Fast approximate 1D modelling and inversion of transient electromagnetic data

A novel, fast, and approximate forward modelling routine for time‐domain electromagnetic responses is presented. It is based on the separation of the forward problem into a configuration‐independent part, mapping conductivity as a function of depth onto apparent conductivity as a function of time, and a configuration‐dependent part, i.e., the half‐space step response. The response of a layered model is then found as the half‐space response for a half‐space conductivity equal to the apparent conductivity. The mapping is ten times faster than traditional accurate forward modelling routines, and through stochastic modelling, it is found that the standard deviation of the modelling error is 0.7 %. The forward mapping lends itself to integration in a modern state‐of‐the‐art inversion formulation in exactly the same way as traditionally computed responses, and a field example is included where inversion results using the approximate forward response are compared with those of an accurate forward response for helicopterborne transient electromagnetic data. In addition to being used in its own right in inversion of transient data, the speed and accuracy of the approximate inversion mean that it is well suited for quality control and fast turnaround data delivery of survey results to a client. It can also be used in hybrid inversion formulations by supplying initial iterations and high‐quality derivatives in an inversion based on accurate forward modelling.     

航空瞬变电磁数据光滑拟二维反演

航空瞬变电磁法适用于浅表地层的大面积探测,由于实测数据量巨大,一维反演作为一种快速高效的方法被广泛应用.在层状地电条件下,横向约束反演能有效的改善传统单点阻尼最小二乘反演结果中界面横向不连续的情况,但其存在反演过程依赖初始模型,且在复杂层状情况下迭代不稳定的问题.本文提出一种基于OCCAM反演并在正则化项中引入横向光滑约束的光滑拟二维反演方法,在保持OCCAM方法对初始模型依赖性小优势的同时,也使得相邻测点电性横向连续.在反演过程中采用令满足迭代误差的测点不再参与后续迭代的策略,以此减少不必要的正演和雅可比计算,提高反演效率.通过对三个不同地电情况的理论模拟数据进行光滑拟二维反演,并与其他传统反演方法对比,验证了该方法能有效的提高反演稳定性,得到与理论模型高度吻合的反演结果.     

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method. Presently, the interpretation is mainly based on resistivity—depth imaging and one-dimensional layered inversion; nevertheless, it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods. 3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data. Thus, we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm. To eliminate the source singularities in the numerical simulations, we split the fields into primary and secondary fields. The primary fields are calculated using homogeneous or layered models with analytical solutions, and the secondary (scattered) fields are solved by the finite-element method. The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver, which greatly improves the computational efficiency. The inversion algorithm was based on damping least-squares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix. Synthetic and field data were used to test the effectiveness of the proposed method.     

基于L1范数的瞬变电磁非线性反演

瞬变电磁反演存在高度的非线性特征,常用的最小二乘等线性反演方法往往对初始模型高度依赖,并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数,采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生,通过指数函数退温机制模拟系统能量最小实现迭代,通过接收概率函数评价当前模型,实现局部最优解的跳出,最终实现全局最优化求解.通过数值算例发现,无论给定的反演层数等于还是大于设计模型,都可以获得较好的反演效果,因而可以在反演初始就设计较多的层数,实现反演模型的自动拟合;同时,利用含噪声数据反演进一步验证算法的稳定性.最后,对实测数据进行了反演测试,结果与钻孔编录基本一致,表明提出的基于L1范数的模拟退火反演可用于实测数据处理.

     

3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

The controlled source extremely low frequency (CSELF) electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) inversion of CSELF electromagnetic data is presented (in which the sources, or primary fields, are included), with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.     

时间域航空电磁2.5维非线性共轭梯度反演

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.     

Piecewise 1D laterally constrained inversion of resistivity data

In a sedimentary environment, layered models are often capable of representing the actual geology more accurately than smooth minimum structure models. Furthermore, interval thicknesses and resistivities are often the parameters to which non‐geophysicist experts can relate and base decisions on when using them in waste site remediation, groundwater modelling and physical planning. We present a laterally constrained inversion scheme for continuous resistivity data based on a layered earth model (1D). All 1D data sets and models are inverted as one system, producing layered sections with lateral smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, e.g. originating from electric logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible to some extent. Information from areas with well‐resolved parameters will migrate through the constraints in a similar way to help resolve the poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters, supporting quantitative evaluation of the inversion result. Examples from synthetic 2D models show that the model recognition of a sublayered 2D wedge model is improved using the laterally constrained inversion approach when compared with a section of combined 1D models and when compared with a 2D minimum structure inversion. Case histories with data from two different continuous DC systems support the conclusions drawn from the synthetic example.     

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.     

Practical techniques for 3D resistivity surveys and data inversion1

Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole-pole array is used to make the potential measurements. The number of measurements required can be reduced to about one-third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness-constrained least-squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half-space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi-Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.     

三维频率域航空电磁反演研究

航空电磁数据的三维解释由于数据量大需要有高效的反演算法作为支撑.本文利用两种目前主流的数值优化技术（非线性共轭梯度和有限内存的BFGS法）实现了三维频率域航空电磁反演,并进一步比较了两种方法的有效性和运算效率.在反演过程中,为了更好地反演异常体的空间位置,模型方差矩阵中的光滑系数在反演起始阶段取值较大;当数据拟合差下降趋于平缓时,再利用较小的光滑因子约束反演过程来实现聚焦和获得精确的反演结果.理论数据反演表明这两种优化策略具有相似的内存需求,但是有限内存的BFGS技术比非线性共轭梯度法在计算时间和模型反演分辨率上具有一定的优越性,因此有限内存BFGS法更适合于求解大规模三维反演问题. 模型试验进一步表明目前主流的迭代法求解技术不适合大规模航空电磁数据反演,未来移动平台多源电磁数据快速正反演可通过引入矩阵分解技术来实现.     

Appraisal of a new 1D weighted joint inversion of ground based and helicopter‐borne electromagnetic data

In order to couple spatial data from frequency‐domain helicopter‐borne electromagnetics with electromagnetic measurements from ground geophysics (transient electromagnetics and radiomagnetotellurics), a common 1D weighted joint inversion algorithm for helicopter‐borne electromagnetics, transient electromagnetics and radiomagnetotellurics data has been developed. The depth of investigation of helicopter‐borne electromagnetics data is rather limited compared to time‐domain electromagnetics sounding methods on the ground. In order to improve the accuracy of model parameters of shallow depth as well as of greater depth, the helicopter‐borne electromagnetics, transient electromagnetics, and radiomagnetotellurics measurements can be combined by using a joint inversion methodology. The 1D joint inversion algorithm is tested for synthetic data of helicopter‐borne electromagnetics, transient electromagnetics and radiomagnetotellurics. The proposed concept of the joint inversion takes advantage of each method, thus providing the capability to resolve near surface (radiomagnetotellurics) and deeper electrical conductivity structures (transient electromagnetics) in combination with valuable spatial information (helicopter‐borne electromagnetics). Furthermore, the joint inversion has been applied on the field data (helicopter‐borne electromagnetics and transient electromagnetics) measured in the Cuxhaven area, Germany. In order to avoid the lessening of the resolution capacities of one data type, and thus balancing the use of inherent and ideally complementary information content, a parameter reweighting scheme that is based on the exploration depth ranges of the specific methods is proposed. A comparison of the conventional joint inversion algorithm, proposed by Jupp and Vozoff ( 1975 ), and of the newly developed algorithm is presented. The new algorithm employs the weighting on different model parameters differently. It is inferred from the synthetic and field data examples that the weighted joint inversion is more successful in explaining the subsurface than the classical joint inversion approach. In addition to this, the data fittings in weighted joint inversion are also improved.     

Laterally constrained inversion of helicopter-borne frequency-domain electromagnetic data

Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter.     

On the inversion of global electromagnetic induction data

The initial phase of any inversion of geophysical data must examine the question of the existence of globally distinct solutions. Previous inversion st point of view. A basic inversion strategy for geophysical data is considered. It is concluded that future progress depends on the use of synthetic data to resolve questions about the potential constraining power of GEMI data.     

基于主成分的时间域航空电磁数据神经网络反演仿真研究(英文)

传统上,时间域航空电磁数据通过拟合迭代反演计算得到大地模型,然而,由于航空电磁数据道间的较强相关性,导致病态反演,并引起超定问题;同时电磁数据的相关性使其与模型参数的映射关系复杂,增加了反演的复杂度。采用主成分分析法将航空电磁数据变换为正交的较少数量的主成分,不仅降低了数据道间的相关性,减小了数据量,同时压制了数据的不相关噪声。本文利用人工神经网络(ANN)逼近主成分与大地模型参数间的映射关系,避免了传统反演算法中雅克比矩阵的复杂计算。层状模型的主成分神经网络与数据神经网络的反演结果对比显示,主成分神经网络反演方法网络结构简单,训练步数少,反演结果好,特别是对于含噪数据。准二维模型的主成分ANN、数据ANN以及Zhody方法的反演结果显示了主成分神经网络具有更接近真实模型的反演效果,进一步证明了主成分神经网络反演方法适合海量航空电磁探测数据反演。     

