Inversion of time domain three-dimensional electromagnetic data

We present a general formulation for inverting time domain electromagnetic data to recover a 3-D distribution of electrical conductivity. The forward problem is solved using finite volume methods in the spatial domain and an implicit method (Backward Euler) in the time domain. A modified Gauss–Newton strategy is employed to solve the inverse problem. The modifications include the use of a quasi-Newton method to generate a pre-conditioner for the perturbed system, and implementing an iterative Tikhonov approach in the solution to the inverse problem. In addition, we show how the size of the inverse problem can be reduced through a corrective source procedure. The same procedure can correct for discretization errors that inevidably arise. We also show how the inverse problem can be efficiently carried out even when the decay time for the conductor is significantly larger than the repetition time of the transmitter wave form. This requires a second processor to carry an additional forward modelling. Our inversion algorithm is general and is applicable for any electromagnetic field  ( E , H , d B / dt )  measured in the air, on the ground, or in boreholes, and from an arbitrary grounded or ungrounded source. Three synthetic examples illustrate the basic functionality of the algorithm, and a result from a field example shows applicability in a larger-scale field example.     

基于电磁感应数据的膜下滴灌土壤水分动态变化研究

快速、无损监测农田土壤水分含量,是智慧农业的重要研究内容.以新疆南疆阿拉尔国家农业科技园区膜下滴灌棉田为研究对象,运用EM38-MK2大地电导率仪快速、高效的获取了4组不同时期的棉田土壤表观电导率数据,并同步采集表层土壤(0～20 cm)样品,通过构建表观电导率数据与室内测定含水量数据间的反演模型获取了测点的含水量数据...     

The Fréchet derivative for the one-dimensional electromagnetic induction problem

Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Fréchet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free-oscdlation problem for the elastic earth. The remainder term in the Fréchet formula is shown to be O|δσ|² and a numerical estimate is made of the bounding constant for a restricted class of conductivity models.     

Inversion of Love-wave data for velocity and anelasticity using exact kernels

Summary. The general problem of inverting Love-wave dispersion and amplitude data to obtain a velocity and Q_s structure is considered. A formulation is used which incorporates attenuation into the Haskell-Thompson matrix method in an exact manner and thus retains the inherent non-linearity in the anelasticity. The resulting exact inversion kernels allow simultaneous inversion for velocity and intrinsic attenuation parameters. The method is applied to synthetic data which allows a comparison to be made with inexact kernels. The results indicate that the use of inexact kernels may introduce spurious oscillations into the Q_s structure and that a simultaneous inversion can be more stable than inverting for velocity alone.     

The forward problem of electromagnetic induction: accurate finite-difference approximations for two-dimensional discrete boundaries with arbitrary geometry

We describe finite-difference approximations to the equations of 2-D electromagnetic induction that permit discrete boundaries to have arbitrary geometrical relationships to the nodes. This allows finite-difference modelling with the flexibility normally ascribed to finite-element modelling. Accuracy is demonstrated by comparison with finite-element computations. We also show that related approximations lead to substantially improved accuracy in regions of steep, but not discontinuous, conductivity gradient.     

Bimodal electromagnetic induction in non-uniform thin sheets with an application to the northern Pyrenean induction anomaly

In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived. The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.     

Inversion of seismic data using tomographical reconstruction techniques for investigations of laterally inhomogeneous media

Summary. For the determination of lateral velocity or absorption inhomogeneities, methods such as the generalized matrix inversion and its damped versions, for example the stochastic inverse, are usually applied in seismology to travel-time or amplitude anomalies. These methods are not appropriate for the solution of very extensive systems of equations. Reconstruction techniques as developed for computer tomography are suitable for operations with extremely large numbers of equations and unknown parameters. In this paper solutions obtained with the BPT (Back Projection Technique), ART (Algebraic Reconstruction Technique) and SIRT (Simultaneous Iterative Reconstruction Technique) are compared with those obtained from a damped version of the generalized inverse method. Data of 2-D model-seismic experiments are presented for demonstration.     

Inversion of controlled-source seismic tomography and gravity data with the self-adaptive wavelet parametrization of velocities and interfaces

A self-adaptive automated parametrization approach is suggested for the sequential inversion of controlled-source seismic tomography and gravity data. The velocities and interfaces are parametrized by their Haar wavelet expansion coefficients. Only those coefficients that are well constrained by the data, as measured by the number of rays that cross the corresponding wavelet function support area and their angular coverage, are inverted for, others are set to zero. This approach results in a reasonable distribution of resolution throughout the model even in cases of irregular ray coverage and does overcome the trade-off between different types of model parameters. A modified sequential inversion approach is suggested to join the traveltimes and gravity anomalies inversion. An algorithm is developed that inverts for smooth velocity and density variations inside the seismic layer, the position of its bottom interface as well as for optimal values of the velocity-to-density regression coefficients. The algorithm makes use of direct (diving), reflected and head (critically refracted) wave traveltimes. The algorithm workflow is demonstrated on a synthetic data example.     

Interpretation of long-offset transient electromagnetic data from the Odenwald area, Germany, using two-dimensional modelling

The standard 1-D inversion approach for the interpretation of transient electromagnetic (TEM) data usually fails in the presence of near-surface conductivity anomalies. Since multidimensional inversion codes are not routinely available, the only alternative to discarding the data may be trial-and-error forward modelling. We interpret data from a long-offset transient electromagnetic (LOTEM) survey which was carried out in 1995 in the Odenwald area, using 2-D finite-difference modelling. We focus on a subsegment of the LOTEM profile, which was shot with two different electric dipole transmitters. A model is found which consistently explains the electric and magnetic field data at eight locations for both transmitters. First, we introduce a conductive dyke under the receiver spread to explain sign reversals in the magnetic field transients. A conductive slab under one of the transmitters is required to obtain a reasonable quantitative fit for that transmitter. Consideration of the electric field data then requires a modification of the layered earth background. Finally, we study the response of a crustal conductor, which was the original target of the survey. The data are sensitive to the conductor, and for the investigated subset of the data the fits are slightly better without the conductive layer.     

基于SAIL模型的多角度多光谱遥感叶面积指数反演

随着多角度传感器的陆续出现及植被遥感传输机理研究的深入,多角度遥感逐渐成为地表信息反演的热点问题.以SAIL冠层反射率模型为基础,通过联合多角度和多光谱数据,可以从物理机理角度进行植被叶面积指数(LAI)反演的应用研究.首先通过计算得到多角度多光谱遥感影像的角度信息,并经6S模型纠正后得到多光谱多角度植被冠层反射率数据.然后将PROSPECT模型模拟出的植被叶片反射率和透过率,以及多角度观测数据、LAI和其它实测数据输入SAIL模型,模拟得到了多角度多光谱冠层反射率,进而建立多角度多光谱冠层反射率与LAI的查找表.最后,将影像的多角度多光谱冠层反射率与查找表进行匹配,实现植被LAI的反演.最后对反演结果进行了验证和分析,结果表明反演精度较高,误差均在合理范围之内.