径向基函数(RBF)神经网络及其应用

介绍了径向基函数(RBF)神经网络的原理、 学习算法及其在地震预报专家系统ESEP 3.0中的应用。 实际应用结果表明, 该神经网络可以很好地克服BP神经网络学习过程的收敛过分依赖于初值和可能出现局部收敛的缺陷, 具有较快的运算速度、 较强的非线性映射能力和较好的预报效能。     

起伏地表QR径向基函数有限差分及其在弹性波逆时偏移中的应用

弹性波逆时偏移不受倾角和偏移孔径的限制, 能够实现任意复杂构造的高精度多波成像, 是目前最精确的多分量资料偏移成像方法之一.逆时偏移算法的核心是波场延拓, 传统波场延拓以水平基准面为边界条件, 基于固定采样步长进行规则网格剖分, 采用阶梯近似法处理起伏地表和复杂构造界面时会产生台阶散射, 严重影响起伏地表复杂构造的成像精度.基于无网格节点模型, 定量分析了弹性波模拟中径向基函数有限差分法的频散关系和稳定性条件.基于此, 提出一种基于QR径向基函数的高精度有限差分方法, 并提出一种优化的起伏地表自适应节点剖分方法, 推导了精确的无网格自由边界条件和弹性波无网格混合吸收边界条件, 形成了新的基于无网格的起伏地表弹性波数值模拟方法.此外, 本文将此无网格径向基函数有限差分方法应用于精确的纵横波场矢量分解公式, 实现了起伏地表弹性波逆时偏移成像.通过对高斯山丘模型, 起伏凹陷模型和起伏地表Marmousi-2模型进行数值试算, 验证了本文方法的有效性和可行性.

     

利用径向基函数RBF解算GRACE全球时变重力场

本文利用GRACE（Gravity Recovery And Climate Experiment）level 1b数据和径向基函数RBF（radial basis function）方法解算了全球时变地球重力场.RBF基函数相比传统球谐（spherical harmonic）基函数,其高度的空域局部特性使得正则化过程易于添加先验协方差信息,从而可能揭示更加准确的重力场信号.本文研究表明,RBF基函数算法在精化现有的GRACE全球时变重力场模型,如提升部分区域信号幅度等方面具有一定优势.本文通过将RBF的尺度因子作为待解参数,基于GRACE卫星的Level 1b数据和变分方程法,成功获取了2009-2010年90阶无约束全球时变重力场RBF模型Hust-IGG03,以及正则化全球时变重力场RBF模型Hust-IGG04.通过与GRACE官方数据处理中心GFZ发布的最新90阶球谐基时变模型RL05a进行对比,结果表明：（1）无约束RBF模型Hust-IGG03和GFZ RL05a在空域和频域表现基本一致;（2）正则化RBF模型Hust-IGG04无需进行后处理滤波已经显示较高信噪比,噪音水平接近于球谐基模型GFZ RL05a经400 km高斯滤波后的效果;（3）Hust-IGG04相比400 km高斯滤波GFZ RL05a在周年振幅图和趋势图上显示出更多的细节信息,并且呈现出更强的信号幅度,如在格陵兰冰川融化趋势估计上Hust-IGG04比GFZ RL05a提高了24.2%.以上结果均显示RBF方法有助于进一步挖掘GRACE观测值所包含的时变重力场信息.

     

基于泊松小波径向基函数融合多源数据的局部重力场建模

融合多源数据的高精度、高分辨率的局部重力场建模是物理大地测量学的前沿和热点问题.本文研究了基于径向基函数融合多源数据的局部重力场建模方法,利用Monte-Carlo方差分量估计实现了不同类型的观测数据的合理定权,引入了最小标准差法确定基函数的适宜网络,分析了地形因素对于基函数网络确定及局部重力场建模精度的影响.以泊松小波基函数为构造基函数,结合残差地形模型,融合实测的陆地重力异常、船载重力异常及航空重力扰动数据构建了局部区域陆海统一的似大地水准面模型.研究结果表明:引入残差地形模型平滑了地形质量引入的高频扰动信号,简化了基函数的网络设计;并提高了重力似大地水准面的精度,平原地区其精度提高了4 mm,地形起伏较大的山区其精度提高了约5 cm.总体而言,基于"三步法"构建的局部重力似大地水准面在荷兰、比利时及德国相关区域,其精度分别达到1.12 cm、2.80 cm以及2.92 cm.     

应用径向基概率神经网络研究地震滑坡

地震滑坡是一种有着严重危害的次生地震灾害形式,形成机制复杂,涉及因素较多。地震滑坡在空间上不是完全随机分布的,换言之,地震滑坡的影响因素和它的分布规律之间存在着相关性。利用径向基概率神经网络自学习的特性,通过对样本训练、检测,得到一个稳定可靠的模式识别网络,并用其对工作区进行潜在地震滑坡危险性区划,通过结果对比,在本例中识别精度达到89.9%以上,显示是一次有效的尝试     

等参函数及其在重力场中的应用

本文介绍了等参函数和等参超曲面的概念和理论,提出了更广义的平行概念,证明了平行重力场就是平面场,球面场,圆柱面场之一,平行重力场中几何水准测量不存在理论闭合差;无扰动的流体静力平衡状态下的地球重力场是平行重力场,它的物质密度分布是球对称的。     

精细解释技术在苏仁诺尔油田开发中的应用

文中以苏仁诺尔油田为例,分析了主要产油层南屯组精细解释技术的应用效果.苏仁诺尔油田处在北东向苏仁诺尔构造带上,南屯组顶底界面及内部分界面(T23)为区域标准等时面,精细对比研究时参考局部等时面,可获得高精度地层格架.油田内断裂关系复杂,精细断层解释结果阐明了苏仁诺尔油田内部储层不连通、注采关系不对应等现象原因,以及对油田油气聚集规律产生的影响.采用多级次断裂空间配比关系来解决开发地质问题,同时结合生产动态资料反过来验证地质问题,对于油田开发过程中注采关系调整,剩余油分布特征研究具有一定指导意义.     

一种基于径向基神经网络的地磁场K指数实时标定方

K指数是一种重要的地磁活动指数,标定K指数的难点在于规则日变化SR的确定,尽管FMI（Finnish Meteorological Institute,芬兰气象学院）方法能够比较准确地识别规则日变化SR,给出合理的K指数,但是该方法存在一天的延迟,无法实现实时标定.为了解决这一问题,本文提出了一种基于径向基神经网络的K指数实时标定方法：首先用修正后的FMI方法提取H分量的时均值序列,接着以径向基神经网络对该序列进行建模,最后基于神经网络模型实时获取规则日变化,并结合H分量分均值观测数据标定K指数.实验结果表明：该方法能够以3.8598 nT的标准误差实时获取规则日变化SR;实时标定的K指数与直接用FMI-H方法延迟一天标定的K指数相比,完全吻合的占69.8%,差别大于一个标度的仅占0.77%.     

用径向基函数神经网络方法预报太阳黑子数平滑月均值

简单介绍了径向基函数神经网络方法的原理和应用,发展了用径向基函数（RBF）对平滑月平均黑子数进行预报的方法. 用不同的数据序列对网络进行训练,对未来8个月的平滑月平均黑子数进行预报. 用该方法对第23周开始后的平滑月平均黑子数进行逐月预报,并与实测值进行比较,结果表明随着预报实效的延长预报误差被逐渐放大,该方法可以较准确地做出未来４个月的预报,绝对误差可以控制在20以内,标准差为4.8,相对误差控制在38％以内,大部分相对误差不超过15%（占总预报数的89％）,具有较好的应用价值. 用于网络训练的样本数量对预报结果会产生一定的影响.     

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.     

Reservoir induced earthquakes analyzed via radial basis function networks

Estimation of the magnitude of reservoir induced seismicity is essential for seismic risk analysis of dam sites. Different geological and empirical methods dealing with the mechanism or magnitude of such earthquakes are available in the literature. In this study, a method based on an artificial neural network utilizing radial basis functions (RBF network) was employed to analyze the problem. The network has only two input neurons, one representing the maximum depth of the reservoir and the other being a comprehensive parameter representing reservoir geometry. Magnitudes of the induced earthquakes predicted using the RBF network were compared with the actual recorded data. Compared with the conventional statistical approach, the proposed method gives a better prediction, both in terms of coefficients of correlation and error rates.     

The choice of the spherical radial basis functions in local gravity field modeling

The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and the radial multipoles are well known, while for the Poisson wavelet new closed analytical expressions are derived for arbitrary orders using recursions. The performance of each SRBF in local gravity field modelling is analyzed using real data. A penalized least-squares technique is applied to estimate the gravity field parameters. As follows from the analysis, almost the same accuracy of gravity field modelling can be achieved for different types of the SRBFs, provided that the depth of the SRBFs is chosen properly. Generalized cross validation is shown to be a suitable technique for the choice of the depth. As a good alternative to generalized cross validation, we propose the minimization of the RMS differences between predicted and observed values at a set of control points. The optimal regularization parameter is determined using variance component estimation techniques. The relation between the depth and the correlation length of the SRBFs is established. It is shown that the optimal depth depends on the type of the SRBF. However, the gravity field solution does not change significantly if the depth is changed by several km. The size of the data area (which is always larger than the target area) depends on the type of the SRBF. The point-mass kernel requires the largest data area.     

Time series forecasting by combining the radial basis function network and the self‐organizing map

Based on a combination of a radial basis function network (RBFN) and a self‐organizing map (SOM), a time‐series forecasting model is proposed. Traditionally, the positioning of the radial basis centres is a crucial problem for the RBFN. In the proposed model, an SOM is used to construct the two‐dimensional feature map from which the number of clusters (i.e. the number of hidden units in the RBFN) can be figured out directly by eye, and then the radial basis centres can be determined easily. The proposed model is examined using simulated time series data. The results demonstrate that the proposed RBFN is more competent in modelling and forecasting time series than an autoregressive integrated moving average (ARIMA) model. Finally, the proposed model is applied to actual groundwater head data. It is found that the proposed model can forecast more precisely than the ARIMA model. For time series forecasting, the proposed model is recommended as an alternative to the existing method, because it has a simple structure and can produce reasonable forecasts. Copyright © 2005 John Wiley & Sons, Ltd.     

Study on tectonic stress of Zhongyuan oil field with wellbore breakout data

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Probability of radial anisotropy in the deep mantle

It is well established that the Earth's uppermost mantle is anisotropic, but observations of anisotropy in the deeper mantle have been more ambiguous. Radial anisotropy, the discrepancy between Love and Rayleigh waves, was included in the top 220 km of PREM, but there is no consensus whether anisotropy is present below that depth. Fundamental mode surface waves, for commonly used periods up to 200 s, are sensitive to structure in the first few hundred kilometers and therefore do not provide information on anisotropy below. Higher mode surface waves, however, have sensitivities that extend to and below the transition zone and should thus give insight about anisotropy at greater depths, but they are very difficult to measure. We previously developed a new technique to measure higher mode surface wave phase velocities with consistent uncertainties. These data are used here to construct probability density functions of a radially anisotropic Earth model down to approximately 1500 km. In the uppermost mantle, we obtain a high probability of faster horizontally polarized shear wave speed, likely to be related to plate motion. In the asthenosphere and transition zone, however, we find a high probability of faster vertically polarized shear wave speed. To a depth of 1500 km in the lower mantle, we see no significant shear wave anisotropy. This is consistent with results from laboratory measurements which show that lower mantle minerals are anisotropic but LPO is unlikely to develop in the pressure–temperature conditions present in the mid-mantle.     

经验正交函数分解在地壳垂直形变场分析中的应用

论述了应用经验正交函数分解方法分析地壳垂直形变场,处理分析了甘肃河西地区的实测资料,结果显示,地壳垂直形变场的第一典型场对中强以上地震发震地点的判定有重要意义;而地壳垂直形变场的时间权系数能够表示区域地壳运动的相对强弱,它可以作为区域地震危险性判定的时间判据。     

大港油田官104断块储层非均质性研究

利用研究区测井二次解释的成果,对储层非均质性特征和在生产中的反映进行了分析,并结合高分辨率层序地层学理论,总结储层非均质性形成的控制因素.针对大港油田官104断块开发过程中层间矛盾突出、单层突进严重的问题,重点分析了研究区储层层间非均质性.通过对研究区的分析可知,地层旋回性、沉积微相和隔层的分布是主要的储层非均质控制因素.并且隔层和沉积相的分布规律受沉积旋回的控制.因此,层间非均质性受控于基准面旋回变化造成的A/S值的变化,A/S值小非均质性弱,A/S值大非均质性强.应用产液、吸水剖面资料验证储层非均质性,并提出下一步挖潜和措施的方向,指导油田的生产.     

地磁前兆异常的动态从属函数

地震前兆涉及到多种地球物理观测方法,且计量单位各不相同,因此,各类前兆异常之间无法进行直接的定量对比,这给地震预报研究带来了困难.应用异常从属函数值（无量纲量）可统一规划不同性质、不同计量单位的地震前兆异常.本文通过研究地磁资料从属函数,发现1995年9月20日山东苍山Ms5.2级地震前有明显的前兆异常.增强了对地震前兆异常的识别能力,文中提出该方法在地磁场研究中应注意的问题.