联合小波变换与偏振分析自动拾取微地震P波到时

对微地震P波到时的自动拾取是微地震信号分析和数据处理的主要目标之一。基于小波变换的多尺度分析思想,对微地震信号进行小波处理后的小波系数代替原始信号,应用包含在小波变换系数中的信号偏振信息,提出了联合小波变换与偏振分析自动拾取微地震信号P波到时的方法。通过对嘉阳煤矿监测的实际微地震数据进行小波变换,用多尺度小波分解的各个尺度单支重构信号构成协方差矩阵,求解不同尺度协方差矩阵的最大特征值和次大特征值求取P波到时定位函数,实现P波到时的自动拾取,取得了满意的结果.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.     

Detecting multi-scale riverine topographic variability and its influence on Chinook salmon habitat selection

Quantifying geomorphic conditions that impact riverine ecosystems is critical in river management due to degraded riverine habitat, changing flow and thermal conditions, and increasing anthropogenic pressure. Geomorphic complexity at different scales directly impacts habitat heterogeneity and affects aquatic biodiversity resilience. Here we showed that the combination of continuous spatial survey at high resolution, topobathymetric light detection and ranging (LiDAR), and continuous wavelet analysis can help identify and characterize that complexity. We used a continuous wavelet analysis on 1-m resolution topobathymetry in three rivers in the Salmon River Basin, Idaho (USA), to identify different scales of topographic variability and the potential effects of this variability on salmonid redd site selection. On each river, wavelet scales characterized the topographic variability by portraying repeating patterns in the longitudinal profile. We found three major representative spatial wavelet scales of topographic variability in each river: a small wavelet scale associated with local morphology such as pools and riffles, a mid-wavelet scale that identified larger channel unit features, and a large wavelet scale related to valley-scale controls. The small wavelet scale was used to identify pools and riffles along the entire lengths of each river as well as areas with differing riffle-pool development. Areas along the rivers with high local topographic variability (high wavelet power) at all wavelet scales contained the largest features (i.e., deepest or longest pools) in the systems. By comparing the wavelet power for each wavelet scale to Chinook salmon redd locations, we found that higher small-scale wavelet power, which is related to pool-riffle topography, is important for redd site selection. The continuous wavelet methodology objectively identified scales of topographic variability present in these rivers, performed efficient channel-unit identification, and provided geomorphic assessment without laborious field surveys.     

Stochastic analysis of immiscible displacement of the fluids with arbitrary viscosities and its dependence on support scale of hydrological data

Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterize the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow.     

Statistical characteristics of flow as indicators of channeling in heterogeneous porous and fractured media

We introduce two new channeling indicators D_ic and D_cc based on the Lagrangian distribution of flow rates. On the basis of the participation ratio, these indicators characterize the extremes of both the flow-tube width distribution and the flow rate variation along flow lines. The participation ratio is an indicator biased toward the larger values of a distribution and is equal to the normalized ratio of the square of the first-order moment to the second-order moment. Compared with other existing indicators, they advantageously provide additional information on the flow channel geometry, are consistently applicable to both porous and fractured media, and are generally less variable for media generated using the same parameters than other indicators. Based on their computation for a broad range of porous and fracture permeability fields, we show that they consistently characterize two different geometric properties of channels. D_ic gives a characteristic scale of low-flow zones in porous media and a characteristic distance between effectively flowing structures in fractured cases. D_cc gives a characteristic scale of the extension of high-flow zones in porous media and a characteristic channel length in fractured media. D_ic is mostly determined by channel density and permeability variability. D_cc is, however, more affected by the nature of the correlation structure like the presence of permeability channels or fractures in porous media and the length distribution in fracture networks.     

