基于瞬变电磁矩变换的快速三维反演方法

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.     

Extracting the Virtual Reflected Wavelet from TEM Data Based on Regularizing Method

A pseudo-seismic interpretation method is an alternative way to process and explain transient electromagnetic (TEM) data, and has become a popular research field in recent years. TEM signals which satisfy the diffusion equation can be converted by means of a mathematical transformation into ones which obey the wave equation. For an ill-posed problem of this kind of transformation, a sub-regularization algorithm is developed in this paper to extract a virtual wavelet of the TEM field. According to the conventional designation of TEM recordings, the entire integration period is divided into seven time intervals. In order to avoid low accuracy in the calculations, high-density wavefield data has been calculated based on the former sub-division. Therefore, the virtual wavelet can be extracted successfully by using an optimized algorithm to obtain high-density integral coefficients for all time windows, and a satisfactory condition number of the coefficient matrix while taking a different channel number in each time period. The Tikhonov regularization inversion scheme is used to determine the optimal parameters based on minimizing a least squares misfit, and the Newton iterative formula is used to obtain optimal regularization parameters. Both synthetic model simulations and a real data interpretation example indicate that the proposed pseudo-seismic wavefield method is a suitable alternative way to interpret TEM data.     

核磁共振与瞬变电磁三维联合解释方法

传统核磁共振地下含水量解释多采用基于均匀半空间或层状导电模型的一维反演,分层给出地下含水信息.然而,这些方法忽略了地下复杂电阻率分布信息对结果的影响,也不能很好地反映局部三维含水构造.本文从三维电介质中核磁共振响应的正演理论出发,提出首先利用瞬变电磁数据进行基于等效导电平面法的快速电阻率成像,然后将成像结果作为核磁共振三维反演的电性模型,进行联合解释.激发磁场的分布采用有限元法直接求解,通过引入伪δ源实现电流源的加载,并强加散度条件排除了三维磁场模拟中"弱解"的影响.针对核磁共振灵敏度矩阵的病态性和数据中存在的干扰信号,提出考虑罚项的非线性拟合目标函数,利用线性化方法进行核磁共振反演.模型数据表明该方法能较准确反映地下三维含水构造,实测算例进一步证明了方法的有效性.本研究将促使核磁共振方法在岩溶、裂隙水、孤立水体等复杂水文地质条件及隧道、矿井灾害水源探测等方面得到有效应用.     

瞬变电磁场资料的联合时-频分析解释

本文充分利用瞬变电磁（TEM）信号包含的信息,采用联合时-频分析方法解释了TEM资料。文章选取了Wigner-Ville分布和Gabor展开的联合时-频分布（或表示）,将一维时间域信号拓展到时-频二维平面上,不仅将不同地电断面的响应成功地分开来,而且所显示的信号特征与地层电性结构之间有着明确的物理意义,从时间和频率两个方面同时描述了瞬变涡流场在地层中的激发和衰减的过程。利用时间窗数据和频率窗数据所进行的联合时-频反演,缩小了拟合差,提高了定量解释精度。     

Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements during transient flow in the vadose zone

Methods for estimating the parameter distributions necessary for modeling fluid flow and contaminant transport in the shallow subsurface are in great demand. Soil properties such as permeability, porosity, and water retention are typically estimated through the inversion of hydrological data (e.g., measurements of capillary pressure and water saturation). However, ill-posedness and non-uniqueness commonly arise in such non-linear inverse problems making their solutions elusive. Incorporating additional types of data, such as from geophysical methods, may greatly improve the success of inverse modeling. In particular, ground-penetrating radar (GPR) methods have proven sensitive to subsurface fluid flow processes and appear promising for such applications. In the present work, an inverse technique is presented which allows for the estimation of flow parameter distributions and the prediction of flow phenomena using GPR and hydrological measurements collected during a transient flow experiment. Specifically, concepts from the pilot point method were implemented in a maximum a posteriori (MAP) framework to allow for the generation of permeability distributions that are conditional to permeability point measurements, that maintain specified patterns of spatial correlation, and that are consistent with geophysical and hydrological data. The current implementation of the approach allows for additional flow parameters to be estimated concurrently if they are assumed uniform and uncorrelated with the permeability distribution. (The method itself allows for heterogeneity in these parameters to be considered, and it allows for parameters of the petrophysical and semivariogram models to be estimated as well.) Through a synthetic example, performance of the method is evaluated under various conditions, and some conclusions are made regarding the joint use of transient GPR and hydrological measurements in estimating fluid flow parameters in the vadose zone.     

