共查询到20条相似文献，搜索用时 343 毫秒
1.
S. A. Greenhalgh L. Marescot B. Zhou M. Greenhalgh T. Wiese 《Pure and Applied Geophysics》2009,166(4):673-699
In this paper we develop analytic solutions for the electric potential, current density and Fréchet derivatives at any interior
point within a 3-D transversely isotropic medium having a tilted axis of symmetry. The current electrode is assumed to be
on the surface of the Earth and the plane of stratification given arbitrary strike and dip. Profiles can be computed for any
azimuth. The equipotentials exhibit an elliptical pattern and are not orthogonal to the current density vectors, which are
strongly angle dependent. Current density reaches its maximum value in a direction parallel to the longitudinal conductivity
direction. Illustrative examples of the Fréchet derivatives are given for the 2.5-D problem, in which the profile is taken
perpendicular to strike. All three derivatives of the Green’s function with respect to longitudinal conductivity, transverse
resistivity and dip angle of the symmetry axis (dG/dσl, dG/dσt, dG/dθ0) show a strongly asymmetric pattern compared to the isotropic case. The patterns are aligned in the direction of the tilt
angle. Such sensitivity patterns are useful in real-time experimental design as well as in the fast inversion of resistivity
data collected over an anisotropic earth. 相似文献
2.
谱元法已成为区域性乃至大陆性尺度地震波场模拟的重要工具.对于区域或大陆尺度层析成像而言,地球曲率不可忽略,此时模拟地震波传播采用球坐标系更为合适.本文从球坐标系下弹性波动方程弱形式出发,基于球坐标系变分原理给出了球坐标系下求解三维地震波方程的谱元法.另一方面,计算Fréchet敏感核是进行全波形反演的关键,本文借助伴随原理,推导了全波走时层析成像三维Fréchet敏感核表达式.为了验证球坐标系下谱元法的精度,我们将数值模拟结果与normal mode方法得到的解析解在1-D PREM模型下进行了对比.同时,我们将此方法应用到华北克拉通区域,以期获得地球内部结构精确成像.基于3-D全球径向各向异性地幔模型S362ANI和3-D地壳模型Crust1.0,我们建立了华北克拉通初始3-D背景模型,并将数值模拟结果与实际观测台站记录波形资料进行对比分析,利用互相关方法提取走时残差,最后给出了Fréchet敏感核在3-D空间中的分布,这些工作为下一步开展球坐标系下三维大尺度全波形反演奠定了基础. 相似文献
3.
In order to perform resistivity imaging, seismic waveform tomography or sensitivity analysis of geophysical data, the Fréchet derivatives, and even the second derivatives of the data with respect to the model parameters, may be required. We develop a practical method to compute the relevant derivatives for 2.5D resistivity and 2.5D frequency-domain acoustic velocity inversion. Both geophysical inversions entail the solution of a 2.5D Helmholtz equation. First, using differential calculus and the Green's functions of the 2.5D Helmholtz equation, we strictly formulate the explicit expressions for the Fréchet and second derivatives, then apply the finite-element method to approximate the Green's functions of an arbitrary medium. Finally, we calculate the derivatives using the expressions and the numerical solutions of the Green's functions. Two model parametrization approaches, constant-point and constant-block, are suggested and the computational efficiencies are compared. Numerical examples of the derivatives for various electrode arrays in cross-hole resistivity imaging and for cross-hole seismic surveying are demonstrated. Two synthetic experiments of resistivity and acoustic velocity imaging are used to illustrate the method. 相似文献
4.
— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry. 相似文献
5.
A novel hybrid approach to earthquake location is proposed which uses a combined coarse global search and fine local inversion
with a minimum search routine. The method exploits the advantages of network ray tracing and robust formulation of the Fréchet
derivatives to simultaneously update all sampled initial source parameters in the solution space to determine the best solution.
Synthetic examples, involving a three-dimensional (3-D) complex velocity model and a challenging source–receiver layout, are
used to demonstrate the advantages over direct grid search algorithms in terms of solution accuracy, computational efficiency,
and sensitivity to noise. Therefore, this is a promising scheme for earthquake early warning, tsunami early warning, rapid
hazard assessment, and emergency response after strong earthquake occurrence. 相似文献
6.
