2D多尺度非线性地震速度成像

将遗传算法和单纯形算法相结合,得到了一种高效、健全的2D混合地震走时反演方法.把速度场划分为不同的空间尺度,定义网格节点上的速度作为待反演参数,采用双三次样条函数模型参数化,正问题采用有限差分走时计算方法,反问题采用多尺度混合反演方法.首先在较大的空间尺度内反演,然后减小空间尺度,将大尺度的反演结果作为次一级尺度反问题的初始模型,再进行混合反演,如此类推逐次逼近全局最优解.一个低速度异常体的数值模拟试验和抗走时扰动试验表明该方法是有效和健全的.我们将该方法应用到青藏高原东北缘阿尼玛卿缝合带东段上部地壳速度结构研究中,并与前人的成果进行了对比.     

频率多尺度全波形速度反演

以二维声波方程为模型,在时间域深入研究了全波形速度反演.全波形反演要解一个非线性的最小二乘问题,是一个极小化模拟数据与已知数据之间残量的过程.针对全波形反演易陷入局部极值的困难,本文提出了基于不同尺度的频率数据的"逐级反演"策略,即先基于低频尺度的波场信息进行反演,得出一个合理的初始模型,然后再利用其他不同尺度频率的波场进行反演,并且用前一尺度的迭代反演结果作为下一尺度反演的初始模型,这样逐级进行反演.文中详细阐述和推导了理论方法及公式,包括有限差分正演模拟、速度模型修正、梯度计算和算法描述,并以Marmousi复杂构造模型为例,进行了MPI并行全波形反演数值计算,得到了较好的反演结果,验证了方法的有效性和稳健性.     

Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves

Multichannel Analysis of Surface Waves utilizes a multichannel recording system to estimate near-surface shear (S)-wave velocities from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity (v_S) section is constructed by aligning 1D models at the midpoint of each receiver spread and using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. The receiver spread length sets the theoretical lower limit and any v_S structure with its lateral dimension smaller than this length will not be properly resolved in the final v_S section. A source interval smaller than the spread length will not improve the horizontal resolution because spatial smearing has already been introduced by the receiver spread.In this paper, we first analyze the horizontal resolution of a pair of synthetic traces. Resolution analysis shows that (1) a pair of traces with a smaller receiver spacing achieves higher horizontal resolution of inverted S-wave velocities but results in a larger relative error; (2) the relative error of the phase velocity at a high frequency is smaller than at a low frequency; and (3) a relative error of the inverted S-wave velocity is affected by the signal-to-noise ratio of data. These results provide us with a guideline to balance the trade-off between receiver spacing (horizontal resolution) and accuracy of the inverted S-wave velocity. We then present a scheme to generate a pseudo-2D S-wave velocity section with high horizontal resolution using multichannel records by inverting high-frequency surface-wave dispersion curves calculated through cross-correlation combined with a phase-shift scanning method. This method chooses only a pair of consecutive traces within a shot gather to calculate a dispersion curve. We finally invert surface-wave dispersion curves of synthetic and real-world data. Inversion results of both synthetic and real-world data demonstrate that inverting high-frequency surface-wave dispersion curves – by a pair of traces through cross-correlation with phase-shift scanning method and with the damped least-square method and the singular-value decomposition technique – can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution.     

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks, which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block, and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization, which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models. The damped least squares method is employed in seismic traveltime inversion, which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.     

非线性反演方法的新进展

线性方法在许多具体反演问题中遇到困难的情况下，人们提出了非线性方法，同时，计算技术的发展为非线性方法的应用提供了基础。最近几年，人们对非线性方法又进行了改进和发展，例如：Vasco(1993)提出了集合推论的思想；Sambridge(1995)基于Voronoi单元的思想，提出了自然相邻对不规则数据参数化和插值的方法，相邻算法正是基于以上思想和理论，以及其他非线性方法的实践而提出的一种新的非线性反演方法。     

