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.     

Calibrating a Salt Water Intrusion Model with Time‐Domain Electromagnetic Data

Salt water intrusion models are commonly used to support groundwater resource management in coastal aquifers. Concentration data used for model calibration are often sparse and limited in spatial extent. With airborne and ground‐based electromagnetic surveys, electrical resistivity models can be obtained to provide high‐resolution three‐dimensional models of subsurface resistivity variations that can be related to geology and salt concentrations on a regional scale. Several previous studies have calibrated salt water intrusion models with geophysical data, but are typically limited to the use of the inverted electrical resistivity models without considering the measured geophysical data directly. This induces a number of errors related to inconsistent scales between the geophysical and hydrologic models and the applied regularization constraints in the geophysical inversion. To overcome these errors, we perform a coupled hydrogeophysical inversion (CHI) in which we use a salt water intrusion model to interpret the geophysical data and guide the geophysical inversion. We refer to this methodology as a Coupled Hydrogeophysical Inversion‐State (CHI‐S), in which simulated salt concentrations are transformed to an electrical resistivity model, after which a geophysical forward response is calculated and compared with the measured geophysical data. This approach was applied for a field site in Santa Cruz County, California, where a time‐domain electromagnetic (TDEM) dataset was collected. For this location, a simple two‐dimensional cross‐sectional salt water intrusion model was developed, for which we estimated five uniform aquifer properties, incorporating the porosity that was also part of the employed petrophysical relationship. In addition, one geophysical parameter was estimated. The six parameters could be resolved well by fitting more than 300 apparent resistivities that were comprised by the TDEM dataset. Except for three sounding locations, all the TDEM data could be fitted close to a root‐mean‐square error of 1. Possible explanations for the poor fit of these soundings are the assumption of spatial uniformity, fixed boundary conditions and the neglecting of 3D effects in the groundwater model and the TDEM forward responses.     

Three-dimensional interpretation considering the static and the sea-effects of magnetotelluric data obtained in Jeju,Korea

Three-dimensional (3D) magnetotelluric (MT) surveys have been performed in Jeju, the largest volcanic island in Korea to figure out any possible structures or potential anomaly for remnant deep geothermal resources. Various approaches have been applied to interpret MT data observed in Jeju. MT dataset shows generally simple stratigraphy of four layers, though contains the severe static and the sea-effects. In our previous works, the induction vectors and 3D inversion results have commonly indicated the existence of a conductive anomaly in central parts of the island, beneath Mt. Halla. The 3D inversion dealt the static shifts as inversion parameters. The Jeju MT dataset, however, still contains the effect of conductive sea water surrounding the island.The sea-effect on MT impedance can be represented as a distortion tensor and excluded from the Jeju MT dataset by an iterative sea-effect correction. In this study, 3D inversion incorporating static shift parameterization was conducted using MT dataset corrected using 1D resistivity model obtained from the iterative scheme. Reasonably reconstructed images are obtained through the 3D inversion and using the MT dataset with sea-effect correction. The inversion result still shows the conductive anomaly in a similar depth. RMS misfits converged to a lower value than that of inversion using MT data before the sea-effect correction. From the fact, it is highly possible that the conductive anomaly is not an artifact but a real underground structure. Further investigation about the anomaly including exploration drilling is needed to see if it is from a fracture containing conductive sea water or related to the old volcanic activities.     

基于GPU混合反演的隧道电阻率超前探测成像研究

隧道施工期超前探测对于避免突涌水灾害的发生具有重要作用,为满足隧道三维电阻率超前探测快速化解译与成像的要求,本文提出了一种基于GPU并行的蚁群算法与最小二乘方法相结合的混合反演算法.该方法结合线性反演与非线性反演的优点,利用蚁群算法全局搜索能力强的优点为最小二乘反演提供较优的初始模型,以克服最小二乘算法容易陷入局部最优的缺点,提高了隧道三维电阻率反演成像的精度.同时,基于蚁群算法的天然并行性,提出了CUDA环境下的GPU并行策略,实现了三维电阻率反演的快速化成像.其次,开展了基于GPU混合反演的数值算例,与传统最小二乘线性反演进行了对比,基于GPU并行计算的混合反演计算效率得到了显著提高,对含水构造的位置、形态有较好的反映,压制了三维反演的多解性.最后开展了物理模型试验,结果表明基于GPU混合反演探测的低阻异常体与实际含水构造的位置较为相符,发现基于GPU加速的混合反演方法在提高探测精度与加快反演速度方面具有显著优势,为三维电阻率混合反演方法在隧道超前探测实际工程中的应用奠定了基础.     