瞬变电磁快速成像解释系统研究

为了提高瞬变电磁测深法对地探测的垂向分辨能力,文中研究了磁偶源瞬变电磁法快速成像的方法.详细讨论了电磁波与地震波在介质中的传播规律,分析了磁偶源瞬变电磁场在远区的响应特性.根据磁偶源瞬变电磁场与反射地震波的传播规律的相似性,提出了TEM资料拟地震快速成像解释的思路.理论模型正、反演计算结果表明方法理论是可行的,野外实测资料处理结果进一步说明了该方法是有效的.     

回线源瞬变电磁法有限体积三维任意各向异性正演及分析

目前,瞬变电磁法(TEM)数据基本都是基于各向同性模型进行反演解释,这对于存在明显电性各向异性的勘探区域会产生较大的反演解释误差.为分析电各向异性对回线源瞬变电磁信号的影响方式与程度,本文通过求解离散化的全张量电导率时间域Helmholtz方程,实现了基于有限体积法的TEM任意各向异性的三维正演算法.该算法采用基于交错网格的拟态有限体积法(MFV)对时域Maxwell方程组进行空间域离散,并利用后退欧拉算法(Backward Euler Method)进行时间域离散.为提高时域电磁场的求解精度与效率,该算法将时间分段等步长算法与方程直接求解法相结合.通过对一维各向异性模型以及三维复杂各向同性模型进行测试,验证了本算法对于回线源瞬变电磁响应计算的正确性及有效性.最后,通过对几类典型电各向异性介质中大回线源瞬变电磁信号响应的分析,总结了不同电各向异性类型对TEM电磁信号的影响模式,结果表明,主轴各向异性情况下TEM信号主要受水平方向电导率的影响,倾斜各向异性对TEM信号的影响程度远大于水平各向异性,而通过水平各向异性信号能较清晰判断出各向异性主轴方向.     

瞬变电磁合成孔径成像方法研究

瞬变电磁法虽然广泛应用于资源勘探和工程勘察中,但仍存在一些亟待解决问题.迫切需要引进一些新的技术与方法,以进一步提高解释精度.由于瞬变电磁资料可以通过数学公式转换成虚拟波;多孔径瞬变电磁物理模拟证明TEM多孔径具有相干性;相邻位置上同一地质体的反射回波具有较好的相关性.所以,对于瞬变电磁资料可以进行多孔径合成成像.本文借助于合成孔径雷达的基本思想,提出一套新的数据处理方法,即采用相关叠加技术,实现多孔径数据合成.在完成瞬变电磁虚拟波提取后,将传统的以剖面为主的处理方式发展成为以测点为中心的多孔径合成,将传统的以单点处理方式发展成为逐点推移多次覆盖的处理方法.采用相关叠加的方法来进行合成孔径,由此大大提高瞬变电磁法的分辨率.从波场的角度拓展和丰富了瞬变电磁场的内涵,使得从实测资料中提取到常规瞬变电磁法提取不到的信息,对地下目标体成像更为有利.通过对所设计模型和实测资料处理,结果表明合成孔径成像效果较好.研究成果为发展瞬变电磁成像技术,提高分辨率提供了一条新途径.     

Interpretation of borehole magnetometer data for the detection and characterisation of unexploded bombs

Unexploded war-time bombs (UXB) can be found at the ground surface or buried at depths of up to 20 m, where surface-based detection methods become ineffective due to signal weakness and interference. A total-field borehole magnetometer can penetrate to such depths and collect relatively quiet data. However, conventional interpretation techniques suffer from the inherent non-uniqueness in the borehole dimension. In this paper, a constrained optimisation method is utilised for the interpretation of total-field borehole magnetometer data for the detection of deeply buried unexploded bombs. The major advantage over conventional techniques comes from the analytically-derived constraints imposed on the parameter vector by excluding non-geosensible results from consideration and hence reducing the non-uniqueness to a minimal level. A depth dependant objective function is defined to minimise the interference and measurement errors. A test site has been developed for evaluation using real world data. The interpretation results demonstrate its superior capability in handling real-world problems with high non-uniqueness. Furthermore, this method provides a way to estimate the moment strength without knowing the exact position. Together with the modelled signature data for different objects, characterisation of a particular bomb is possible from the inversion of a single total-field borehole profile.     

