A new approach for separating mixed model parameters: application to simultaneous inversion of earthquake source parameters

A method for simultaneous determination of mixed model parameters, which have different physical dimensions or different responses to data, is presented. Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system, the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the trade-offs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history, source geometry, and hypocentral location from regional seismograms, although it is applicable to any geophysical inversion.     

Nonlinear simultaneous inversion of pore structure and physical parameters based on elastic impedance

Carbonate reservoirs have complex pore structures, which not only significantly affect the elastic properties and seismic responses of the reservoirs but also affect the accuracy of the prediction of the physical parameters. The existing rockphysics inversion methods are mainly designed for clastic rocks, and the inversion objects are generally porosity and water saturation. The data used are primarily based on the elastic parameters, and the inversion methods are mainly linear approximations. To date, there has been a lack of a simultaneous pore structure and physical parameter inversion method for carbonate reservoirs. To solve these problems, a new Bayesian nonlinear simultaneous inversion method based on elastic impedance is proposed. This method integrates the differential effective medium model of multiple-porosity rocks, Gassmann equation,Amplitude Versus Offset(AVO) theory, Bayesian theory, and a nonlinear inversion algorithm to achieve the simultaneous quantitative prediction of the pore structure and physical parameters of complex porous reservoirs. The forward modeling indicates that the contribution of the pore structure, i.e., the pore aspect ratio, to the AVO response and elastic impedance is second only to that of porosity and is far greater than that of water saturation. The application to real data shows that the new inversion method for determining the pore structure and physical parameters directly from pre-stack data can accurately predict a reservoir's porosity and water saturation and can evaluate the pore structure of the effective reservoir.     

多震相走时联合三参数同时反演成像

采用新近研制的分区多步不规则最短路径多震相地震射线追踪正演技术,结合流行的子空间反演算法,提出了一种联合多震相走时资料进行地震三参数 （速度、反射界面和震源位置） 同时反演的方法技术.数值模拟反演实例、以及与双参数 （速度和反射界面或速度和震源位置） 同时反演的对比分析表明：三参数同时反演成像结果大体接近双参数同时反演成像的结果.另外,噪声敏感性试验表明：所提算法对到时数据中可容许的随机误差并不敏感,结果说明多震相走时的联合三参数同时反演成像方法技术不失为一种提高走时成像空间分辨率、进而降低重建模型参数失真度、行之有效的方法技术.     

基于地质统计先验信息的储层物性参数同步反演

本文提出的储层物性参数同步反演是一种高分辨率的非线性反演方法,该方法综合利用岩石物理和地质统计先验信息,在贝叶斯理论框架下,首先通过变差结构分析得到合理的变差函数,进而利用快速傅里叶滑动平均模拟算法（Fast Fourier TransformMoving Average,FFT-MA）和逐渐变形算法（Gradual Deformation Method,GDM）得到基于地质统计学的储层物性参数先验信息,然后根据统计岩石物理模型建立弹性参数与储层物性参数之间的关系,构建似然函数,最终利用Metropolis算法实现后验概率密度的抽样,得到物性参数反演结果。并将此方法处理了中国陆上探区的一块实际资料,本方法的反演结果具有较高的分辨率,与测井数据吻合度较高;由于可以直接反演储层物性参数,避免了误差的累积,大大减少了不确定性的传递,且计算效率较高。     

球坐标系下多震相走时三参数同时反演成像

球坐标系下多震相走时三参数(速度、震源位置和反射界面)同时反演需要解决两个关键问题:(1)球坐标系下3D速度模型中多次透射、反射(折射)及转换波精确、快速的射线追踪;(2)同时反演时三种不同参数间的强耦合问题.为此,我们将直角坐标系下分区多步不规则最短路径算法推广至球坐标系中,进行区域或者全球尺度的多震相射线追踪.然后将其与适合多参数同时反演的子空间算法相结合,形成一种球坐标系下联合多震相走时三参数同时反演的方法技术.与双参数(速度和反射界面或速度和震源位置)同时反演的数值模拟对比分析显示:三参数与双参数的同时反演结果大体接近,并且它们对到时数据中可容许的随机噪声不太敏感.结果说明本文中的同时反演成像为一种提高成像分辨率,同时反演速度、震源位置和反射界面的有效方法.     