本文基于球谐展开群速度表达式计算走时关于各向异性参数的Fréchet核函数,利用共轭梯度法对两种参数化方法进行了VTI介质中多参数联合反演方法研究.经过理论分析和数值试验发现,与经典的Thomsen参数化方法相比,垂直慢度、水平慢度与动校正慢度的参数化方式更有利于VTI介质多参数联合走时层析反演.为了克服走时对ε参数的不敏感性,我们采用了两步法进行双参数反演,理论模型试验反演得到了与垂直速度精度相当的ε参数.可以将两步法扩展到三步法以同时反演各向异性介质中的三个参数,数值试验展示了该策略的应用潜力. 相似文献
7.
各向异性介质弹性波方程全波形反演过程中多参数之间的相互耦合,使得弱参数在反演过程中难得到理想的结果.本文以VTI介质为例,在各参数辐射模式分析的基础上,基于改进的散射积分算法实现目标函数梯度的直接求取,进一步构建高斯牛顿方向,实现Hessian矩阵的有效利用,以考虑Hessian矩阵非主对角线元素包含的各参数间的耦合效应,在不使用任何反演策略的情况下实现高精度的VTI介质弹性波方程多参数同步反演.同时,该方法在计算过程中无需存储庞大的核函数矩阵,且无需传统截断牛顿法中额外的正演计算,因此内存占用小,计算效率高.本文数值试验验证了该方法的有效性,为各向异性多参数全波形反演提供了一种新的解决方案. 相似文献
8.
Fresnel zone inversion for lateral heterogeneities in the earth 总被引：2，自引：0，他引：2
Kiyoshi Yomogida 《Pure and Applied Geophysics》1992,138(3):391-406
We propose a different kind of seismic inversion from travel-time or waveform inversion for lateral heterogeneities in the earth: Fresnel zone inversion. Amplitude and phase delay of data in several frequency ranges are inverted for model space around ray paths with a width corresponding to the considered frequency so that primary effect of finiteness of wavelength be included. For vertically heterogeneous media, Fréchet derivatives for inversion are obtained very efficiently using the paraxial ray approximation, with nearly similar amounts of computation compared to travel-time inversion. As an example, Fréchet derivatives are computed for a teleseismic observation system for a three-dimensional structure in the lithosphere beneath an array of seismic stations. Even if the used frequency is around 2 Hz, the width of Fréchet derivatives cannot be neglected, particularly near the bottom of the lithosphere. Sensitivity of model parameters to observations is, moreover, different in our approach from conventional travel-time inversion: it is zero along ray paths but large slightly away from them. Some model calculations show that travel-time inversion, particularly with models divided into very fine meshes or blocks, might give misleading results. An example of inversion for a simple Camembert model, in the event that travel-time inversion gives no reliable results, shows how this technique works with much smaller data sets and computation than waveform inversions. 相似文献
9.
The Connolly (1999) elastic impedance (EI) equation is a function of P-wave velocity, S-wave velocity, density, and incidence
angle. Conventional inversion methods based on this equation can only extract P-velocity, S-velocity, and density data directly
and the elastic impedance at different incidence angles are not at the same scale, which makes comparison difficult. We propose
a new elastic impedance equation based on the Gray et al. (1999) Zoeppritz approximation using Lamé parameters to address
the conventional inversion method’s deficiencies. This equation has been normalized to unify the elastic impedance dimensions
at different angles and used for inversion. Lamé parameters can be extracted directly from the elastic impedance data obtained
from inversion using the linear relation between Lamé parameters and elastic impedance. The application example shows that
the elastic parameters extracted using this new method are more stable and correct and can recover the reservoir information
very well. The new method is an improvement on the conventional method based on Connolly’s equation.
Wang Baoli graduated with a Bachelor’s degree in Prospecting Information and Engineering from the China University of Petroleum (East
China) in 2004 and earned her Master’s degree from the department of Geophysical Prospecting and Information Technology in
the China University of Petroleum ((East China) in 2006. She now studies for her PhD at the China University of Petroleum
(East China). Her research interest is elastic impedance inversion. 相似文献
10.