Multi-scale iterative techniques and adaptive mesh refinement for flow in porous media

Multi-component flow in porous media involves localized phenomena that could be due to several features, such as concentration fronts, wells or geometry of the media. Our approach to treating the localized phenomena is to use high-resolution discretization methods in combination with adaptive mesh refinement (AMR). The purpose of AMR is to concentrate the computational work near the regions of interest in the flow. When properly designed, AMR can significantly reduce the computational effort required to obtain a desired level of accuracy in the simulation. Necessarily, AMR requires appropriate techniques for communication between length scales in a hierarchy. The selection of appropriate scaling rules as well as computationally efficient data structures is essential to the success of the overall method. However, the emphasis here is on the development of efficient techniques for solving linear systems that arise in the numerical discretization of an elliptic equation for the incompressible pressure field. In this paper, the combined AMR technique has been applied to a two-component single-phase model for miscible flooding. Numerical results are discussed in one-dimensional and two-dimensional.     

流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法

本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.     

上海佘山钻孔形变观测资料正常背景噪声变化特征分析

对上海佘山钻孔形变观测资料正常的背景噪声进行初步分析并定量刻画其正常信息场的变化特征。结果显示:上海佘山形变观测资料的小波变换细节部分不同尺度包含着不同的信号成分,通过研究形变观测资料小波变换各尺度信号的非震异常特征变化,可能会捕捉到与地震孕育过程有关的前兆异常信息。     

Modeling the velocity field during Haines jumps in porous media

When nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid–fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid–fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid–fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid–fluid displacement.     

An objective method for determining principal time scales of coherent eddy structures using orthonormal wavelets

A new, parameter-free method, based on orthonormal wavelet expansions is proposed for calculating the principal time scale of coherent structures in atmospheric surface layer measurements. These organized events play an important role in the exchange of heat, mass, and momentum between the land and the atmosphere. This global technique decomposes the energy contribution at each scale into organized and random eddy motion. The method is demonstrated on vertical wind velocity measurements above bare and vegetated surfaces. It is found to give nearly identical results to a local thresholding approach developed for signal de-noising that assigns the wavelet coefficients to organized and random motion. The effect of applying anti- and/or near-symmetrical wavelet basis functions is also investigated.     

Covariance functions motivated by spatial random field models with local interactions

Random fields based on energy functionals with local interactions possess flexible covariance functions, lead to computationally efficient algorithms for spatial data processing, and have important applications in Bayesian field theory. In this paper we address the calculation of covariance functions for a family of isotropic local-interaction random fields in two dimensions. We derive explicit expressions for non-differentiable Spartan covariance functions in \({\mathbb{R}}^2\) that are based on the modified Bessel function of the second kind. We also derive a family of infinitely differentiable, Bessel-Lommel covariance functions that exhibit a hole effect and are valid in \({\mathbb{R}}^{d}\), where d > 2. Finally, we define a generalized spectrum of correlation scales that can be applied to both differentiable and non-differentiable random fields in contrast with the smoothness microscale.     

区间B样条小波有限元GPR模拟双相随机混凝土介质

基于可分离小波理论,由一维区间B样条小波尺度函数的张量积构造二维B样条小波基,并将它作为GPR波动方程求解的插值函数,通过引入转换矩阵,实现小波系数空间与雷达电磁场之间的转换.应用Galerkin算法,推导了二维区间B样条小波有限元GPR波动方程离散格式,求出了2阶1尺度与2阶2尺度BSWI尺度函数的积分值及联系系数,给出了该算法的详细求解过程.编制了BSWI的Matlab模拟程序,应用该程序对两个典型实例进行了正演,结果表明:BSWI能采用较少的单元达到与FEM相似的精度,而BSWI算法尺度提升能提高解的精度,但耗时会急剧增加.最后,将BSWI算法应用于双相随机混凝土模型,说明随机介质模型理论能灵活、有效地描述实际混凝土介质的分布,正演剖面与实测剖面特征更相符,能更真实地模拟雷达波的传播过程,可为提高GPR的探测效果和解释准确性提供理论基础.     