Minimizing Interpretation Ambiguities Through Joint Inversion of Surface Electrical Data

Joint inversion is an extension of standard least-squares inversion techniques. With this approach, it is possible to construct a model that is simultaneously consistent with surface observations made using more than one geophysical method. Specifically, discussion focuses on applications to the Schlumberger and audiomagnetotelluric sounding methods, although the technique is not limited to these.
The authors have found that the non-uniqueness problems that often plague the interpretation of electrical sounding data can be substantially reduced if the model is required to be consistent with more than one set of surface measurements. If geological ground truth is available to further constrain the model, the chances of arriving at the true physical property distribution of the subsurface are far better than if a single data set is interpreted.
To demonstrate the power of joint inversion, the authors present a study using synthetic data obtained from a three-layer resistivity model. Finally, two case histories are presented to demonstrate that a much better representation of the true earth can be obtained with joint inversion than with standard interpretation methods.     

Electrical conductivity profiles and implications for the absence or presence of partial melting beneath central and southeast Australia

A previous paper presented measurements by Australian magnetometer arrays of Earth response to the magnetic daily-variation source field, and interpreted these data by simple representative models of one-dimensional structure found by “forward model-fitting”. This paper now supplements the earlier interpretation by seeking to clarify the ranges of acceptable models which fit the data; that is, to demonstrate the extent of the non-uniqueness of the interpretation. Searches for models which fit the data have been carried out on both a systematic and a random basis, with similar results.The major conclusion of the earlier paper is confirmed; that there is a substantial difference in conductivity structure between central and southeast Australia. Beneath central Australia, the structure is consistent with a traditional continental geotherm and published laboratory measurements on the temperature dependence of the electrical conductivity of recognized upper-mantle crystalline olivine materials. Beneath southeast Australia, a higher conductivity by an order of magnitude in the depth range 200–300 km is most directly interpreted in terms of a small degree (perhaps 5%) of basalt melt.Such a partial-melt zone under southeast Australia is consistent with previous natural electromagnetic measurements for the area; has earlier and independently been indicated by a variety of seismic studies; and correlates with proposed thermal models which involve crustal intrusion from some sub-lithospheric magma source.     

层状介质中地下瞬变电磁场全空间效应

全空间效应是矿井瞬变电磁方法固有的特殊理论问题之一.建立了3种典型的层状地质模型,采用时域有限差分法求解Maxwell方程,并引入电磁波衰减因子EA(dB),来分析全空间效应的影响特征及影响因素.研究结果表明,地下瞬变电磁法工作装置中,分离回线装置对低阻目标层的探测效果优于重叠回线装置;相对于半空间低阻层瞬变响应,全空间低阻层瞬变响应的时间范围更宽,因而需要更长的观测时间;全空间效应影响因素为顶、底板内低阻层相对电阻率差异大小和目标层深度与厚度,当目标层电阻率大于顶板内低阻层电阻率时,所观测响应主要为低阻层响应,此时将会增大资料解释的难度.此外,研究还显示,瞬变电磁法对低阻层的纵向分辨率与低阻层厚度相关,厚度越小分辨率越高,当厚度较大时,其纵向分辨能力较差.研究成果为实际工作参数选择及资料处理与解释提供了参考.     

Spatial weighting functions: transient hydraulic tests and heterogeneous media

To improve understanding of property measurements in heterogeneous media, an energy-based weighting function concept is developed. In (assumed) homogeneous media, the instrument spatial weighting function (ISWF) depends only on the energy dissipation distribution set up by the measurement procedure and it reduces to simply inverse sample volume (uniform weighting) for 1-D parallel flow case (ideal permeameter). For 1-D transient flow in homogeneous media, such as with slug tests, the ISWF varies with position and time, with 95% of the total weighting contained within 115 well radii, even late in the test. In the heterogeneous case, the determination of the ISWF is connected to the problem of determining an equivalent hydraulic conductivity (K), where the criterion for equivalence is based on equal energy dissipation rate rather than equal volume discharge. The discharge-based equivalent K (K(E)) and the energy-based equivalent K in heterogeneous media (K(eh)) are not equal in general, with K(eh) typically above the nodal arithmetic mean K. The possibly more fundamental problem is that as one makes K measurements in heterogeneous media at different locations or on different cores of heterogeneous materials, the ISWF will be heterogeneity dependent, implying that the averaging process resulting in the equivalent K value also varies with position. If the testing procedure is transient, then the averaging process varies with time. This suggests a fundamental ambiguity in the interpretation of hydraulic conductivity measurements in heterogeneous media that may impact how we approach modeling and prediction in a practical sense (Molz 2003). Further research is suggested.     

