LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).     

COMPLETE INVERSION OF ZERO-OFFSET SEISMIC DATA*

The one-dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane-wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections. An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero-offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities.     

A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*

A new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non-linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.     

WAVE SCATTERING DECONVOLUTION BY SEISMIC INVERSION*

We propose a wave scattering approach to the problem of deconvolution by the inversion of the reflection seismogram. Rather than using the least-squares approach, we study the full wave solution of the one-dimensional wave equation for deconvolution. Randomness of the reflectivity is not a necessary assumption in this method. Both the reflectivity and the section multiple train can be predicted from the boundary data (the reflection seismogram). This is in contrast to the usual statistical approach in which reflectivity is unpredictable and random, and the section multiple train is the only predictable component of the seismogram. The proposed scattering approach also differs from Claerbout's method based on the Kunetz equation. The coupled first-order hyperbolic wave equations have been obtained from the equation of motion and the law of elasticity. These equations have been transformed in terms of characteristics. A finite-difference numerical scheme for the downward continuation of the free-surface reflection seismogram has been developed. The discrete causal solutions for forward and inverse problems have been obtained. The computer algorithm recursively solves for the pressure and particle velocity response and the impedance log. The method accomplishes deconvolution and impedance log reconstruction. We have tested the method by computer model experiments and obtained satisfactory results using noise-free synthetic data. Further study is recommended for the method's application to real data.     

DECOMPOSITION AND INVERSION OF SEISMIC DATA–AN INSTANTANEOUS SLOWNESS APPROACH*

Interpretation techniques are presented that aim at the estimation of seismic velocities. The application of localized slant stacks, weighted by coherency, produces a decomposition of multichannel seismic data into single trace instantaneous slowness p(x, t) components. Colour displays support the interpretation of seismic data relevant to the near surface velocity structure. Since p(x, t) is directly related to stacking velocities and the depth of reflection, or bottoming points, in the subsurface, this data transformation provides a powerful tool for the inversion of reflection and refraction data.     

地震道非线性反演的参数反馈控制及效果

基于非线性动力学,阐明地震道广义线性反演系统的动力学性质,并以微分动力系统理论分析了反演的数值计算过程及结果．应用混沌控制理论对反演数值计算中的非线性发散进行了讨论,并给出了一种新的控制方案,数值模型实验表明此控制方案对反演中出现的非线性发散能够进行有效控制,反演结果与理论模型完全吻合．在此基础上对大庆某地的地震剖面进行处理,取得了一定的效果．     

地震道非线性最优化反演

在非线性最优化理论的基础上提出了地震道反演的非线性最优化方法,推导出地震道非线性最优化反演所需的梯度向量、Hasse矩阵,并对测井约束反演、反演稳定性等问题进行了探讨.理论模型和实际资料的反演结果表明,这一方法是地震道反演的一种有效手段.     

PRESTACK INVERSION OF GROUP-FILTERED SEISMIC DATA1

Three methods for least-squares inversion of receiver array-filtered seismic data are investigated: (1) point receiver inversion where array effects are neglected; (2) preprocessing of the data with an inverse array filter, followed by point receiver inversion; (3) array inversion, where the array effects are included in the forward modelling. The methods are tested on synthetic data generated using the acoustic wave equation and a horizontally stratified earth model. It is assumed that the group length and the group interval are identical. For arrays that are shorter than the minimum wavelength of the emitted wavefield, and when the data are appropriately muted, point receiver inversion (first method) gives satisfactory results. For longer arrays, array inversion (third method) should be used. The failure of the inverse array filter (second method) is due to aliasing problems in the data.     

INVERSION OF REFLECTION DATA *

An iterative inversion method which also takes into account wave energy absorption is described. This method allows estimates of the acoustic impedance in sedimentary layers with nearly plane and parallel stratification. A set of reflection data has been inverted and an impedance model was obtained which correlates well with the essential features of the borehole velocity log.     

SOME ASPECTS OF HANDLING VELOCITY INVERSION AND HIDDEN LAYER PROBLEMS IN SEISMIC REFRACTION WORK*

There are two types of masked layers in seismic refraction work: the velocity reversal (low-velocity layer) and the hidden layer (insufficient velocity contrast or layer thickness). On the basis of an analytical formulation of the general case of a masked layer under an overburden of plane and parallel multiple refractors the two limiting cases are discussed: the solution resulting from an uncritical interpretation of the measured time-distance curve and the blind zone solution. Between these two limiting cases there is a variety of possible masked layer solutions. These no-blind zone solutions—as well as the blind zone solution itself—are formulated separately for the velocity inversion and the hidden layer case. For the evaluation of some no-blind zone solution a diagram is presented which can be used for any case of multiple refractors in the overburden of the masked layer. However, it is only for the three- and the four-layer case that a blind zone interpretation by use of diagrams is advisable. Such diagrams are presented together with the basic sets of formulae which contain as parameters only ratios of velocities and layer thicknesses. As the velocity of the masked layer is usually unknown the diagrams are principally constructed to show the dependence on the masked layer velocity. This is useful for estimation of the largest possible error.     