Translation-invariant wavelet denoising of full-tensor gravity –gradiometer data

Denoising of full-tensor gravity-gradiometer data involves detailed information from field sources, especially the data mixed with high-frequency random noise. We present a denoising method based on the translation-invariant wavelet with mixed thresholding and adaptive threshold to remove the random noise and retain the data details. The novel mixed thresholding approach is devised to filter the random noise based on the energy distribution of the wavelet coefficients corresponding to the signal and random noise. The translationinvariant wavelet suppresses pseudo-Gibbs phenomena, and the mixed thresholding better separates the wavelet coefficients than traditional thresholding. Adaptive Bayesian threshold is used to process the wavelet coefficients according to the specific characteristics of the wavelet coefficients at each decomposition scale. A two-dimensional discrete wavelet transform is used to denoise gridded data for better computational efficiency. The results of denoising model and real data suggest that compared with Gaussian regional filter, the proposed method suppresses the white Gaussian noise and preserves the high-frequency information in gravity-gradiometer data. Satisfactory denoising is achieved with the translation-invariant wavelet.     

Theory and seismic applications of the eigenimage discrete wavelet transform

Discrete wavelet transforms are useful in a number of signal processing applications. To improve the scale resolution, a joint function of time, scale and eigenvalue that describes the energy density or intensity of a signal simultaneously in the wavelet and eigenimage domains is constructed. A hybrid method, which decomposes eigenimages in the wavelet domain, is developed and tested on field data with a variety of noise types. Several illustrative examples examine the ability of wavelet transforms to resolve features at several scales. Successful applications to time‐lapse seismic reservoir monitoring are presented. In reservoir monitoring, the scale‐dependent properties of the eigenstructure of the 4D data covariance matrix enable us to extract the low‐frequency time‐lapse signal that is the result of internal diffusive losses caused by fluid flow.     

An efficient probabilistic finite element method for stochastic groundwater flow

We present an efficient numerical method for solving stochastic porous media flow problems. Single-phase flow with a random conductivity field is considered in a standard first-order perturbation expansion framework. The numerical scheme, based on finite element techniques, is computationally more efficient than traditional approaches because one can work with a much coarser finite element mesh. This is achieved by avoiding the common finite element representation of the conductivity field. Computations with the random conductivity field only arise in integrals of the log conductivity covariance function. The method is demonstrated in several two- and three-dimensional flow situations and compared to analytical solutions and Monte Carlo simulations. Provided that the integrals involving the covariance of the log conductivity are computed by higher-order Gaussian quadrature rules, excellent results can be obtained with characteristic element sizes equal to about five correlation lengths of the log conductivity field. Investigations of the validity of the proposed first-order method are performed by comparing nonlinear Monte Carlo results with linear solutions. In box-shaped domains the log conductivity standard deviation σ_Y may be as large as 1.5, while the head variance is considerably influenced by nonlinear effects as σ_Y approaches unity in more general domains.     

自适应多尺度第二代小波配点法探地雷达数值模拟

基于第二代小波变换的提升方案构造了插值小波,将雷达波场函数进行了二维小波变换,得到所有尺度上与计算网格相联系的小波系数和尺度系数.对所有尺度上的小波系数进行分析,根据解的局部性与小波系数阈值的控制,实现网格压缩和配点的自适应调节.保留大于给定阈值的小波系数及对应网格点,令小于给定阈值的小波系数为零,并舍弃其对应网格点.达到光滑区域采用较少的计算网格点,在奇异性较大的区域采用较多的计算网格点的目的.通过对自适应网格进行邻域校正、重构检查等附加修正,推导了场值更新的显式时间迭代方案.最后,以均匀、阶梯与复杂三个典型GPR模型为例,与常规数值计算结果对比表明：自适应小波配点法（AWCM）利用第二代小波的多尺度分解和快速变换的特点,可以使计算网格随着时间步适应解的移动和变化,允许计算资源更有效地使用,具有高压缩率,达到跟踪奇异性的目的,特别适合于探地雷达正演中波传问题的模拟.     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields

The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees.