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1.
Model Fusion and Joint Inversion 总被引：1，自引：1，他引：0
Inverse problems are inherently non-unique, and regularization is needed to obtain stable and reasonable solutions. The regularization adds information to the problem and determines which solution, out of the infinitely many, is obtained. In this paper, we review and discuss the case when a priori information exists in the form of either known structure or in the form of another inverse problem for a different property. The challenge is to include such information in the inversion process. To use existing known structure, we review the concept of model fusion, where we build a regularization functional that fuses the inverted model to a known one. The fusion is achieved by four different techniques. Joint inversion of two data sets is achieved by using iterative data fusion. The paper discusses four different methods for joint inversion. We discuss the use of correspondence maps or the petrophysics of the rocks, as well as structure. In particular, we suggest to further stabilize the well-known gradient cross product and suggest a new technique, Joint Total Variation, to solve the problem. The Joint Total Variation is a convex functional for joint inversion and, as such, has favorable optimization properties. We experiment with the techniques on the DC resistivity problem and the borehole tomography and show how model fusion and joint inversion can significantly improve over existing techniques. 相似文献
2.
Michael S. Zhdanov 《Geophysical Prospecting》2009,57(4):463-478
The interpretation of potential and electromagnetic fields observed over 3D geological structures remains one of the most challenging problems of exploration geophysics. In this paper I present an overview of novel methods of inversion and imaging of gravity and electromagnetic data, which are based on new advances in the regularization theory related to the application of special stabilizing functionals, which allow the reconstruction of both smooth images of the underground geological structures and models with sharp geological boundaries. I demonstrate that sharp-boundary geophysical inversion can improve the efficiency and resolution of the inverse problem solution. The methods are illustrated with synthetic and practical examples of the 3D inversion of potential and electromagnetic field data. 相似文献
3.
4.
David Beamish 《Journal of Applied Geophysics》1994,32(4)
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. 相似文献
5.
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
6.
Mohammad Israil 《Acta Geophysica》2006,54(2):126-141
Two techniques have been presented for the delineation of boundaries from smooth models obtained by smooth inversion techniques
of geoelectrical sounding data, such as straightforward inversion scheme, Occam’s and Zohdy’s methods. The smooth model consists
of a large number of equally spaced layers, wherein the real geological boundaries are missing. The techniques proposed here
suppress the geologically irrelevant boundaries and support the real structural boundaries present in the geoelectrical data.
In the first technique, solution of linear inverse problem is improved iteratively through weighted minimum norm inverse,
the weight being taken from the current solution. The technique is referred as Iterative Straightforward Inversion Scheme.
The second method is analytical, based on the application of smoothing filter, referred in the literature as edge-preserving
smoothing. A few examples of theoretical magnetotelluric, dc resistivity and field sounding data have been presented to demonstrate
the capabilities of the techniques. The methodologies also reduce the conspicuous oscillations in the smooth solutions caused
by the conversion of sharp boundaries to the smooth ones. 相似文献
7.
利用伴随算子L*,直接的偏移方法通常导致一个低分辨率或模糊的地震成像.线性化偏移反演方法需求解一个最小二乘问题.但直接的最小二乘方法的数值不稳定,为目视解译带来困难.本文建立约束正则化数学模型,研究了地震偏移反演成像问题的迭代正则化求解方法.首先对最小二乘问题施加正则化约束,接着利用梯度迭代法求解反演成像问题,特别是提出了共轭梯度方法的混合实现技巧.为了表征该方法的可实际利用性,分别对一维,二维和三维地震模型进行了数值模拟.结果表明该正则偏移反演成像方法是有效的,对于实际的地震成像问题有着良好的应用前景. 相似文献
8.
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
9.
本文讨论地球内部构造反演问题的某些新途径.其内容如下:地球构造反问题与固有值反问题;反散射问题中介质间断性的成象与因果广义Radon变换,包含地球构造反问题的新提法,反散射问题的线性化,古典Radon变换与广义Radon变换,线性化反问题的渐近解,渐近解和偏移格式. 相似文献
10.
Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface 总被引：4，自引：1，他引：3
Mark E. Everett 《Surveys in Geophysics》2012,33(1):29-63
Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques
and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe
some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are
widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion,
heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques
are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics,
and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting
new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology,
contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climate. 相似文献
11.
真振幅成像是一种代表性的定量估计模型参数扰动高波数部分的地震波成像方法.经典的真振幅成像方法在高频近似和理想照明假设条件下求取显式对角Hessian逆矩阵作为偏移振幅加权算子,用以校正波传播过程中的几何扩散效应,得到模型参数扰动的带限估计.真振幅保真成像方法在利用逆时偏移（RTM）框架实现时会产生低波数噪声,影响对高波数参数估计的精度.本文给出了一种新的基于RTM框架的真振幅保真成像条件,该成像条件针对反射波数据,在高频近似下散射模式对应正问题及Bayes反问题框架下导出.与传统基于高频渐进反演的波动方程成像方法类似,利用本文提出RTM成像条件能够保证计算结果与高频近似下反演结果的一致性.同时,利用本文提出RTM真振幅成像条件能够在成像过程中自动保真的消除传统真振幅RTM算法中存在低波数噪声,模型数值实验结果验证了本文方法的正确性和有效性. 相似文献
12.
Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application 总被引：12，自引：1，他引：11
The whole subject of three-dimensional (3-D) electromagnetic (EM) modelling and inversion has experienced a tremendous progress
in the last decade. Accordingly there is an increased need for reviewing the recent, and not so recent, achievements in the
field. In the first part of this review paper I consider the finite-difference, finite-element and integral equation approaches
that are presently applied for the rigorous numerical solution of fully 3-D EM forward problems. I mention the merits and
drawbacks of these approaches, and focus on the most essential aspects of numerical implementations, such as preconditioning
and solving the resulting systems of linear equations. I refer to some of the most advanced, state-of-the-art, solvers that
are today available for such important geophysical applications as induction logging, airborne and controlled-source EM, magnetotellurics,
and global induction studies. Then, in the second part of the paper, I review some of the methods that are commonly used to
solve 3-D EM inverse problems and analyse current implementations of the methods available. In particular, I also address
the important aspects of nonlinear Newton-type optimisation techniques and computation of gradients and sensitivities associated
with these problems. 相似文献
13.
Iv. M. Varentsov 《Surveys in Geophysics》1983,6(1-2):55-78
The main results obtained during the last 5–8 yr in the solution of forward and inverse problems of 3D induction studies are summarized. The up-to-date status of 3D modelling is presented and prospective improvements in the formulation and numerical solution of forward problems are discussed. Approximate techniques and practical aspects of 3D modelling are specially considered. The general scheme of 3D interpretation of electromagnetic geophysical observations is outlined and realistic formalized approaches to solving 3D inverse problems, namely direct inversion and formalized model fitting, are studied. 相似文献
14.
Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling 总被引：1，自引：0，他引：1
Despite impressive progress in the development and application of electromagnetic (EM) deterministic inverse schemes to map the 3-D distribution of electrical conductivity within the Earth, there is one question which remains poorly addressed—uncertainty quantification of the recovered conductivity models. Apparently, only an inversion based on a statistical approach provides a systematic framework to quantify such uncertainties. The Metropolis–Hastings (M–H) algorithm is the most popular technique for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. However, all statistical inverse schemes require an enormous amount of forward simulations and thus appear to be extremely demanding computationally, if not prohibitive, if a 3-D set up is invoked. This urges development of fast and scalable 3-D modelling codes which can run large-scale 3-D models of practical interest for fractions of a second on high-performance multi-core platforms. But, even with these codes, the challenge for M–H methods is to construct proposal functions that simultaneously provide a good approximation of the target density function while being inexpensive to be sampled. In this paper we address both of these issues. First we introduce a variant of the M–H method which uses information about the local gradient and Hessian of the penalty function. This, in particular, allows us to exploit adjoint-based machinery that has been instrumental for the fast solution of deterministic inverse problems. We explain why this modification of M–H significantly accelerates sampling of the posterior probability distribution. In addition we show how Hessian handling (inverse, square root) can be made practicable by a low-rank approximation using the Lanczos algorithm. Ultimately we discuss uncertainty analysis based on stochastic inversion results. In addition, we demonstrate how this analysis can be performed within a deterministic approach. In the second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach. 相似文献
15.
16.
Remarkable progress has been made in electromagnetic (EM) techniques as applied to the petroleum industry in instruments,
data acquisition, and processing and interpretation in China. Included here is equipment, such as high-power Controlled Source
EM (CSEM) acquisition systems, acquisition methods, such as the three dimensional small-bin Continuous Electromagnetic Array
acquisition method, Time and Frequency Domain Controlled Source Electromagnetic, Borehole-to-surface Electromagnetic technique
and marine magnetotelluric method. Data processing methods, such as fast three dimensional inversion using nonlinear conjugate
gradients, and data interpretation methods, like Induced Polarization and Resistivity anomalies for hydrocarbon detection,
are also included. These new techniques have been applied in petroleum survey and many cases are in complicated areas. They
have successfully served the investigation of deep igneous rock reservoirs, and prediction of potential hydrocarbon targets.
The cases indicate that electromagnetic techniques can help seismic survey to effectively detect hydrocarbon reservoir and
remarkably improve drilling successes. 相似文献
17.
To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical. 相似文献
18.
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. 相似文献
19.
对于迭代方式的参数化反演方法,如何使反演结果稳定地收敛到整体极小仍是目前大地电磁（MT）反演中急需解决的问题．本文利用小波变换理论中的多尺度分析方法将大地电磁反问题分解为依赖于尺度变量的反问题序列,然后按尺度从大到小的次序依次求解,求解过程中前一个尺度反问题的解作为下一个尺度反问题的初始模型,直到来出对应于尺度为0的原反问题的解为止．该方法称为多尺度反演方法．数值试验和实际资料的反演结果表明,该方法可有效改善传统广义逆反演方法易陷入局部极小的弊端． 相似文献
20.
传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性. 相似文献