A non-linear regularized constrained impedance inversion

Inversion for seismic impedance is an inherently complicated problem. It is ill‐posed and band‐limited. Thus the inversion results are non‐unique and the process is unstable. Combining regularization with constraints using sonic and density log data can help to reduce these problems. To achieve this, we developed an inversion method by constructing a new objective function, including edge‐preserving regularization and a soft constraint based on a Markov random field. The method includes the selection of proper initial values of the regularization parameters by a statistical method, and it adaptively adjusts the regularization parameters by the maximum likelihood method in a fast simulated‐annealing procedure to improve the inversion result and the convergence speed. Moreover, the method uses two kinds of regularization parameter: a ‘weighting factor’λ and a ‘scaling parameter’δ. We tested the method on both synthetic and field data examples. Tests on 2D synthetic data indicate that the inversion results, especially the aspects of the discontinuity, are significantly different for different regularization functions. The initial values of the regularization parameters are either too large or too small to avoid either an unstable or an over‐smoothed result, and they affect the convergence speed. When selecting the initial values of λ, the type of the regularization function should be considered. The results obtained by constant regularization parameters are smoother than those obtained by adaptively adjusting the regularization parameters. The inversion results of the field data provide more detailed information about the layers, and they match the impedance curves calculated from the well logs at the three wells, over most portions of the curves.     

An efficient non-linear least-squares 1D inversion scheme for resistivity and IP sounding data

Non-linear least-squares inversion operates iteratively by updating the model parameters in each step by a correction vector which is the solution of a set of normal equations. Inversion of geoelectrical data is an ill-posed problem. This and the ensuing suboptimality restrict the initial model to being in the near vicinity of the true model. The problem may be reduced by introducing damping into the system of equations. It is shown that an appropriate choice of the damping parameter obtained adaptively and the use of a conjugate-gradient algorithm to solve the normal equations make the 1D inversion scheme efficient and robust. The scheme uses an optimal damping parameter that is dependent on the noise in the data, in each iterative step. The changes in the damping and relative residual error with iteration number are illustrated. A comparison of its efficacy over the conventional Marquardt and simulated annealing methods, tested on Inman's model, is made. Inversion of induced polarization (IP) sounding is obtained by inverting twice (true and modified) DC apparent resistivity data. The inversion of IP data presented here is generic and can be applied to any of the IP observables, such as chargeability, frequency effect, phase, etc., as long as these observables are explicitly related to the DC apparent resistivity. The scheme is used successfully in inverting noise-free and noisy synthetic data and field data taken from the published literature.     

Two-step interface and velocity inversion

This paper studies the computation method of two-step inversion of interface and velocity in a region. The 3-D interface is described by a segmented incomplete polynomial; while the reconstruction of 3-D velocity is accomplished by the principle of least squares in functional space. The computation is carried out in two steps. The first step is to inverse the shape of 3-D interface; while the second step is to do 3-D velocity inversion by distributing the remaining residual errors of travel time in accordance with their weights. The data of seismic sounding in the Tangshan-Luanxian seismic region are processed, from which the 3-D structural form in depth of the Tangshan seismic region and the 3-D velocity distribution in the crust below the Tangshan-Luanxian seismic region are obtained. The result shows that the deep 3-D structure in the Tangshan seismic region trends NE on the whole and the structure sandwiched between the NE-trending Fengtai-Yejituo fault and the NE-trending Tangshan fault is an uplifted zone of the Moho. In the 3-D velocity structure of middle-lower crust below that region, there is an obvious belt of low-velocity anomaly to exist along the NE-trending Tangshan fault, the position of which tallies with that of the Tangshan seismicity belt. The larger block of low-velocity anomaly near Shaheyi corresponds to a denser earthquake distribution. In that region, there is an NW-trending belt of high-velocity anomaly, probably a buried fault zone. The lower crust below the epicentral region of the Tangshan M _S=7.8 earthquake is a place where the NE-trending belt of low-velocity anomaly meets the NW-trending belt of high-velocity anomaly. The two sets of structures had played an important role in controlling the preparation and occurrence of the M _S=7.8 Tangshan earthquake. Contribution RCEG97006, Research Center of Exploration Geophysics, China Seismological Bureau, China. This project is supported by the Chinese Joint Seismological Science Foundation.     