瞬变电磁传感器阻尼特性的标定研究

传统瞬变电磁法（TEM）认为临界阻尼匹配时传感器响应快、无振荡,为最佳匹配方式.本文通过建立基于标定环的TEM系统标定模型,理论证明当略欠阻尼匹配时传感器响应最快、时域畸变最小,为最佳匹配方式.本文采用基于实测数据的背景场剔除方法将一次场和大地响应剔除,通过对不同阻尼状态下标定环早期响应畸变的定量评价,实验证明传感器在略欠阻尼匹配状态下二次场响应畸变最小.本文理论和标定实验均证明,在纯二次场观测方式下,采用略欠阻尼匹配方式能够显著降低早期响应畸变、提高系统浅层探测能力,是浅层探测时传感器最佳匹配方式.     

The feasibility of electromagnetic gradiometer measurements

The quantities measured in transient electromagnetic (TEM) surveys are usually either magnetic field components or their time derivatives. Alternatively it might be advantageous to measure the spatial derivatives of these quantities. Such gradiometer measurements are expected to have lower noise levels due to the negative interference of ambient noise recorded by the two receiver coils. Error propagation models are used to compare quantitatively the noise sensitivities of conventional and gradiometer TEM data. To achieve this, eigenvalue decomposition is applied on synthetic data to derive the parameter uncertainties of layered-earth models. The results indicate that near-surface gradient measurements give a superior definition of the shallow conductivity structure, provided noise levels are 20–40 times smaller than those recorded by conventional EM instruments. For a fixed-wing towed-bird gradiometer system to be feasible, a noise reduction factor of at least 50–100 is required. One field test showed that noise reduction factors in excess of 60 are achievable with gradiometer measurements. However, other collected data indicate that the effectiveness of noise reduction can be hampered by the spatial variability of noise such as that encountered in built-up areas. Synthetic data calculated for a vertical plate model confirm the limited depth of detection of vertical gradient data but also indicate some spatial derivatives which offer better lateral resolution than conventional EM data. This high sensitivity to the near-surface conductivity structure suggests the application of EM gradiometers in areas such as environmental and archaeological mapping.     

Fast-decaying IP in frozen unconsolidated rocks and potentialities for its use in permafrost-related TEM studies

We investigate the early time induced polarization (IP) phenomenon in frozen unconsolidated rocks and its association with transient electromagnetic (TEM) signals measured in northern regions. The distinguishing feature of these signals is the distortion of the monotony or sign reversals in the time range from a few tens to a few hundreds of microseconds. In simulating TEM data, the IP effects in frozen ground were attributed to the dielectric relaxation phenomenon rather than to the frequency‐dependent conductivity. This enabled us to use laboratory experimental data available in the literature on dielectric spectroscopy of frozen rocks. In our studies we focused on simulating the transient response of a coincident‐loop configuration in three simple models: (i) a homogeneous frozen earth (half‐space); (ii) a two‐layered earth with the upper layer frozen; (iii) a two‐layered earth with the upper layer unfrozen. The conductivities of both frozen and unfrozen ground were assumed to exhibit no frequency dispersion, whereas the dielectric permittivity of frozen ground was assumed to be described by the Debye model. To simplify the presentation and the comparison analysis of the synthetic data, the TEM response of a frozen polarizable earth was normalized to that of a non‐polarizable earth having the same structure and resistivities as the polarizable earth. The effect of the dielectric relaxation on a TEM signal is marked by a clearly defined minimum. Its time coordinate t_min is approximately three times larger than the dielectric relaxation time constant τ. This suggests the use of t_min for direct estimation of τ, which, in turn, is closely associated with the temperature of frozen unconsolidated rock. The ordinate of the minimum is directly proportional to the static dielectric permittivity of frozen earth. Increasing the resistivity of a frozen earth and/or decreasing the loop size results in a progressively stronger effect of the dielectric relaxation on the TEM signal. In the case of unfrozen earth, seasonal freezing is not likely to have an appreciable effect on the TEM signal. However, for the frozen earth, seasonal thawing of a near‐surface layer may result in a noticeable attenuation of the TEM signal features associated with dielectric relaxation in a frozen half‐space. Forward calculations show that the dielectric relaxation of frozen unconsolidated rocks may significantly affect the transient response of a horizontal loop laid on the ground. This conclusion is in agreement with a practical example of inversion of the TEM data measured over the permafrost.     