On Two-Dimensional Modeling Of Magnetotelluric Field Data

In this paper, some recent topics on the modeling of magnetotelluric data are introduced. The focus is on the handling of real field data for two-dimensional resistivity modeling. First, the removal of the effects of near surface heterogeneity is reviewed. It covers telluric distortions (phase mixing and static shift) and magnetic distortions using conventional Groom-Bailey type 3D/2D model (three-dimensional local anomaly underlain by regional two-dimensional structure). The extension of a 3D/2D distortion model for multi-site, multi-frequency is a new development. Magnetic distortion seems to be less significant for land observations, but significant for sea floor data, where the regional magnetic field is weak due to seawater. In special cases involving for example, distortion due to topography and bathymetry, explicit removal is possible. There are some schemes proposed for a 3D/3D model (three-dimensional local anomaly underlain by regional three-dimensional structure). Along with the removal of the distortion, it is important to recognize the dimensionality of the dataset prior to modeling. A property using strike estimates for each site is an indicator for dimensionality which is unaffected by local distortion. Mapping the local strike or a rose diagram is an effective visualization of the dimensionality.Two-dimensional inversion is becoming routine. For the fast calculation of derivatives, approximate calculation, reciprocity or conjugate gradient methods are used. In order to incorporate a priori information and to overcome the intrinsic ill-posed nature of the inversion problem, imposing constraints on the model structure is important. A proper tradeoff between the data fit and constraints should be optimized to obtain minimum structures that are required by the field data. However, the choice of constraints is rather subjective and depends on the geological situations. For field data, two-dimensional inversion has limits on modes, area, and period range. Special care must be taken for the structure outside the profile. Two-dimensional inversion incorporating anisotropy is interesting and becoming popular, but the structure may not be unique. Future development in three-dimensional inversion for real datasets should take the above points into consideration.     

SOTEM数据一维OCCAM反演及其应用于三维模型的效果

本文基于垂直磁场分量研究了SOTEM数据的一维OCCAM反演方法,并将其应用于理论三维数据及野外实测数据的反演.对于大部分一维模型,OCCAM反演可取得较好的反演效果,且反演结果不依赖于偏移距;噪声对SOTEM数据的OCCAM反演具有较大影响,但当信号含噪水平不超过5%时,反演结果仍具有较好的准确性;若浅层存在较厚的低阻层,OCCAM反演结果对下部地层的分辨能力下降,仅能获得具有平均效应的电阻率.将一维算法应用于SOTEM三维数据的反演,会产生较大的误差,尤其是在异常体边缘地带影响最为严重.该影响程度与异常体和背景电阻率之间的差异有关,对于大多数电性近似呈连续变化的真实大地而言,一维OCCAM反演算法仍可获得较好的效果.最后通过陕西某煤田深部富水性调查的实测SOTEM数据反演验证了本文的研究成果.     

磁化强度矢量反演新方法及其在卡拉塔格铜多金属矿床找矿中的应用

磁异常的反演是地球物理勘探的重要手段,三维磁化率反演是磁异常定量解释中的一种重要方法.由于剩磁的存在使得磁化方向与地磁场方向产生偏差,从而影响了磁异常反演与解释的精度.本文基于磁异常模量反演和磁化强度矢量反演方法得到了一种新的磁化强度矢量反演方法.与以往的磁化强度矢量反演方法相比,该方法以磁异常模量反演得到的磁化率模型为约束,采用Lp范数正则化方法求解,提高了磁化强度矢量反演的精度和效率.本文通过模拟试验的反演计算,验证了这种磁化强度矢量反演方法的有效性.最后,将本文方法应用于新疆东天山卡拉塔格地区航磁数据的解释,获得了地下空间不同磁性差异的磁性体的空间分布特征,为进一步分析研究区隐伏矿床提供了重要信息.     

基于印模法的地面磁电阻率数据三维非线性共轭梯度反演

本文提出了能提高异常体分辨能力,同时得到绝对电导率的地面磁电阻率数据三维反演方法.磁电阻率响应用准直流的低频磁场代替;数值模拟由频率域电场满足的Helmholtz方程出发,采用三维交错网格有限差分法;长直导线源作为发射源,其中源的计算包含在背景场中;结合地面磁电阻率数据各分量的特点,选择y分量进行反演研究;反演采用三维非线性共轭梯度反演技术,为了提高异常体的深度分辨能力,进行迭代重构反演;用印模法对初始模型进行重构,采用的是辅模型在浅部,元模型在深部的组合方式.从合成数据和实际数据的反演结果可以得到以下的认识:(1)由频率域麦克斯韦方程组出发,低频磁场数据反演可以直接得到电导率,而不是相对电导率之比;(2)采用印模法组合初始模型,进行迭代重构反演,可以提高地面磁电阻率数据反演对异常体的分辨能力,确定埋深位置,同时不会丧失对于浅部异常体的分辨能力;(3)在结合印模法的地面磁电阻率数据三维反演中,深部异常体的分辨能力受地表不均匀导电体影响较小;(4)确定印模深度可以采用上一次重构反演结束时的模型变化量,通过相邻两次重构反演结束时的模型变化量之差来确定迭代重构是否终止.因为静磁场与重力场在数学上的相似性,本文的反演方法可以被运用到重力场等位场的地面数据的反演中.     

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.     

复杂介质有限元法2.5维可控源音频大地电磁法数值模拟

利用有限元2.5维可控源音频大地电磁法（简称CSAMT）数值模拟方法,对100Ωm均匀半空间介质中有限长度的电偶极源产生的电场、磁场及视电阻率、相位特征进行了数值模拟,研究了场的空间变化规律. 在一个象限中,场的特征存在双叶现象,当收发距大于4个趋肤深度时,电阻率较接近介质真实的电阻率,这些结果为观测系统和收发距的选择提供了依据. 波数域场的特征表明,低波数对源的贡献占较大的比例. 有限元法2.5维CSAMT数值模拟的优势在于能较准确地获得复杂介质结构的波场特征. 本文结合直立异常体、倾斜异常体及断陷模型对CSAMT电阻率、相位剖面特征及频率曲线特征的可靠性进行了研究. 数值模拟结果直观地给出了异常体的剖面异常形态. 通过对比研究异常体的剖面异常形态和半空间场的特征进一步说明本文方法和软件在模拟复杂介质结构场特征时是可靠的. 这为认识观测数据,指导反演解释提供了较好的依据.     

基于交叉梯度耦合的大地电磁与地震走时资料三维联合反演

为了有效解决目前大地电磁和地震走时资料单方法反演结果一致性不好的问题,同时克服基于岩石不同物性参数间关系耦合约束联合反演的局限性,本文研究了基于交叉梯度耦合约束的大地电磁与地震走时资料的三维联合反演算法.以较为成熟的天然地震走时资料三维正反演和大地电磁三维正反演算法为基础,实现了具有共同的反演网格,以交叉梯度结构耦合约束,并能同时获得电阻率和速度模型的三维联合反演算法.分别利用单棱柱体模型和双棱柱体模型合成数据进行了联合反演试算.结果表明:无论是单棱柱体模型还是双棱柱体模型,联合反演结果比单独反演对异常体的空间形态都有更好的恢复,其中单棱柱体模型反演的异常体电阻率更接近于真实电阻率,双棱柱体模型的联合反演结果不仅消除了围岩的部分电阻率假异常,而且增强了对异常体深部速度结构特征的恢复程度.联合反演还能同时改善电阻率和速度反向变化异常体的单独反演结果,进一步证明交叉梯度耦合不依赖于岩石物性关系,而强调地下结构的相似性,具有更普遍的适用性.     

Mapping Coastal Aquifers by Joint Inversion of DC and TEM Soundings-Three Case Histories

Electrical and electromagnetic methods are well suited for coastal aquifer studies because of the large contrast in resistivity between fresh water-bearing and salt water-bearing formations. Interpretation models for these aquifers typically contain four layers: a highly resistive unsaturated zone; a surficial fresh water aquifer of intermediate resistivity; an underlying conductive, salt water saturated aquifer; and resistive substratum. Additional layers may be added to allow for variations in lithology within the fresh water and salt water layers. Two methods are evaluated: direct current resistivity and time domain electromagnetic soundings. Use of each method alone produces nonunique solutions for resistivities and/or thicknesses of the different layers. We show that joint inversion of vertical electric and time domain electromagnetic soundings produces a more tightly constrained interpretation model at three test sites than is produced by inversion methods applied to each data set independently.     

基于三维正演的音频大地电磁阻抗相位不变量校正技术

复杂地形、地质条件的大地电磁数据解释容易出现假象,采用三维正演技术模拟地形和地表不均匀体的背景响应,对实测数据阻抗相位不变量进行校正,实现更准确的定性分析;对三维异常体模型的合成数据进行一维、二维多参数反演试算,以确定地形剧变区选择反演技术的最佳方案.合成数据的试反演结果显示一维反演水平切片假异常较多,二维反演能压制测向假异常,但不能压制走向的假异常,水平切片多出现测向条带.使用本文提出的阻抗相位不变量校正法扣除地形、地表背景响应,结合一维、二维反演,能使实际资料解释成果更加可靠.     

Sharp spatially constrained inversion with applications to transient electromagnetic data

Time‐domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam‐type regularization constraints, which are meant to address the ill‐posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non‐vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large‐scale time‐domain electromagnetic data inversions.     

2D and 3D resistivity inversion of Schlumberger vertical electrical soundings in Wadi El Natrun,Egypt: A case study

The Wadi El Natrun area is characterized by a very complicated geological and hydrogeological system. 45 vertical electrical soundings (Schlumberger array) were measured in the study area to elucidate the peculiarity of this unique regime, specifically the nature of waterless area. 2D and 3D resistivity inversion based on the finite element technique and regularization method were applied on the data set. 2D and 3D model resolution was investigated through the use of the Depth and Volume of Investigation Indexes. A very good matching was found between the zones of high resistivity, the waterless area, and the non-productive wells. The low resistivity zones (corresponding to Lower Pliocene clay) were also identified. The middle resistivity fresh water aquifer zones were recognized. Available results can assist in the aquifer management by selecting the most productive zone of groundwater.     

Three-dimensional forward modeling and inversion of borehole-to-surface electrical imaging with different power sources

Borehole-to-surface electrical imaging (BSEI) uses a line source and a point source to generate a stable electric field in the ground. In order to study the surface potential of anomalies, three-dimensional forward modeling of point and line sources was conducted by using the finite-difference method and the incomplete Cholesky conjugate gradient (ICCG) method. Then, the damping least square method was used in the 3D inversion of the formation resistivity data. Several geological models were considered in the forward modeling and inversion. The forward modeling results suggest that the potentials generated by the two sources have different surface signatures. The inversion data suggest that the low-resistivity anomaly is outlined better than the high-resistivity anomaly. Moreover, when the point source is under the anomaly, the resistivity anomaly boundaries are better outlined than when using a line source.     

龙门山断裂带地壳结构的三维建模

为了实现龙门山区域地质信息的科学管理与共享,推动该区域地球物理资料的统一管理,本文在整理现有二维地球物理探测数据的基础上构造了龙门山断裂带区域的三维地壳结构模型,并结合实测的布格重力异常数据对模型进行了分析。结果表明,地层模型正演的整体重力场与实测布格重力异常基本吻合,初步证明该模型的正确性。局部重力场显示:在该模型的尺度下,沉积层对整体重力场的变化贡献较小;中上地壳有不同程度的隆起和坳陷,与前人研究所揭示的低速异常体吻合;地幔表现为规则的自西北至东南单调上升的重力异常梯度带,与前人反演结果的趋势一致,从而证明了模型的可靠性。最后在重力资料约束下对模型进行了反演,进一步修正了模型。      

1D joint multi‐offset inversion of time‐domain marine controlled source electromagnetic data

The accurate estimation of sub‐seafloor resistivity features from marine controlled source electromagnetic data using inverse modelling is hindered due to the limitations of the inversion routines. The most commonly used one‐dimensional inversion techniques for resolving subsurface resistivity structures are gradient‐based methods, namely Occam and Marquardt. The first approach relies on the smoothness of the model and is recommended when there are no sharp resistivity boundaries. The Marquardt routine is relevant for many electromagnetic applications with sharp resistivity contrasts but subject to the appropriate choice of a starting model. In this paper, we explore the ability of different 1D inversion schemes to derive sub‐seafloor resistivity structures from time domain marine controlled source electromagnetic data measured along an 8‐km‐long profile in the German North Sea. Seismic reflection data reveal a dipping shallow amplitude anomaly that was the target of the controleld source electromagnetic survey. We tested four inversion schemes to find suitable starting models for the final Marquardt inversion. In this respect, as a first scenario, Occam inversion results are considered a starting model for the subsequent Marquardt inversion (Occam–Marquardt). As a second scenario, we employ a global method called Differential Evolution Adaptive Metropolis and sequentially incorporate it with Marquardt inversion. The third approach corresponds to Marquardt inversion introducing lateral constraints. Finally, we include the lateral constraints in Differential Evolution Adaptive Metropolis optimization, and the results are sequentially utilized by Marquardt inversion. Occam–Marquardt may provide accurate estimation of the subsurface features, but it is dependent on the appropriate conversion of different multi‐layered Occam model to an acceptable starting model for Marquardt inversion, which is not straightforward. Employing parameter spaces, the Differential Evolution Adaptive Metropolis approach can be pertinent to determine Marquardt a priori information; nevertheless, the uncertainties in Differential Evolution Adaptive Metropolis optimization will introduce some inaccuracies in Marquardt inversion results. Laterally constrained Marquardt may be promising to resolve sub‐seafloor features, but it is not stable if there are significant lateral changes of the sub‐seafloor structure due to the dependence of the method to the starting model. Including the lateral constraints in Differential Evolution Adaptive Metropolis approach allows for faster convergence of the routine with consistent results, furnishing more accurate estimation of a priori models for the subsequent Marquardt inversion.     

三维频率域可控源电磁反演研究

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环工作面三维直流电阻率法研究及应用

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