Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Comparative Seismic Risk Studies for German Earthquake Regions on the Basis of the European Macroseismic Scale EMS-98

Within the framework of recent research projects, basic tools for GIS-based seismic risk assessment technologies were developed and applied to the building stock and regional particularities of German earthquake regions. Two study areas are investigated, being comparable by the level of seismic hazard and the hazard-consistent scenario events (related to mean return periods of 475, 2475 and 10000 years). Significant differences exist with respect to the number of inhabitants, the grade and extent of urbanisation, the quality and quantity of building inventory: the case study of Schmölln in Eastern Thuringia seems to be representative for the majority of smaller towns in Germany, the case study of Cologne (Köln) stands for larger cities. Due to the similarities of hazard and scenario intensities, the considerable differences do not only require proper decisions concerning the appropriate methods and acceptable efforts, they enable conclusions about future research strategies and needs for disaster reduction management. Not least important, results can sharpen the focus of public interest. Seismic risk maps are prepared for different scenario intensities recognising the scatter and uncertainties of site-dependent ground motion and also of the applied vulnerability functions. The paper illustrates the impact of model assumptions and the step-wise refinements of input variables like site conditions, building stock or vulnerability functions on the distribution of expected building damage within the study areas. Furthermore, and in contrast to common research strategies, results support the conclusion that in the case of stronger earthquakes the damage will be of higher concentration within smaller cities like Schmölln due to the site-amplification potential and/or the increased vulnerability of the building stock. The extent of damage will be pronounced by the large number of masonry buildings for which lower vulnerability classes have to be assigned. Due to the effect of deep sedimentary layers and the composition of building types, the urban centre of Cologne will be less affected by an earthquake of comparable intensity.     

T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1

Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they are layer specific and include uncertainty caused by using variance estimates.     

方差体技术在地震勘探中的应用

三维地震数据体反映了地下一个规则网格的反射情况。当遇到地下有断层或某个局部区域地层不连续变化时，一些地震道的反射特征就会与附近地震道出现差异而导致地震首局部的不连续性。三维方差体技术就是求取三维数据体所有样点的方差值来反映这种不连续性信息。通过该技术在济宁2号井某采区的实际应用，可看出，方差体技术在三维地震信息的自动拾取以及提高地震资料解释成果精度等方面有明显优势，对断层、陷落柱有良好的自动识别能力。     

水气两相流系统K-S-P模型参数反演的最优估计

应用渗流力学和参数反演辨识最优化理论,建立了水气两相流控制方程,给出了控制两相流系统K-S-P模型参数之间的本构关系,并对其中的相关参数进行数值反演辨识,得出待求参数的最优估计值。对不同质地土壤的实验测试值进行对比分析,其结果吻合较好,验证了模型的适定性和可靠性,解决了实验数据处理以及结果对初值的敏感性问题,并且该数值方法可通过多组初值参数进行数值实验,结合实验结果来满足实际工程的需求。这不仅对非饱和带内污染物传输、气藏工程试井计算、填埋气体的释放以及挥发性有机污染物的去污分析中两相流数值计算提供基础,而且对K-S-P本构关系之间参数的确定提供了可靠的理论依据。     

GIS叠置图层方差分量的极大似然估计

针对GIS叠置中的同名点,以维希特分布密度为似然函数,提出了各图层方差分量的极大似然估计方法。该方法不依赖残差,不需要迭代就能估计未知参数和方差分量。     

平差系统的模型误差及其识别方法研究

论述了模型误差影响参数估值的一些理论问题,指出了随机模型误差和函数模型误差之间的相互作用和转化。为讨论平差系统最优模型的选取,给出了与现有文献将模型误差纳入平差系统的思路不同的一个估计和识别模型误差的理论基础公式,由此导出了相应的实用公式,给出了平差系统模型的优选方法。     

基于立体补偿的遥感立体像对压缩方法

提出研究遥感立体像对的压缩问题。主要讨论了左右影像的视差补偿和辐射补偿。针对遥感立体像对视差分布不均以及左右影像存在辐射差的特点,提出了一种基于立体补偿的遥感立体像对压缩算法。该算法以左片为基准图像,采用自适应视差估计计算出右片的视差矢量,结合辐射校正和重叠块视差补偿技术得到平滑的右片的预测图像,以右片减去预测图像得到残差图像,然后采用小波压缩算法对残差图像进行压缩。实验结果表明,该算法能显著提高遥感立体像对的压缩性能。     

Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate

In this contribution, we introduce a new bootstrap-based method for Global Navigation Satellite System (GNSS) carrier-phase ambiguity resolution. Integer bootstrapping is known to be one of the simplest methods for integer ambiguity estimation with close-to-optimal performance. Its outcome is easy to compute due to the absence of an integer search, and its performance is close to optimal if the decorrelating Z-transformation of the LAMBDA method is used. Moreover, the bootstrapped estimator is presently the only integer estimator for which an exact and easy-to-compute expression of its fail-rate can be given. A possible disadvantage is, however, that the user has only a limited control over the fail-rate. Once the underlying mathematical model is given, the user has no freedom left in changing the value of the fail-rate. Here, we present an ambiguity estimator for which the user is given additional freedom. For this purpose, use is made of the class of integer aperture estimators as introduced in Teunissen (2003). This class is larger than the class of integer estimators. Integer aperture estimators are of a hybrid nature and can have integer outcomes as well as non-integer outcomes. The new estimator is referred to as integer aperture bootstrapping. This new estimator has all the advantages known from integer bootstrapping with the additional advantage that its fail-rate can be controlled by the user. This is made possible by giving the user the freedom over the aperture of the pull-in region. We also give an exact and easy-to-compute expression for its controllable fail-rate.