利用多层横波各向异性测量方法计算两层介质的分裂参数

对实际两层各向异性介质,在一层假设条件下利用Silver和Chan（1991）的等效单层各向异性测量方法,以及在两层假设条件下利用剥去法和反演法,计算模型的分裂参数.首先利用理论雷克子波得到经过两层各向异性的观测数据,然后加入噪声之前和之后,分别计算不同反方位角覆盖条件下数据的各向异性,并与理论模型的分裂参数进行比较.结果发现在上层分裂特征已知的基础上,剥去法适用于任何模型,不管是否存在分裂,或者分裂特征在两层中如何分布;而反演法更适用于两层各向异性较强且不同的模型,其结果受噪声和方位角分布的影响.选取不同方位角分布的高信噪比数据,比较剥去法和反演法对下层分裂参数的计算结果,发现当入射方位角在两层快波方向之间时,反演结果比较可靠.最后利用这三种测量各向异性的方法,计算青藏高原东南缘CEArray台站观测到的SKS数据中记录的各向异性.除了云贵高原的台站YN.CUX表现出较明显的两层分裂特征,大部分台站下的岩石圈各向异性呈现一层或者较弱的各向异性.于是针对该台站,用反演法同时对这两层的分裂参数进行估计,上层的结果与接收函数计算的地壳分裂参数一致;下层的结果与剥去法计算的上地幔分裂参数一致,说明反演法同剥去法一样,都能有效的分析具有两层各向异性特征的介质.     

(T2,D)二维核磁共振测井混合反演方法与参数影响分析

一维核磁共振(1D NMR)测井技术在流体识别中具有一定的局限性.二维核磁共振(2D NMR)测井能同时测量到多孔介质中横向弛豫时间(T₂)和扩散系数(D)等信息,利用这两个参数区分流体性质,较一维核磁共振测井技术具有明显的优越性.针对梯度场下的2D NMR测井弛豫机理和数学模型,提出了适用于求解大型稀疏矩阵方程的反演方法-基于非负最小二乘法(LSQR)和截断奇异值分解(TSVD)法的混合算法.为验证方法的有效性,先根据多回波观测模式合成回波串数据,然后再用混合反演算法进行反演,反演得到横向弛豫时间(T₂)和扩散系数(D),并构建T₂-D二维谱图.结果对比表明,该混合反演算法得到的T₂-D二维谱与流体模型一致性好,计算精度均比单一反演方法有较大改善,表明该混合反演方法可用于油气储集层2D NMR测井的反演和流体识别.此外,分别对油水同层和气水同层模型进行了正演模拟和反演实验, 系统考察了不同磁场梯度、不同回波间隔组合对反演效果的影响,为2D NMR参数设计提供依据.     

邻近算法在微地震震源位置和一维速度模型同时反演中的应用

微地震事件的空间分布可以用来监测水力压裂过程中裂缝的发育情况.因此,震源定位是微震监测中重要的环节.震源定位依赖准确的速度模型,而震源位置和速度模型的耦合易导致线性迭代的同时反演方法陷入局部极小值.邻近算法作为一种非线性全局优化算法,能够最大程度地避免陷入局部最优解.本文将邻近算法应用于单井监测的微震定位和一维速度模型...     

Inverting reservoir parameters in a two-phase fractured medium with a niche genetic algorithm

In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversion problem of the wave equation in a two-phase medium. We propose a niche genetic multi-parameter (including porosity, solid phase density and fluid phase density) joint inversion algorithm based on a two-phase fractured medium in the BISQ model. We take the two-phase fractured medium of the BISQ model in a two-dimensional half space as an example, and carry out the numerical reservoir parameters inversion. Results show that this method is very convenient for solving the parameters inversion problem for the wave equation in a two-phase medium, and has the advantage of strong noise rejection. Relative to conventional genetic algorithms, the niche genetic algorithm based on a sharing function can not only significantly speed up the convergence, but also improve the inversion precision.     