斜阶跃电流激励下多匝小回线瞬变电磁场延时特征

采用Duhamel积分对斜阶跃电流激励的瞬变电磁场进行直接计算,应用叠加原理得到了多匝小回线全域瞬变电磁响应.研究了多匝小回线的早、晚延时临界条件以及等磁矩单匝大回线与多匝小回线的延时和关断时间特征,分析了电阻率、厚度等参数变化时斜阶跃电流对层状模型瞬变响应的影响特征,最后采用实测数据验证了关断效应的校正效果.结果显示,回线边长越小或表层电阻率越大,瞬变响应越早离开早期并进入晚期.多匝小回线的关断时间远大于等磁矩的单匝大回线,但由前者激发的瞬变响应进入晚期的时间却大幅提前,更有利于晚期条件下各种理论公式的使用.斜阶跃影响校正结果显示,增加多匝小回线的匝数可以扩展反演深度的范围,减少匝数则可以提高反演电阻率的精确性;实测数据处理结果显示校正方法产生了一定的效果.本研究补充了多匝小回线瞬变电磁理论内容,研究结果可以为复杂环境中小尺寸多匝线圈的工作参数选择提供参考.     

Two-dimensional, regularised inversion of VLF data

Very low frequency electromagnetic (EM) methods using VLF transmitters have found many applications in subsurface geophysical investigations. Surface measurements involving both the vertical component of the magnetic field (VLF-EM or VLF-Z) and of the apparent resistivity (VLF-R) are increasingly common. Although extensive VLF data sets have been successfully used for mapping purposes, modelling and interpretation techniques which asess the third (i.e. depth) dimension appear limited.Given a profile of VLF-R measurements the main purpose of the present study is to demonstrate an automatic method for the construction of a resistivity cross-section. The technique used is one of a new generation of regularised inversion methods. These techniques attempt to overcome the problem of equivalence/non-uniqueness in EM sounding data by constructing the resistivity distribution with the minimum amount of structure that fits the data.VLF data represent a special case of plane-wave EM sounding in that they conform, in practice, to a single-frequency technique. This fact imposes a limitation in the amount of vertical resolution that we can expect using such data. In the case of two-dimensional modelling and inversion, resolution through the cross-section is a resultant attribute from both vertical and lateral resistivity gradients within the subsurface. In order to provide insight into the practical application of regularised inversion techniques to VLF data, both synthetic and field examples are considered. Both sets of examples are primarily concerned with VLF data applied to near-surface fault mapping where the main aim is to assess the location, dip and depth extent of conductive subsurface features.     

Die Zielsetzung einer allgemeinen quantitaiven Methode in der Gravimetrie

Summary After introduction in 1. and definitions in 2.A. the separately well known or evident relations representing the fundamental problems of the interpretation in the gravity are perpicuously summarised in 2.b. by means of the group theory. From the the following conclusions can be drawn (in 2.C.): 1.) from the point of view of the quantitative interpretation all gravity-maps are totally equivalent in respect of both their ambiguity and the informations that they are able to give, 2.) the quantity of the informations obtained from the gravity maps is growing withthe increasing number of other informations and with greater accuracy of the measurements. Therefore the development of a general quantitative method is proposed (with concrete points of views), to realise the theoretical possibilities.-In 3.) some problems of the derivative maps are discused in connection with the foregoings.     

均匀半空间表面大定源瞬变电磁响应的快速算法

大定源是地面瞬变电磁观测的主要方式之一, 该方式在大深度、高密度的面积测量时具有明显的优势. 但当接收点偏离发射框中心时, 由于场源的非对称性(即框边影响), 数据处理和解释比较困难, 特别是全程瞬变响应的精确计算相当耗时. 本文介绍一种数值算法, 它既能实现快速计算, 又能满足精度要求. 该算法通过对瞬变场垂直分量(b_z)及其时间变化率(b_z/t)的核函数Y(Z)和Y'(Z)表现特性的研究, 以参数Z把整个瞬变过程分为早期阶段(Z→0), 中期阶段和晚期阶段(Z→∞). 计算全程响应时, 早期和晚期阶段分别采用Y(Z)和Y'(Z)的渐近表达式;对中期阶段, 内层积分(即误差函数erf)采用有理Chebyshev渐近展开式, 外层积分采用Romberg数值积分法. 理论模型计算表明, 利用该算法可以快速计算空间任意点(除发射边框)的全程响应核函数Y(Z)和Y'(Z). 当测点到边框的距离大于边长的25%时, 计算速度比常规数值积分算法快7倍;其它测点处计算速度比常规数值积分算法快4倍. 全程时段的相对误差<0.0002%.