地震波反演方法研究的某些进展及其数学基础

以地震波反演为背景，对非线性反演问题的某些最新进展做了系统的分析和介绍，着重对地震波反演理论中一些主要方法发展过程中的数学、物理的基本理论和基本假设做了分析、讨论和总结，而非面面俱到的阐述地震波反演理论本身的发展状况，在此基础上，讨论了地震波反演问题的数学研究基础和所面临的问题及假设应注意的方面，并对较强烈地下介质物性异常所造成的非弱散射的反演问题做了分析和展望。     

地震波场反演的BG－逆散射方法

本文讨论利用三维反射地震数据进行波场反演的一种方法，旨在取得高分辨率的地球模型．这种方法用Ｂａｃｋｕｓ－Ｇｉｌｂｅｒｔ的理论构造波动方程非线性反问题的逐次线性化迭代格式，用逆散射原理导出泛函的Ｆｒｅｃｈｅｔ导数，并用最佳折衷准则求解线性化后的方程组．根据迭代过程中不断提高分辨率的思想和减少计算成本的原则，设计了可供实用的反演算法流程．     

结构参数未知条件下的地震动反演研究

本文运用复合反演的观点研究结构参数未知条件下的地震动反演问题。根据地震作用的力学特性，将其具体化为估计输入的修正条件，文中给出了一类反演算法。理论分析及算例表明，该算法具有稳定的收敛特性以及良好的反演效果。     

地震波场反演的BG－逆散射方法

本文讨论利用三维反射地震数据进行波场反演的一种方法,旨在取得高分辨率的地球模型．这种方法用Ｂａｃｋｕｓ－Ｇｉｌｂｅｒｔ的理论构造波动方程非线性反问题的逐次线性化迭代格式,用逆散射原理导出泛函的Ｆｒｅｃｈｅｔ导数,并用最佳折衷准则求解线性化后的方程组．根据迭代过程中不断提高分辨率的思想和减少计算成本的原则,设计了可供实用的反演算法流程．     

地震波场反演的BG－逆散射方法

本文讨论利用三维反射地震数据进行波场反演的一种方法，旨在取得高分辨率的地球模型．这种方法用Ｂａｃｋｕｓ－Ｇｉｌｂｅｒｔ的理论构造波动方程非线性反问题的逐次线性化迭代格式，用逆散射原理导出泛函的Ｆｒｅｃｈｅｔ导数，并用最佳折衷准则求解线性化后的方程组．根据迭代过程中不断提高分辨率的思想和减少计算成本的原则，设计了可供实用的反演算法流程．     

大地电磁与地震正则化同步联合反演

文中在于鹏等提出的电阻率和速度随机分布的大地电磁与地震联合反演方法的基础上,将Tikhonov正则化思想引入到联合反演中,加入先验信息进行模型约束,以最小模型为稳定器,采用L曲线方法来确定近似最佳的正则化因子。考虑到线性寻优算法容易陷入局部极小,文中采用非线性的模拟退火方法来实现大地电磁与地震的同步联合反演。通过模型试验的对比分析,我们认为加入有效模型约束的正则化联合反演可以比单纯考虑数据拟合的联合反演和单独反演方法更有效地提高解的稳定性和计算效率,获得更接近实际而且稳定的解。     

利用多分辨率小波网络进行地震资料反演

在讨论小波网络理论方法的基础上,研究了利用地震纪录小波多尺度分解属性资料进行虚井声波时差反演的技术方法。分析了利用地震信号进行小波分解和网络学习、训练的理论方法。研究中发现:对于相邻的地震道,较小一段的相似性比整个地震道的相似性要好。据此,利用小波时-频分析技术方法,可以把相邻道的信息外推到其它地震道上。通过以上综合研究及对实际资料进行反演计算、分析,认为小波网络与人工神经网络相比其网络结构要容易选定,并且收敛速度快。同时,利用地震资料分段时-频分析的相似性较好和小波网络学习、训练及记忆能力较强的特点,可以较好地把井旁道的高、低频信息转换到相邻道上。这样在提高分辨率的同时,又增加了反演结果的真实可靠性     

二维地震资料波动方程非线性反演

针对反演的要求和实际问题的需要,提出利用地震资料叠前数据进行二维波动方程反演,采用最小平方拟合修正模型参数的非线性反演方法,构造了问题的加速迭代算法．反演算法充分利用了冗余的叠前数据和多道相关性,可以分离噪声和信号,使噪声不参与或很少参与反演,算法抗噪能力强．数值模拟例子表明算法有效和稳定,得到了令人满意的结果．     

INVERSION OF POST-STACK SEISMIC DATA USING SIMULATED ANNEALING1

Model-based inversion of seismic reflection data is a global optimization problem when prior information is sparse. We investigate the use of an efficient, global, stochastic optimization method, that of simulated annealing, for determining the two-way traveltimes and the reflection coefficients. We exploit the advantage of an ensemble approach to the inversion of full-scale target zones on 2D seismic sections. In our ensemble approach, several copies of the model-algorithm system are run in parallel. In this way, estimation of true ensemble statistics for the process is made possible, and improved annealing schedules can be produced. It is shown that the method can produce reliable results efficiently in the 2D case, even when prior information is sparse.