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.     

Fifty-thousand-year vegetation and climate history of Noel Kempff Mercado National Park, Bolivian Amazon

Pollen and charcoal records from two large, shallow lakes reveal that throughout most of the past 50,000 yr Noel Kempff Mercado National Park, in northeastern lowland Bolivia (southwestern Amazon Basin), was predominantly covered by savannas and seasonally dry semideciduous forests. Lowered atmospheric CO₂ concentrations, in combination with a longer dry season, caused expansion of dry forests and savannas during the last glacial period, especially at the last glacial maximum. These ecosystems persisted until the mid-Holocene, although they underwent significant species reassortment. Forest communities containing a mixture of evergreen and semideciduous species began to expand between 6000 and 3000 ¹⁴C yr B.P. Humid evergreen rain forests expanded to cover most of the area within the past 2000 ¹⁴C yr B.P., coincident with a reduction in fire frequencies. Comparisons between modern pollen spectra and vegetation reveal that the Moraceae-dominated rain forest pollen spectra likely have a regional source area at least 2-3 km beyond the lake shore, whereas the grass- and sedge-dominated savanna pollen spectra likely have a predominantly local source area. The Holocene vegetation changes are consistent with independent paleoprecipitation records from the Bolivian Altiplano and paleovegetation records from other parts of southwestern Amazonia. The progressive expansion in rain forests through the Holocene can be largely attributed to enhanced convective activity over Amazonia, due to greater seasonality of insolation in the Southern Hemisphere tropics driven by the precession cycle according to the Milankovitch Astronomical Theory.     

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     

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.     

Caldera formation by magma withdrawal from a reservoir beneath a volcanic edifice

Caldera formation has been explained by magma withdrawal from a crustal reservoir, but little is known about the conditions that lead to the critical reservoir pressure for collapse. During an eruption, the reservoir pressure is constrained to lie within a finite range: it cannot exceed the threshold value for eruption, and cannot decrease below another threshold value such that feeder dykes get shut by the confining pressure, which stops the eruption. For caldera collapse to occur, the critical reservoir pressure for roof failure must therefore be within this operating range. We use an analytical elastic model to evaluate the changes of reservoir pressure that are required for failure of roof rocks above the reservoir with and without a volcanic edifice at Earth's surface. With no edifice at Earth's surface, faulting in the roof region can only occur in the initial phase of reservoir inflation and affects a very small part of the focal area. Such conditions do not allow caldera collapse. With a volcanic edifice, large tensile stresses develop in the roof region, whose magnitude increase as the reservoir deflates during an eruption. The edifice size must exceed a threshold value for failure of the roof region before the end of eruption. The largest tensile stresses are reached at Earth's surface, indicating that faulting starts there. Failure affects an area whose horizontal dimensions depend on edifice and chamber dimensions. For small and deep reservoirs, failure conditions cannot be achieved even if the edifice is very large. Quantitative predictions are consistent with observations on a number of volcanoes.     

Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions

This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions.