分层坐标变换法起伏自由地表弹性波叠前逆时偏移

传统有限差分方法在处理起伏地表时存在一些困难,而坐标变换法可将起伏地表映射为水平地表以克服此缺点.但同时,地下构造被变换得更加复杂,导致了波传播和成像的不准确.本文提出了一种分层的坐标变换方法,并应用到了弹性波逆时偏移中,此方法既可以克服起伏地表的影响,又可以不破坏地下构造.波场正向延拓、逆时延拓和分离是在辅助坐标系下完成的,而成像是在笛卡尔坐标系下完成的.通过对简单起伏模型和中原起伏模型的试算证明了本文提出方法的准确性.同时,对两种极端起伏地层高程不准确的情况进行测试可以看出:分层坐标变换逆时偏移方法的成像效果远好于传统坐标变换方法.     

强噪声环境下基于信噪比的地震P波到时自动提取方法

大数据量、强噪声环境给地震P波到时的自动提取带来很大挑战.针对此问题,本文通过构建特殊的特征函数,建立SNR与STA/LTA的内在联系,提出两种基于SNR的地震P波到时自动提取方法,即基于SNR的STA/LTA方法与基于SNR的综合方法.这两种方法分别是运用SNR概念对传统STA/LTA方法和STA/LTA与AIC综合方法的改进.仿真分析结果表明:对于弱噪声环境(10dB)和一般噪声环境(6dB),本文方法较传统STA/LTA方法对地震P波到时提取的准确度更高;而对于强噪声环境(3dB),本文方法仍能准确提取地震P波到时,而传统STA/LTA方法则出现了较大的误判率(10%)与漏判率(65%).本文方法为STA/LTA赋予了明确的物理意义,使其阈值的选取建立在严密的数学推导之上.另外,本文方法在进行地震P波到时自动提取的同时,兼具数据预处理功能,无需额外的基线校正或高通滤波,因而具有较好的实时性.     

Using the precision of the mean to estimate suitable sample sizes for monitoring total phosphorus in Australian catchments

The effect of the sample size on prediction quality is well understood. Recently, studies have assessed this relationship using near‐continuous water quality samples. However, this is rarely possible because of financial constraints, and therefore, many studies have relied on simulation‐based methods utilizing more affordable surrogates. A limitation of simulation‐based methods is the requirement of a good relationship, which is often not present. Therefore, catchment managers require a direct method to estimate the effect of sample size on the mean using historical water quality data. One measure of prediction quality is the precision with which a mean is estimated; this is the focus of this work. By characterizing the effect of sample size on the precision of the mean, it is possible for catchment managers to adjust the sample size in relation to both the cost and the precision. Historical data are often sparse and generally collected using several different sampling schemes, all without inclusion probabilities. This means that an approach is needed to obtain unbiased estimates of the variance of the mean using a model‐based approach. With the use of total phosphorus data from 17 sub‐catchments in southeastern Australia, the ability of a model‐based approach to estimate the effect of sample size on the precision of event and base‐flow mean concentrations. The results showed that for estimating annual base‐flow mean concentration, little gain in precision was achieved above 12 observations per year. Sample sizes greater than 12 samples per event improved event‐based estimates; however, the inclusion of more than 12 samples per event did not greatly reduce the event mean concentration uncertainties. The precision of the base‐flow estimates was most correlated to percentage urban cover, whereas the precision of the event mean estimates was most correlated with catchment size. The method proposed in this work could be readily applied to other water quality variables and other monitoring sites. Copyright © 2014 John Wiley & Sons, Ltd.     

小波变换应用于日长变化的研究进展

随着空间测地技术的发展,日长变化的观测资料已经达到了空前高的程度,迫切需要合适的数学工具和方法从这些高精度的观测资料中提取有价值的信息.近些年,小波变换被应用于天文学和地球科学的资料分析中,它通过伸缩和平移等运算对时间信号进行多尺度的细化分析,从中提取有效的信息.本文主要介绍了小波变换应用于日长变化的研究进展,并初步探讨该领域以后的研究方向.     

Generation of realistic synthetic catchments to explore fine continental surface processes

Understanding, analysing, and predicting the erosion mechanisms and sedimentary flows produced by catchments plays a key role in environmental conservation and restoration management and policies. Numerical case-testing studies are generally undertaken to analyse the sensitivity of flood and soil erosion processes to the physical characteristics of catchments. Most analyses are conducted on simple virtual catchments with physical characteristics that, unlike real catchments, are perfectly controlled. Virtual catchments generally correspond to V-shaped valley catchments. However, although these catchments are suitable for methodical analysis of the results, they do not provide a realistic representation of the spatial structures of the landscape and field conditions. They can, therefore, lead to potential modelling errors and can make it difficult to extend or generalize their results. Our proposed method bridges the gap between real and traditional virtual catchments by creating realistic virtual catchments with perfectly controllable physical characteristics. Our approach represents a real alternative to traditional test case procedures and provides a new framework for geomorphological and hydrological communities. It combines a field procedural generation approach, geographic information system processing procedures, and the CAESAR-Lisflood landscape evolution model. We illustrate how each of these components acts in the process of generating virtual catchments. Five physical parameters were adjusted and tested for each virtual catchment: drainage density, hypsometric integral, mean slope of the main channel, granulometry, and land use. One of our virtual catchments is compared with a real catchment and a virtual catchment produced by a standard method. This comparison indicates that our approach can produce more realistic virtual catchments than those produced by more traditional methods, while a high degree of controllability is maintained. This new method of generating virtual catchments therefore offers significant research potential to identify the impacts of the physical characteristics of catchments on hydro-sedimentary dynamics and responses.     

Correction of highly noisy strong motion records using a modified wavelet de-noising method

During the past earthquakes, many valuable acceleration time histories were recorded by analog and digital accelerometers. These records are important sources of information in the field of earthquake engineering and engineering seismology. However, a large number of these records are contaminated by noise and it is necessary to correct them for practical applications. On the other hand, only a few records can be corrected using conventional filtering because of mathematical limitations of the method. However, advances in the field of time–frequency analysis and wavelet transform theory provide useful non-linear and adaptive de-noising methods for removing of non-stationary and high-energy noise from the recorded signals. In this paper, the characteristics and capabilities of the modified non-linear adaptive wavelet de-noising method are examined for correction of highly noisy strong motion records. In the frequency domain, it is shown that this method can attenuate the noise in the whole frequency range of engineering interest while in the time domain it can detect and remove non-stationary noise. In addition, the displacement response spectra of these wavelet de-noised records are more stable than conventional filtered records with respect to different correction functions. It is found that a large number of noisy acceleration records that are usually discarded from sets of records used for estimating the ground motions can be corrected using this new method.     

希尔伯特-黄变换地震信号时频分析与属性提取

地震信号属于非线性和非平稳信号,传统的分析方法主要包括短时傅立叶变换、小波变换和Cohen类时频分布等等;希尔伯特-黄变换是分析非平稳信号的新方法,该方法的关键部分是信号的经验模态分解,通过经验模态分解,复杂的信号可以分解为有限的数量很少的几个固有模态函数,从而可以得到信号的希尔伯特时频谱;将该方法应用于单个的地震道数据,可以对地震道进行经验模态分解并得到希尔伯特谱,应用于地震剖面,可以得到意义更加明确的瞬时频率和瞬时振幅等地震属性,模型试算和实际应用表明了该方法的有效性.     

FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*

The difficulty to use master curves as well as classical techniques for the determination of layer distribution (e_i, ρ_i) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.     

