Flexible spectral methods for the generation of random fields with power-law semivariograms

Random field generators serve as a tool to model heterogeneous media for applications in hydrocarbon recovery and groundwater flow. Random fields with a power-law variogram structure, also termed fractional Brownian motion (fBm) fields, are of interest to study scale dependent heterogeneity effects on one-phase and two-phase flow. We show that such fields generated by the spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. To illustrate this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose a new method to generate fBm fields that introduces weighting functions into the spectral method. It leads to a flexible and efficient algorithm. The flexibility permits an optimal choice of summation points (that is points in frequency space at which the weighting function is calculated) specific for the autocovariance structure of the field. As an illustration of the method, comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields are presented. For power-law semivariograms, the proposed spectral method with a cylindrical distribution of the summation points gives optimal results.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Magnetic domain structures and stray fields of individual elongated magnetite grains revealed by magnetic force microscopy (MFM)

In order to clarify the relationship between microscopic and macroscopic magnetic features of a rock, we applied magnetic force microscopy (MFM) as a local probe on a sample with an intense natural remanent magnetisation, a norite from Heskestad, Norway. We studied in detail seven magnetite (Fe₃O₄) exsolution lamellae, five of them were about 30 μm long and a few micrometers wide, two were significantly shorter; all were located in their natural host, a grain of clinopyroxene. By combining MFM images of surface magnetisation with information about shape observed with optical microscopy (OM), the internal domain structure was determined for individual grains. In general, the lamellae were pseudo-single-domain grains with open-flux domain magnetisations parallel to their long axes. The domain sizes were, in cross-section, on the order of a micrometer for the longer lamellae and about 300 nm for the short lamellae. By increasing the separation between the MFM probe and the exposed end of the lamellae, information could be obtained about the decrease in stray fields for the individual grains. Close to the lamellae, stray fields were significant even for grains with multiple domains. The largest fields were found above the largest domains. A separation of approximately one domain width was found to be a characteristic distance, where stray fields from adjacent domains begin to cancel one another.     

中国稻田甲烷产生和排放研究 Ⅰ.产生和排放机理及其影响因子

综合论述了近 2 0年来中国稻田甲烷排放的研究状况 ,包括中国稻田甲烷排放通量的观测 ,稻田甲烷生成的生物学机理及产生、转化、传输的机理研究 ,稻田甲烷排放的影响因子 ,主要介绍了稻田甲烷产生和氧化过程、影响甲烷排放的因子     

云南省红河地区2004年第一场透雨过程分析

利用2004年5月15～21日第一场透雨过程的高空资料,对产生强降雨天气的主要物理量进行分析,总结主要物理量的变化特征,揭示这次强降雨产生发展变化规律,对今后在预报过程中对主要物理量的变化引起重视,具有一定的参考意义。     

长江三峡GPS处理结果和应变背景场

采用BerneseGPSSoftware 4 .2对长江三峡工程诱发地震监测系统GPS监测网络 1998～ 2 0 0 3年的 6期观测数据进行了处理 ,结果表明 ,三峡库区与华南块体的水平相对运动在 0～ 3mm/a(± 0 .1～± 2 .0mm/a) ;蓄水导致的垂直形变区域主要集中在茅坪 香溪 巴东库段 ,近岸点垂直沉降的量级在 10～ 35mm左右 ,最大峰值区域香溪约 35mm(± 8.6mm) ,垂直形变沿远离库中心方向迅速衰减。采用贝塞尔双三次样条函数模型拟合该地区的应变率 ,推算各类水平应变场 ,结果表明 ,蓄水前各种应变背景在 10 -9/a～ 10 -10 /a量级。作为构造稳定地区 ,三峡库区近期因蓄水导致大规模形变 ,从而诱发中强地震的可能性不大     

泰国水稻种植面积月变化的遥感监测

介绍了光学和微波遥感影像相结合进行泰国水稻种植面积监测方法。泰国雨季雨量充足 ,气温适合 ,同一时间耕地上水稻的物候多样 ,每月水稻种植面积都发生变化。利用旱季的TM影像 ,获得耕地信息。同时利用TM影像覆盖的雷达区域进行非耕地去除 ,进行非监督分类 ,提取反映水稻种植不同生长期的雷达影像后向反射系数特征 ,建立各种类型的分类模型 ,采用监督分类的方法对全景雷达数据进行水稻种植情况调查 ,并分别予以识别和统计 ,反映研究区水稻月种植情况。分类结果通过类别检验和面积量算检验进行精度评价和分析。     

Seasonal Variation of the East Asian Subtropical Westerly Jet and Its Association with the Heating Field over East Asia

The structure and seasonal variation of the East Asian Subtropical Westerly Jet （EAWJ） and associations with heating fields over East Asia are examined by using NCEP/NCAR reanalysis data. Obvious differences exist in the westerly jet intensity and location in different regions and seasons due to the ocean-land distribution and seasonal thermal contrast, as well as the dynamic and thermodynamic impacts of the Tibetan Plateau. In winter, the EAWJ center is situated over the western Pacific Ocean and the intensity is reduced gradually from east to west over the East Asian region. In summer, the EAWJ center is located over the north of the Tibetan Plateau and the jet intensity is reduced evidently compared with that in winter. The EAWJ seasonal evolution is characterized by the obvious longitudinal inconsistency of the northward migration and in-phase southward retreat of the EAWJ axis. A good correspondence between the seasonal variations of EAWJ and the meridional differences of air temperature （MDT） in the mid-upper troposphere demonstrates that the MDT is the basic reason for the seasonal variation of EAWJ. Correlation analyses indicate that the Kuroshio Current region to the south of Japan and the Tibetan Plateau are the key areas for the variations of the EAWJ intensities in winter and in summer, respectively. The strong sensible and latent heating in the Kuroshio Current region is closely related to the intensification of EAWJ in winter. In summer, strong sensible heating in the Tibetan Plateau corresponds to the EAWJ strengthening and southward shift, while the weak sensible heating in the Tibetan Plateau is consistent with the EAWJ weakening and northward migration.