Transdimensional Bayesian inversion of time-domain airborne EM data

To reduce the dependence of EM inversion on the choice of initial model and to obtain the global minimum, we apply transdimensional Bayesian inversion to time-domain airborne electromagnetic data. The transdimensional Bayesian inversion uses the Monte Carlo method to search the model space and yields models that simultaneously satisfy the acceptance probability and data fitting requirements. Finally, we obtain the probability distribution and uncertainty of the model parameters as well as the maximum probability. Because it is difficult to know the height of the transmitting source during flight, we consider a fixed and a variable flight height. Furthermore, we introduce weights into the prior probability density function of the resistivity and adjust the constraint strength in the inversion model by changing the weighing coefficients. This effectively solves the problem of unsatisfactory inversion results in the middle high-resistivity layer. We validate the proposed method by inverting synthetic data with 3% Gaussian noise and field survey data.     

基于最小反演拟合差的重磁场源深度计算方法

以等效源及位场物性反演为基础,本文提出一种新的求取重磁场源深度的方法.该方法将一层等效源以一定的间隔从浅部向深部移动,并将等效源作为初始模型进行反演,当反演拟合差最小时,停止反演,此时的等效源底深即为所求场源的中心深度.由于仅需要反演一层等效源,比传统的物性反演计算时间大大减少,并且不需要进行深度加权约束.理论模型数据处理结果表明该方法能够获得较准确的场源深度:以长宽比为7.5的薄板模型为例,深度计算误差约为1个点距(25 m);以长宽比为0.5~1.5的厚板模型为例,深度计算误差小于1个点距(25m).将该方法应用于实测航磁梯度数据,计算的磁源中心深度在200~250m之间,钻井资料显示该异常由埋藏深度在200~300m的闪长岩引起,计算结果与钻井资料较吻合.     

三维复杂层状介质中多震相走时联合反演成像

采用新近提出的改进型不规则最短路径多次波射线追踪正演技术,结合共轭梯度法求解带约束的阻尼最小二乘最优化反演问题,讨论了三维复杂层状模型中利用多震相走时资料进行联合反演成像的技术方法.考虑到不同震相种类走时的拾取误差不同,反演算法中引入了不同震相种类数据的权系数;另外,考虑到同时反演速度模型和反射界面起伏中不同参数变化对...     

子波相位不准对反演结果的影响(英文)

本文重点讨论在振幅谱估计准确的情况下,采用不同相位谱子波作为实际估计子波进行线性最小二乘反演,并对结果进行分析。除子波相位外,所有其它影响反演结果的因素均忽略。稀疏反射系数模型(块状波阻抗模型)反演结果表明:(1)使用不同相位谱子波进行反演,其反演结果合成的记录与原始记录都非常匹配,但反演的反射系数和声波阻抗结果与真实模型有差异;(2)反演结果的可靠程度主要与不同相位子波z变换的根的分布有关,当估计子波与真实子波Z变换的根的分布仅在单位圆附近有差异时,反演的反射系数和声波阻抗与真实模型很接近;(3)尽管反演前后地震记录都匹配了,并且评价反演结果好坏的柯西准则或改进柯西准则(反演参数没有进行自适应处理)已经达到了最优(最小),但反演结果与真实模型仍存在较大差异。最后,针对子波相位估计不准可能导致反演效果较差这个问题,我们提出采用求L1范数、丰度、变分、柯西准则(反演参数进行了自适应处理)或/和改进柯西准则(反演参数进行了自适应处理)的最优值或次优值作为评价准则的一种解决办法,理论上得到了好的效果。     

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.     

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized, we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.     