S变换谱分解技术在深反射地震弱信号提取中的应用

在深反射地震资料处理中,当来自深部的有效弱信号和噪声干扰频带差异较小且难以区分时,传统滤波方法的应用会受到限制.谱分解方法是一种使用离散傅里叶变换,基于信号的频率-振幅谱等信息生成高分辨率地震图像的方法,通常用来识别介质物性横向分布特征,处理复杂介质内频谱变化和局部相位的不稳定性等问题,包括定位复杂断层和小尺度断裂等.S变换作为一种新的时频分析方法,具有自动调节分辨率的能力,近些年来被广泛应用到勘探地震、大地电磁等数据处理中,逐渐成为地球物理方法中噪声压制的有效方法之一.与常规石油反射地震资料相比,深反射主动源地震为了探测深部结构信息,常采用大药量激发方式、长排列观测系统等,导致深部有效信号基本湮灭在噪声干扰之中.针对深反射数据特点,本文结合谱分解和S变换技术,首先设计了简单的脉冲函数实验数据,证实S变换方法的有效性,同时说明谱分解方法的效果受所用时频分析方法影响较大,而其中决定分辨能力的变换窗函数的选取尤为重要.在此基础上,分别应用到深反射地震资料的单道和叠加剖面实际数据上,对比分析了传统变换谱分解和S变换谱分解的应用效果,单道资料对比结果表明:相比传统谱分解,S变换谱分解方法具有自动调节分辨率的能力,能够精确的标定深反射地震资料中弱信号不同时刻的频率分量;叠加剖面资料应用结果表明:由S变换谱分解得到的剖面结果与其他谱分解方法结果整体上具有较高的一致性,同时清晰地刻画出原叠加剖面上被噪声湮灭的低频细节特征,提高了剖面的分辨率及同相轴连续性;对比结果明显看出,Gabor变换谱分解方法得到的结果同相轴较为破碎,分析原因认为这是由Gabor变换的时频分解方法的定长窗函数所致,窗口大小不会随着信号频率的变化来调节长度,只能在处理的过程中根据一定的记录长度范围选取窗函数参数,而S变换谱分解方法在窗函数的选取时,通过时变信号的局部频率特征自动调节窗口长度,能够更好的刻画各个频段的细节特征,在深反射剖面成像应用中效果尤为明显.本文结果表明S变换谱分解技术在深地震叠加剖面上的应用有效地提高了来自深部弱反射信号的信噪比和分辨率,并刻画出了叠加剖面上所不具有的低频细节特征,在实际深反射地震资料处理中能有效保护低频弱信号获得更好的成像效果.本文为深地震反射资料中弱信号的保护处理找到一种有效的方法.     

一种用于小体积偏置探测器锥束CT系统的反投影滤波重建算法

在传统的CT系统中,系统的硬件成本和计算量都是非常巨大的.本文深入分析了一种利用偏移放置的面阵探测器的锥束CT系统,在这种系统中X射线束仅仅覆盖被扫描物体的一半体积,投影数据在探测器方向上是截断的,探测器尺寸和投影数据量都减少为传统CT系统的一半.在这种扫描方式下,现有的重建方法是首先利用重排算法获得180度范围内的平行束投影数据,然后再利用滤波反投影(FBP)算法重建出物体的三维图像.但是重排算法不可避免地会引入误差,降低重建图像的空间分辨率.本文提出了一种反投影滤波(BPF)形式的直接反投影重建方法,该方法不需要对投影数据重排,直接反投影滤波重建出最终的图像.因此,该算法在数学上更简洁,计算速度更快,能够更多地保留重建图像的高频信息.最后,数值模拟实验结果验证了该系统和重建算法能够获得高质量的CT图像.     

面波压制的Ridgelet域方法

面波压制是地震数据处理中的一个重要问题. 常规的处理方法虽然能在一定程度上压制面波,但是在处理过程中只是单一的利用面波的一种特性,例如频率域滤波中利用面波与有效信号频率之间的差别,因此难以有效地压制面波. 利用Ridgelet变换可将原始地震记录拓展到（a,τ,p）三维空间,从而可以同时利用地震记录的视速度、时间和尺度域特性差别,实现有效信号与面波的分离. 文中通过理论合成记录及实际地震记录的算例,证实了基于Ridgelet变换的面波压制方法是有效且可行的.     

瞬变电磁法正演计算进展

详细介绍了瞬变电磁法正演计算的方法、现状和发展趋势.瞬变电磁法一维正演计算需要将电磁场从频率域转换至时间域,转换方法有三种,分别是Gaver-Stehfest算法、余弦变换和Guptasarma算法.在这三种方法中,使用较多的是Gaver-Stehfest算法和余弦变换,Gaver-Stehfest算法速度较快,但精度不及余弦变换.瞬变电磁法的数值模拟主要集中于2.5维和三维,使用的数值计算方法有积分方程法、有限差分法、有限单元法和SLDM法.积分方程法主要在三维数值模拟中使用,现已很少使用;有限差分法和有限单元法是目前瞬变电磁法2.5维和三维数值模拟的主要方法;SLDM法主要应用于三维数值模拟.我国瞬变电磁法正演计算成果主要集中在回线源激发的瞬变电磁场一维数值计算和利用有限单元法进行2.5维和三维数值模拟.瞬变电磁法正演计算的发展趋势有:数值算法的改进、提高计算效率和研究地形对瞬变电磁场的影响规律.     

Nonlinearities and Linearities in Internal Gravity Waves of the Atmosphere and Oceans

The spectrum of internal gravity waves in the atmosphere and oceans is sufficiently intense that nonlinear interactions must occur, if these waves are analyzed in Eulerian coordinates as is usually done. As it happens, however, if these waves are analyzed in Lagrangian coordinates the most important nonlinearity can be entirely avoided: it is an Eulerian mathematical construct only, not a physical process. The mathematical basis for this assertion is developed here, and some of its consequences are discussed. Among the latter is a questioning of the validity of standard Eulerian eikonal methods of calculating ray paths and related functions in a multiwave environment, discussed in an appendix.     

Depth of closure: New calculation method based on sediment data

Obtaining depth of closure (DoC) in an accurate manner is a fundamental issue for coastal engineering, since good results for coastal structures and beach nourishment depend mainly on DoC. Currently, there are two methods for obtaining the DoC, mathematical formulations and profile surveys. However, these methods can incur important errors if one does not take into account the characteristics and morphology of the area, or if one does not have a sufficiently long time series. In this work the DoC is obtained from the break in the trend of the sediment with the depth, that is, in general with the increase of the depth a decrease in the size of the sediment takes place. However, at one point this tendency changes and the size increases, and then decreases again. When comparing the point where the minimum sediment size occurs before the increase, it is observed that the error incurred is small compared to other methods. If the Standard Deviation of Depth Change (SDDC) method is considered as the most accurate method, the error incurred by the proposed method is less than 7%. In addition, it can be seen that the dispersion of the sediment method always occurs outside the zone of bar movement. Whereas in the methods of profiles survey (using 2 cm precision profiles), sometimes the DoC is obtained within the active zone of bar movement. In addition, where the relative minimum of the median sediment size is found, and the sizes of 0.063 and 0.125 mm predominate in the composition of the sample. Therefore, this new method allows the precise location of the DoC to be obtained in a fast and simple way. Furthermore, this method has the advantage that it is not affected by the modifications that may be experienced by both the study area and the cross-shore beach profile.     

基于压缩感知的信号重建方法及在气枪震源信号处理中的应用

在气枪源探测过程中,由于各种干扰因素的影响,导致部分有效信号缺失或受随机干扰严重,为了重构出连续完整的数据,依据气枪源信号在傅里叶变换域中具有稀疏性的特点,构建了一种基于压缩感知(Compressive Sensing,简称CS)的缺失信号重建方法.首先进行数值模拟,并将该方法与传统的插值方法处理效果进行对比,对重建效...     

地震波形多尺度反演的一点讨论

基于在反演过程中对初始模型依赖性强、易陷入局部极值等问题,本文引入小波分析,提出多尺度地震波形反演方法,从而将参数反演问题转化到小波域中重要系数优化问题。利用多尺度之间的内在联系及小波域中重要系数的稀疏性,有将改进了局部极值、计算量等问题。并对几种多尺度反演策略进行了比较讨论。基于波动方程正演及褶积模型的两种反演方法的数值实便结果显示了本方法良好的效果。     

正则化Kaczmarz算法在页岩纳米CT重构中的应用

利用X射线计算机断层成像（CT）方法对页岩的扫描成像是一种无损的,对研究页岩微纳孔隙结构有重要意义的方法.传统的CT重构通常使用的是显式的滤波反投影（Filtered Back Projection,FBP）方法,该算法具有较快的成像速度,但常伴随有伪影或不稳定等情况.对于纳米CT而言,可以通过迭代优化的方法对投影数据进行成像,传统的迭代成像有收敛速度慢导致的计算时间长等缺点.Kaczmarz算法作为一种重要的代数重建技术（ART）,由于其几何意义明显,操作容易等优点,在CT重构中起着重要的作用,我们可以通过块状迭代或随机迭代的方式对其收敛速度进行改进.对于所求解问题的不适定性,代数重建过程中需要引入正则化的技巧来改善解的稳定性.本文根据实际问题的需要,使用页岩数值模型,验证了正则化Kaczmarz方法的有效性,并对重庆漆辽龙马溪组页岩样品的实际数据进行了处理,得到了较好的效果.     

复杂介质小波多尺度井间地震层析成像方法研究

复杂介质井间地震层析成像是一个很复杂的非线性反 演问题，常规的线性化反演方法无法得到好的解. 采用基于图形的弯曲射线追踪方法， 并将小波多尺度思想引入到井间层析成像，提出了小波多尺度井间地震层析成像方法，很好 地解决了非线性成像的难题，提高了图像的质量和分辨率. 物理模型实验结果表明， 该方法适合于复杂介质成像，并具有良好的实用性和效果.     

A Neumann expansion approach to flow through heterogeneous formations

A stochastic approach is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation function characterized by the integral scale. The Laplace transform of the solution of the random partial differential equation is first written as a solution of a stochastic integral equation. This integral equation is solved using a Neumann series expansion. Conditions of convergence of this series are investigated and compared with the convergence of the perturbation series. For mean square convergence, the Neumann expansion method may converge for a larger range of variability in permeability and porosity than the classic perturbation method. Formal expressions for the average and for the correlation moments of the pressure are obtained. The influence of the variability of the permeability and porosity on pressure is analyzed for radial flow. The solutions presented for the pressure at the well, as function of the permeability coefficient of variation, may be of practical interest for evaluating the efficiency of well stimulation operations, such as hydraulic fracturing or acidizing methods, aimed at increasing the permeability around the well.     

利用Hilbert变换计算重力归一化总梯度

针对提高重力勘探正反演解释的分辨率问题,提出利用Hilbert变换计算和研究重力归一化总梯度.文中从理论上详细地证明了方法的可行性,给出了适合计算机实现的计算方法.为探讨该方法对油气藏的分辨能力,在模型计算中,分别利用Fourier级数法、Fourier变换法和本文提出的Hilbert变换法计算模型的GH场值,发现当三度体储油球冠模型（模拟似三度贮油气藏背斜模型）油气藏部分（低密度体）厚度减小到低于球冠厚度的十分之一时,Fourier级数及变换法不能分辨出低密度体所产生的异常,而Hilbert变换法仍然可以清晰地识别,这说明用Hilbert变换法计算的GH场对异常识别的分辨率优于其他两种方法.