模拟退火方法在三维速度模型地震波走时反演中的应用

采用块状建模以及三角形拼接的界面描述方式,并通过立方体速度网格线性插值获得块体内部的速度分布。正演过程中采用逐段迭代射线追踪方法计算三维复杂地质模型中的射线走时,并采用模拟退火方法进行了三维模型中的地震波走时反演研究。模型测试结果表明,使用的射线追踪和走时反演算法有效。     

Sharp boundary inversion of 2D magnetotelluric data

We consider 2D earth models consisting of laterally variable layers. Boundaries between layers are described by their depths at a set of nodes and interpolated laterally between nodes. Conductivity within each layer is described by values at a set of nodes fixed within each layer, and is interpolated laterally within each layer. Within the set of possible models of this sort, we iteratively invert magnetotelluric data for models minimizing the lateral roughness of the layer boundaries, and the lateral roughness of conductivities within layers, for a given level of data misfit. This stabilizes the inverse problem and avoids superfluous detail. This approach allows the determination of boundary positions between geological units with sharp discontinuities in properties across boundaries, while sharing the stability features of recent smooth conductivity distribution inversions.
We compare sharp boundary inversion results with smooth conductivity distribution inversion results on a numerical example, and on inversion of field data from the Columbia River flood basalts of Washington State. In the synthetic example, where true positions and resistivities are known, sharp boundary inversion results determine both layer boundary locations and layer resistivities accurately. In inversion of Columbia flood basalt data, sharp boundary inversion recovers a model with substantially less internal variation within units, and less ambiguity in both the depth to base of the basalts and depth to resistive basement.     

TTI介质的相速度研究

推导了二维TTI介质的相速度表达式,并且依据推导出来的相速度表达式,模拟并分析了二维TTI介质相速度的传播快照以及TI介质相速度的传播快照;对比并分析了TTI介质和TI介质模型的相速度理论计算值的X分量特征的差异。TTI介质的相速度研究具有较高的理论研究价值和实际应用价值．     

Piecewise‐continuous velocity inversion

We suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion.     

Migration velocity analysis and waveform inversion

Least‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.     

地震相关性分段约束多道速度反演

基于模型的波阻抗(速度)反演中,约束是不可缺少的,它可以有效地减少反演多解性和提高运算效率.国内外大量学者均详细论述了一些反演的约束手段,但对于地震道与地震道之间的约束,除了采用测井外推模式之外,就鲜有介绍,相同的约束条件直接应用于全部的地震道,不再变化,这样势必会增加运算时间和影响反演效果.针对这些问题,本文描述了一种地震相关性分段约束速度反演的方法,其目的在于增加内在的道与道之间的约束,主要采用了地震道的相关特征去优化约束条件与减少反演计算量.本文先分析了地震反演的不同内在约束方法,并利用地震的相关性去分段自动选择约束的强弱与范围大小,而不是在全部地震道反演中采用相同的约束参数,即可大大优化运算效率;其次设计两个数学模型进行反演验证,在反演效果比较符合实际的基础上,运算时间大大减少;最后引入中国东部某地区的实例对该方法进行检验,反演剖面上可以清楚观察出冲积扇的沉积特点,各期砂体清晰可见,便于追踪解释与储层预测,具有较高的分辨率与可信度.结果表明该方法是一种有利于提高反演效果和效率的方法.     

Frequency-domain elastic full-waveform multiscale inversion method based on dual-level parallelism

The complexity of an elastic wavefield increases the nonlinearity of inversion. To some extent, multiscale inversion decreases the nonlinearity of inversion and prevents it from falling into local extremes. A multiscale strategy based on the simultaneous use of frequency groups and layer stripping method based on damped wave field improves the stability of inversion. A dual-level parallel algorithm is then used to decrease the computational cost and improve practicability. The seismic wave modeling of a single frequency and inversion in a frequency group are computed in parallel by multiple nodes based on multifrontal massively parallel sparse direct solver and MPI. Numerical tests using an overthrust model show that the proposed inversion algorithm can effectively improve the stability and accuracy of inversion by selecting the appropriate inversion frequency and damping factor in lowfrequency seismic data.     