Automatic 1D inversion of multifrequency airborne electromagnetic data with artificial neural networks: discussion and a case study

Artificial neural networks were used to implement an automatic inversion of frequency‐domain airborne electromagnetic (AEM) data that do not require a priori information about the survey area. Two classes of model, i.e. homogeneous half‐space models and horizontally layered half‐space models with two layers, are used in this 1D inversion, and for each data point the selection of the class of 1D model is performed prior to the inversion, also using an artificial neural network. The proposed inversion method was tested in a survey area situated in Austria, northwest of Vienna in the Bohemian Massif. The results of the inversion were compared with the geological setting, logging results, and seismic and gravimetric measurements. This comparison shows a good correlation between the AEM models and the known geological and geophysical data.     

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions. We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.     

飞行高度同时反演的固定翼航空瞬变电磁-维反演

航空电磁测量记录中,不仅感生电动势测量数据有观测误差,而且高度计测量数据也有误差,直接进行常规反演往往导致反演结果不可靠,研究飞行高度数据有误差下的反演算法具有实际意义.本文以层状模型的固定翼时间域航空电磁多分量理论响应数据为例,提出了两种针对飞行高度计记录数据有误差时的正则化反演算法,一个是自适应正则化反演方法,另一...     

2D磁异常分步反演方法分析研究

2D磁异常分步反演方法是利用二维(剖面)磁测数据确定场源几何参数以及物性参数的一种反演方法,该方法的优点是构造的形态函数S不受场源磁化特征的影响,因此可以在未知场源物性参数的前提下,通过拟合依次反演得到磁性源形体横截面几何参数、磁化强度以及磁化方向.本文阐述了2D磁异常分步反演方法的原理及步骤,对形态函数S的特征及求取方法进行了讨论,分析了区域背景干扰(正常场)对反演结果的影响并提出了初步解决方案.在方法研究的基础上,进行了单一理论模型及组合理论模型的试算,得到了较好的反演结果.为了验证该方法的效果,对实测剖面进行了试算,得到了场源的边界及场源埋深信息,为进一步反演提供了有用的参考.     

Effects of the sea floor topography on the 1D inversion of time‐domain marine controlled source electromagnetic data

Time‐domain marine controlled source electromagnetic methods have been used successfully for the detection of resistive targets such as hydrocarbons, gas hydrate, or marine groundwater aquifers. As the application of time‐domain marine controlled source electromagnetic methods increases, surveys in areas with a strong seabed topography are inevitable. In these cases, an important question is whether bathymetry information should be included in the interpretation of the measured electromagnetic field or not. Since multi‐dimensional inversion is still not common in time‐domain marine controlled source electromagnetic methods, bathymetry effects on the 1D inversion of single‐offset and multi‐offset joint inversions of time‐domain controlled source electromagnetic methods data are investigated. We firstly used an adaptive finite element algorithm to calculate the time‐domain controlled source electromagnetic methods responses of 2D resistivity models with seafloor topography. Then, 1D inversions are applied on the synthetic data derived from marine resistivity models, including the topography in order to study the possible topography effects on the 1D interpretation. To evaluate the effects of topography with various steepness, the slope angle of the seabed topography is varied in the synthetic modelling studies for deep water (air interaction is absent or very weak) and shallow water (air interaction is dominant), respectively. Several different patterns of measuring configurations are considered, such as the systems adopting nodal receivers and the bottom‐towed system. According to the modelling results for deep water when air interaction is absent, the 2D topography can distort the measured electric field. The distortion of the data increases gradually with the enlarging of the topography's slope angle. In our test, depending on the configuration, the seabed topography does not affect the 1D interpretation significantly if the slope angle is less or around 10°. However, if the slope angle increases to 30° or more, it is possible that significant artificial layers occur in inversion results and lead to a wrong interpretation. In a shallow water environment with seabed topography, where the air interaction dominates, it is possible to uncover the true subsurface resistivity structure if the water depth for the 1D inversion is properly chosen. In our synthetic modelling, this scheme can always present a satisfactory data fit in the 1D inversion if only one offset is used in the inversion process. However, the determination of the optimal water depth for a multi‐offset joint inversion is challenging due to the various air interaction for different offsets.