Generalised Series Expansion (GSE) used in DC geoelectric–seismic joint inversion

Horizontally layered (1D) earth models are often assumed as a model estimate for the interpretation of geophysical data measured along 2D geological structures. In this process, the individual data sets are usually inverted independently, and it is considered only in a later phase of interpretation that these local (1D) models have common characteristic features. Taking account of these common attributes, instead of the successive independent interpretations, the lateral variations of geometrical and petrophysical parameters can be efficiently determined for the whole 2D structure by applying a series expansion. Using global basis functions, two advantages can be achieved: (i) choosing an appropriate number of basis functions helps us to restrict the complexity of the model; (ii) the integration of all the data sets measured along the profile gives rise to the application of simultaneous or joint inversion methods. This results in a decrease of the number of independent unknowns, a higher stability during the inversion and a more accurate and reliable parameter estimation.In this paper, a joint inversion algorithm is presented using DC geoelectric apparent resistivities and refraction seismic travel times measured along various layouts above a 2D geological model. To describe lateral variations series, expansions are used, and furthermore, to improve the often used approximation of a (locally) 1D forward modelling, the integral mean value of the horizontally changing model parameters (calculated along an appropriately defined interval) is introduced. We call the inversion procedure that combines series expansions and the concept of integral mean Generalised Series Expansion (GSE) inversion. The method was developed and tested for both the simultaneous (integrating data sets of one method or methods on the same physical basis) and the joint inversion (where data sets of methods on different physical bases are joined together), using synthetic and field data sets. It is also demonstrated that the equivalence problem inherent in the independent inversion of DC geoelectric data can efficiently be resolved by the use of the joint GSE inversion method in the cases of conductive and resistive equivalent geological models.     

变阻尼约束层析成像及其在VSP资料中的应用(英文)

初至波走时层析成像已经取得了广泛的应用,然而,由于观测系统的限制,射线在模型中分布不均匀,导致层析结果的分辨能力不足。变阻尼约束方法应用不均匀的先验信息来匹配不均匀的数据分布,可以减小速度模型校正量与射线覆盖程度的相关性。本文将变阻尼约束方法应用于初至波旅行时层析成像中,并将平滑约束方法加入正则化方程组中来避免单独使用变阻尼约束带来的不稳定性,利用阿尔法滤波器对反演中间迭代结果进行平滑和去噪,采用LSQR算法求解线性方程组来提高收敛速度和压制误差传递。本文应用上述层析成像算法对VSP观测系统进行速度反演,分别应用于检测板速度模型数据和实际VSP资料速度反演中,结果表咀变阻尼约束层析成像可以改善射线不均匀覆盖带来的影响,从而提高速度反演结果的质量;VSP资料检波点附近的速度反演结果可靠性高。     

3-D simultaneous inversion for velocity and reflector geometry using multiple classes of arrivals in a spherical coordinate frame

The two key requirements in conducting 3-D simultaneous traveltime tomography on real data at the regional and global scale with multiple classes of arrival time information are (1) it needs an efficient and accurate arrival tracking algorithm for multiply transmitted, reflected (or refracted) and converted waves in a 3-D variable velocity model with embedded velocity discontinuities (or subsurface interfaces), and (2) a subdimensional inversion solver is required which can easily search for different types of model parameters to balance the trade-off between the different types of model parameter updated in the simultaneous inversion process. For these purposes, we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm (the multistage irregular shortest-path ray tracing method), which previously worked only in Cartesian coordinate at the local scale, to spherical coordinates appropriate to the regional or global scale. We then incorporated a fashionable inversion solver (the subspace method) to formulate a simultaneous inversion algorithm, in which the multiple classes of arrivals (including direct and reflected arrivals from different velocity discontinuities) can be used to simultaneously update both the velocity fields and the reflector geometries. Numerical tests indicate that the new inversion method is both applicable and flexible in terms of computational efficiency and solution accuracy, and is not sensitive to a modest level of noise in the traveltime data. It offers several potential benefits over existing schemes for real data seismic imaging.     

地震与大地电磁测深数据的自适应正则化同步联合反演

在传统的联合反演研究中,地球物理学者往往更多地关注数据拟合,很少涉及正则化理论.本文在电阻率和速度随机分布的大地电磁测深(MT)与地震联合反演研究的基础之上,将正则化思想引入到同步联合反演中,加入先验信息进行模型约束,选取最小模型为稳定泛函,并首次采用自适应正则化算法来确定联合反演的正则化因子.根据以往研究成果,采用非...     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.