基于平均速度分析的近地表纵波速度反演

面波频散曲线对于横波速度、纵波速度、层厚等近地表地球物理参数的敏感度相差较大, 现阶段通过频散曲线可以获得较为精确的近地表横波速度与厚度信息, 但无法直接对纵波速度进行反演.研究表明, 泊松比对于波长(W)-探测深度(D)关系较为敏感.基于这一发现, 本文根据频散曲线与反演获取的横波速度结构计算平均速度, 获取W-D关系曲线.但合成数据测试证明, 因近地表浅层对应的W-D曲线变化较小, 且浅层纵波速度反演不准确会使误差累积, 直接反演W-D曲线无法获取可靠的纵波速度剖面.本文改进了基于平均速度分析的近地表纵波速度反演方法, 在目标函数中加入了对浅层信息较为敏感的W/D-D信息, 同时对W-D曲线与W/D-D曲线进行联合反演.合成数据测试证明可以获取较为准确地浅层与深层纵波速度.将该方法应用于实际地震数据中, 联合反演得到的纵波速度剖面与微测井数据较为吻合, 证明本文提出的方法可以不借助其他信息, 仅通过面波频散信息, 获取更为准确地近地表纵波信息.

     

Feasibility of joint 1D velocity model and event location inversion by the Neighbourhood algorithm

Using a set of synthetic P‐ and S‐wave onsets, computed in a 1D medium model from sources that mimic a distribution of microseismic events induced by hydrofrac treatment to a monitoring geophone array(s), we test the possibility to invert back jointly the model and events location. We use the Neighbourhood algorithm for data inversion to account for non‐linear effects of velocity model and grid search for event location. The velocity model used is composed of homogeneous layers, derived from sonic logging. Results for the case of one and two monitoring wells are compared. These results show that the velocity model can be obtained in the case of two monitoring wells, if they have optimal relative position. The use of one monitoring well fails due to the trade‐off between the velocity model and event locations.     

3D resistivity inversion using 2D measurements of the electric field

Field and 'noisy' synthetic measurements of electric-field components have been inverted into 3D resistivities by smoothness-constrained inversion. Values of electrical field can incorporate changes in polarity of the measured potential differences seen when 2D electrode arrays are used with heterogeneous 'geology', without utilizing negative apparent resistivities or singular geometrical factors. Using both the X - and Y -components of the electric field as measurements resulted in faster convergence of the smoothness-constrained inversion compared with using one component alone. Geological structure and resistivity were reconstructed as well as, or better than, comparable published examples based on traditional measurement types. A 2D electrode grid (20 × 10), incorporating 12 current-source electrodes, was used for both the practical and numerical experiments; this resulted in 366 measurements being made for each current-electrode configuration. Consequently, when using this array for practical field surveys, 366 measurements could be acquired simultaneously, making the upper limit on the speed of acquisition an order of magnitude faster than a comparable conventional pole–dipole survey. Other practical advantages accrue from the closely spaced potential dipoles being insensitive to common-mode noise (e.g. telluric) and only 7% of the electrodes (i.e. those used as current sources) being susceptible to recently reported electrode charge-up effects.     

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.     

Real time 2D inversion of induction logging data

Real time 2D inversion for an induction logging instrument may be achieved using a fast forward modeling and special inversion strategy. The fast forward modeling employs a low-frequency approximation of an induction response known as Doll's geometric factor. Modeling geometric factors is much faster than modeling the electromagnetic field in the frequency domain. To transform real data into the Doll's limit, multi-frequency skin-effect correction is applied. The correction technique involves an asymptotic theory of the integral equation for a 2D boundary value problem. The inversion is based on separating the parameter space into subspaces of lower dimension. Initially, adaptive overlapping windows split logging data into manageable portions. Each window consists of three subwindows: the predictor, corrector and upgrader. Further separation of parameters is introduced by Doll's approximation: the low-frequency response is linear with respect to formation conductivity. This allows us to split inversion for conductivity and geometric parameters. The next level of splitting inversion is achieved by independently determining parameters of the near borehole zone and remote formation areas. This is done by utilizing different subsets of sensors. The inversion does not require initial guess: layers are introduced dynamically, if necessary. The resolution is improved in sequential iterations by adding finer details to the previously obtained models. The final selection of parameters satisfies a variety of a priori constraints formulated as target resistivity distributions. The technique for imposing constraints is based on the analysis of data mapping into the model space. Interpretation of synthetic and real data confirms the viability of the method.