《Advances in water resources》2005,28(10):1057-1075
The theory of a pumping test or a slug test to measure aquifer transmissivity or storativity assumes that the aquifer properties are uniform around the well. The response of the drawdown to small spatial variations in aquifer properties in the volume of influence is determined by spatial weighting functions or Fréchet kernels, which in general are functions of space and time. The Fréchet kernels determine the effective “volume of influence” of the measurements at any time. Under the assumption that the well is a line sink we derive explicit analytical expressions for the Fréchet kernels for storativity and for transmissivity for both pumping and slug tests. We also derive the total sensitivity functions for uniform variations in storativity and transmissivity and show that they are the spatial integrals of the Fréchet kernels. We consider both the case of separate pumping and observation wells and also the radially symmetric case of observations made at the pumped or slugged well. The “volume of influence” is symmetric with respect to the pumping or slugged well and the observation well, and far from the well the contours of equal spatial sensitivity approach the shapes of ellipses with a well at each focus, rather than circles centered on the pumping well. We use the analytical solutions to investigate the nature of the singularities in the spatial sensitivity functions around the wells, which govern the importance of inhomogeneities close to the well or observation point. 相似文献
11.
A fundamental step in the solution of most non-linear inverse problems is to establish a relationship between changes in a proposed model and resulting changes in the forward modelled data. Once this relationship has been established, it becomes possible to refine an initial model to obtain an improved fit to the observed data. In a linearized analysis, the Fréchet derivative is the connecting link between changes in the model and changes in the data. In some simple cases an analytic expression for the Fréchet derivative may be derived. In this paper we present three techniques to accomplish this and illustrate them by computing the Fréchet derivative for the ID resistivity problem. For more complicated problems, where it is not possible to obtain an expression for the Fréchet derivative, it is necessary to parameterize the model and solve numerically for the sensitivities - partial derivatives of the data with respect to model parameters. The standard perturbation method for computing first-order sensitivities is discussed and compared to the more efficient sensitivity-equation and adjoint-equation methods. Extensions to allow for the calculation of higher order, directional and objective function sensitivities are also presented. Finally, the application of these various techniques is illustrated for both the 1D and 2D resistivity problems. 相似文献
12.
储层弹性与物性参数可直接应用于储层岩性预测和流体识别,是储层综合评价和油气藏精细描述的基本要素之一.现有的储层弹性与物性参数地震同步反演方法大都基于Gassmann方程,使用地震叠前数据,通过随机优化方法反演储层弹性与物性参数;或基于Wyllie方程,使用地震叠后数据,通过确定性优化方法反演储层弹性与物性参数.本文提出一种基于Gassmann方程、通过确定性优化方法开展储层弹性和物性参数地震叠前反演的方法,该方法利用Gassmann方程建立储层物性参数与叠前地震观测数据之间的联系,在贝叶斯反演框架下以储层弹性与物性参数的联合后验概率为目标函数,通过将目标函数的梯度用泰勒公式展开得到储层弹性与物性参数联合的方程组,其中储层弹性参数对物性参数的梯度用差分形式表示,最后通过共轭梯度算法迭代求解得到储层弹性与物性参数的最优解.理论试算与实际资料反演结果证明了方法的可行性. 相似文献
13.
在常规地震采集中,被动源地震波场往往被视为噪声而去除,这就造成了部分有用信息的丢失.在目标区进行主动源和被动源弹性波地震数据的多分量混合采集,并对两种数据进行联合应用,使其在照明和频带上优势互补,能显著提高成像和反演的质量.本文针对两种不同类型的主被动源混采地震数据,分别提出了相应的联合全波形反演方法.首先,针对主动源与瞬态被动源弹性波混采地震数据,为充分利用被动源对深部照明的优势,同时有效压制被动震源点附近的成像异常值,提出了基于动态随机组合的弹性波被动源照明补偿反演策略.然后,针对低频缺失主动源与背景噪声型被动源弹性波混采地震数据,为充分利用被动源波场携带的低频信息,并避免对被动源的定位和子波估计,提出了基于地震干涉与不依赖子波算法的弹性波主被动源串联反演策略.最后,分别将两种方法在Marmousi模型上进行反演测试.结果说明,综合利用主动源和被动源弹性波混采地震数据,不仅能增强深部弹性参数反演效果,还能更好地构建弹性参数模型的宏观结构,并有助于缓解常规弹性波全波形反演的跳周问题. 相似文献
14.
15.
P. Novák 《Studia Geophysica et Geodaetica》2007,51(3):351-367
Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite
tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients.
The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed
satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into
values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic
series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete
values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have
a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions
exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches
are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous
gravity data through integral equations is also outlined in the article.
panovak@kma.zcu.cz 相似文献
16.
地震数据与地下介质物性参数之间的复杂关系,决定了地震全波形反演在理论方法上面临着强烈的非线性难题.地下不同物性参数的不同分量在地震数据上具有不同的表现,勘探的不同阶段对地下介质模型的精度也具有不同的要求,这就决定了在地震全波形反演过程中不必时刻追求地震数据全部信息的匹配,部分信息的匹配就有可能解决现阶段的某些问题,还可以一定程度上规避匹配全部地震信息所遇到的强烈非线性难题.基于这样的考虑,我们提出了利用地震数据子集进行波形反演的思路,给出了统一的反演方法,并通过基于包络数据子集以及反射波数据子集的波形反演的理论模型与实际资料反演试验,证明了所提出的波形反演思路和方法的正确性. 相似文献
17.
Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users 总被引：5，自引：1，他引：4
Weerachai Siripunvaraporn 《Surveys in Geophysics》2012,33(1):5-27
In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven
the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT
code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues
involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing
several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed
along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the
data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear
conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling,
sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and
are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems
regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades. 相似文献
18.
使用阻尼最小二乘法进行震源参数和地壳三维速度结构的走时联合反演．所用资料为Ｓ波和Ｐ波到时差,并用人工地震资料的二维解释结果作为三维速度模型的特定约束条件．为建立初始模型,又利用天然地震构成了准二维剖面．在走时反演基础上,利用遗传算法进行了几个地震事件的波形反演尝试,并对走时反演获得的地壳速度结构模型的局部进行了修正．以３４°～４２°Ｎ,９４°～１１２°Ｅ作为研究区域,在该区域中收集了１９８６年以来大量地震的Ｓ波和Ｐ波到时差资料,７条人工地震二维速度剖面资料和２个数字化地震台的几个地震的三分向记录资料．对这些资料进行了处理,最后得出了０～２５ｋｍ深度不同截面的速度分布,并对所得结果进行了分析． 相似文献
19.
Robert Tenzer Pavel Novák Ilya Prutkin Artu Ellmann Peter Vajda 《Studia Geophysica et Geodaetica》2009,53(2):157-167
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric
geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration
sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions
to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical
harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation
coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in
solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s
integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly.
We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used
in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities
is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model
and a detailed digital terrain model are used as input data. 相似文献
20.
Analytic expressions for the velocity sensitivity to the elastic moduli for the most general anisotropic media 总被引：1，自引：0，他引：1
For non‐linear kinematic inversion of elastic anisotropy parameters and related investigations of the sensitivity of seismic data, the derivatives of the wavespeed (phase velocity and group velocity) with respect to the individual elastic moduli are required. This paper presents two analytic methods, called the eigenvalue and eigenvector methods, to compute the derivatives of the wavespeeds for wave propagation in a general anisotropic medium, which may be defined by up to 21 density‐normalized elastic moduli. The first method employs a simple and compact form of the eigenvalue (phase velocity) and a general form of the group velocity, and directly yields general expressions of the derivatives for the three wave modes (qP, qS1, qS2). The second method applies simple eigenvector solutions of the three wave modes and leads to other general forms of the derivatives. These analytic formulae show that the derivatives are, in general, functions of the 21 elastic moduli as well as the wave propagation direction, and they reflect the sensitivity of the wavespeeds to the individual elastic moduli. Meanwhile, we give results of numerical investigations with some examples for particular simplified forms of anisotropy. They show that the eigenvalue method is suitable for the qP‐, qS1‐ and qS2‐wave computations and mitigates the singularity problem for the two quasi‐shear waves. The eigenvector method is preferable to the eigenvalue method for the group velocity and the derivative of the phase velocity because it involves simpler expressions and independent computations, but for the derivative of the group velocity the derivative of the eigenvector is required. Both methods tackle the singularity problem and are applicable to any degree of seismic anisotropy for all three wave modes. 相似文献