasi-Newton algorithm are necessary in order to obtain an excellent convergence. The data window was 0–2.8 s, the maximum offset was 250 m, and the residual energy after the first inversion step was only 5% of the energy of the observed data. When the earth model estimated in the first inversion step is used to model data at moderate offsets (900 m, time window 0.0–1.1 s), the data fit is very good. In the second step, only a small improvement in the data fit could be obtained, and the convergence was slow. This is probably due to the strong non-linearity of the inversion problem with respect to the velocity model. Nevertheless, the final residual energy for the moderate offsets was only 11%. The estimated model was compared to sonic and density logs obtained from a nearby well. The comparison indicated that the present algorithm can be used to estimate normal incidence reflectivity from real data with good accuracy, provided that absorption phenomena play a minor role in the depth interval considered. If details in the velocity model are required, large offsets and an elastic inversion algorithm should be used. 相似文献
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时域有限差分(FDTD)方法使用Yee网格剖分电磁场的空间采样,通过时间步迭代实现电磁场数值模拟,具有内存消耗低、计算简单等特点,常用于瞬变电磁三维正演.然而,常规FDTD方法的时间迭代步长Δt受Courant-Friedrich-Lewy(CFL)条件严格限制,过多的迭代次数以及过密的采样往往导致计算速度慢、累积误差不断增大.本文提出一种不受CFL条件约束的无条件稳定隐式差分算法Crank-Nicolson FDTD(CN-FDTD)用于瞬变电磁三维正演.基于Crank-Nicolson差分方法对Maxwell方程组重新离散,空间网格仍然采用Yee元胞,时间步进采用在整时间步电场、磁场同时采样的策略,建立无条件稳定FDTD格式,突破CFL条件限制.与常规FDTD交替采样相比,CN-FDTD电场、磁场同时采样的策略构成的隐式差分格式,需要求解大型稀疏矩阵方程组.通常,瞬变电磁三维正演模型中产生的矩阵阶数往往较大,需要占用大量内存和求解时间.为解决上述问题,采用Crank-Nicolson-cycle-sweep-uniform(CNCSU-FDTD)方法近似求解CN-FDTD方程,在保证求解精度的同时,计算效率大幅提高.在边界条件处理上,采用双线性变换推导了复频率参数完全匹配层(CFS-PML)吸收边界.采用均匀半空间模型、四类三层模型进行精度验证,发现CN-FDTD三维正演结果与解析解、线性数字滤波解吻合较好.之后,与接触带上的低阻复杂模型进行对比,结果显示CN-FDTD正演结果与矢量有限元、有限体积法以及FDTD计算结果吻合较好.在此基础上,研究了时间步放大对CN-FDTD计算精度的影响,发现最大时间步放大到常规FDTD的3200倍时才会在晚期出现较明显的误差.在一台CPU为Intel Core i5-7300HQ的笔记本电脑单线程计算条件下,模拟到关断后30 ms仅需要50 min.在进行并行化后,将有望实现复杂模型分钟级的三维正演,从而为三维反演提供可靠、快速的正演方法. 相似文献
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为进一步了解井间地下介质结构及其电性特征,本文用时域有限差分方法(FDTD),实现了井间电磁场响应的数值模拟.激发源是探测深度相对磁偶极子更大一些的电偶极子,首先选择一个位于井轴上的垂直电偶极子作为场源,并假设参与计算的介质相对于发射井井轴是轴向对称的,这样可将研究区域作为二维问题处理.推导了二维井间电磁波传播时域差分公式.该方法适用于任何方向入射的电偶极子源,尤其善于解决频域差分方法所难以描述的宽频脉冲.给出了井间金属圆柱和矿体圆柱数值模拟2个例子,结果表明,时域有限差分方法能有效的模拟井间地下介质中电磁波的传播,揭示电磁波传播规律.该方法速度快、精度高、结果稳定,适合用于井间电磁场反演成像的正演响应计算. 相似文献
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光滑约束技术在线性反演中具有重要的作用，但在遗传算法的反演中则很难直接施加于模型参数，其原因是采用光滑处理后的模型参与迭代后，模型的多样性受到很强的压制，并在少量的迭代过程中使种群的各个模型趋向一致，从而得不到满足条件的最优解．本文给出了一种可用于遗传算法反演的间接光滑约束方法．该方法将遗传算法迭代过程中产生的模型经处理后得到的光滑模型，作为误差函数计算的输入模型．迭代过程仍采用原模型，避免了模型的多样性损失，在面波反演和接收函数反演的试验中取得了良好的效果．我们利用该方法对青藏高原地区的瑞利波相速度资料进行了反演，揭示了青藏高原中部地区S波速度结构的横向变化特征．结果表明，青藏高原北部地区地壳Ｓ波速度较南部地区低；大多数路径在15～40ｋｍ 深度范围内，存在12～25ｋｍ 厚的地壳低速层；上地幔低速层位于100ｋｍ 深度以下，厚度主要在40～80ｋｍ 范围内变化，个别路径可达100ｋｍ 以上．安多台以北、玛沁和玉树以西之间，在上地幔90～230ｋｍ 深度范围存在明显的低速层，最低速度约4.2～ 4.3km／s．根据不同路径的S波速度结构和前人的资料，我们认为印度板块的俯冲可能以雅鲁藏布缝合带附近为界． 相似文献
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IntroductionThe dispersion phenomena, which can be observed when surface wave travels through the Earth interior, has been extensively applied in investigating the velocity structure of the Earth interior. Usually, the dispersion curve is a nonlinear function of the thickness, S and P wave velocities and density of each layer. Because surface wave inversion is a multiple-minima problem, the result strongly depends on the initial model in traditional linear inversion. Genetic algorithm (GA) … 相似文献
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对于三维可控源电磁,反演计算效率、张量测量、旁侧效应以及阴影效应是目前研究的热点.本文正演采用基于库仑规范条件的耦合势有限体积算法,反演采用有限内存BFGS(L-BFGS)算法.合成数据反演结果表明:(1)有限内存BFGS法比非线性共轭梯度法,在反演计算效率上具有一定的优势,更适合求解大规模三维可控源电磁反演问题.(2)张量可控源电磁法相对于标量可控源电磁法,前者在模型分辨率上优于后者.(3)在某个区域无法布置测网的情况下,我们可利用旁侧效应在异常体周围布置测网进行三维反演,从而获得真实异常体的信息.同时,为避免阴影效应,我们应在测网外增加可控源电磁控制点,使得三维反演的数据更加完备. 相似文献
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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