Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a membrane to a thin steel plate), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.On leave from the Department of Physical Geography and Cartography, Comenius University, Mlynská dolina, Bratislava, Czechoslovakia.On leave from the Institute of Physics, Dúbravská cesta 9, Bratislava, Czechoslovakia.     

内蒙古中西部宝音图群石榴角闪岩的地球化学、变质作用及年代学特征

宝音图群分布于内蒙古中西部狼山、图古日格和达茂旗一带，主要由云母片岩、石英片岩、石英岩、角闪岩和大理岩组成。在狼山格尔敖包沟和图古日格西南地区发育十分典型的石榴角闪岩，均以似层状或透镜状产自云母片岩中，但两地具有不同的矿物组合，前者主要以石榴石+角闪石+斜长石+含钛矿物（金红石和钛铁矿）为特征，后者主要以石榴石+角闪石+绿帘石+含钛矿物（金红石和钛铁矿）为特征。地球化学研究显示两个地区的石榴角闪岩原岩具有相似的化学组成，均为亚碱性玄武岩的拉斑系列。宝音图群的石榴角闪岩具有右倾的稀土配分模式，REE总量为83.31×10^-6~125.9×10^-6，（La/Yb）_N比值为2.17~6.48，δEu=0.87~0.98。Ta、Nb、Ti没有明显的负异常，其配分型式类似E-MORB特点。微量元素构造判别图解表明这些石榴角闪岩的原岩产于板内拉张环境中。本文通过模拟格尔敖包沟样品LS01和图古日格西南地区样品LS35的P-T视剖面图研究其变质作用及矿物演化过程，结果显示这两个样品均经历了早期进变质，峰期以及峰后近等温减压的顺时针型P-T轨迹。样品LS01的峰期温压条件为~11kbar/~735℃，模拟得到的峰期矿物组合可能为石榴石+角闪石+斜长石+黑云母+透辉石+金红石+熔体，P-M（H₂O）视剖面图显示，由于峰后演化过程中存在饱和流体渗透，导致峰期透辉石无法保留。样品LS35的峰期温度压力条件为~8kbar/675℃，其峰期组合为石榴石+角闪石+绿帘石+金红石。两个地区的石榴角闪岩的温度压力条件明显不同，推测宝音图群中呈透镜体或似层状产出的变质基性岩，存在着递增型的变质作用。锆石LA-ICP-MS U-Pb年代学的研究结果显示石榴角闪岩样品LS01的变质锆石年龄为394±8Ma。由此推测这些石榴角闪岩的原岩可能形成于华北北缘在新元古代发育的裂陷盆地，在泥盆纪中期，宝音图群作为华北克拉通的一部分，被卷入到与古亚洲洋闭合有关的造山过程，发育中压型递增变质作用。     

Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Characterizing heterogeneous permeable media using flow and transport data typically requires solution of an inverse problem. Such inverse problems are intensive computationally and may involve iterative procedures requiring many forward simulations of the flow and transport problem. Previous attempts have been limited mostly to flow data such as pressure transient (interference) tests using multiple observation wells. This paper discusses an approach to generating stochastic permeability fields conditioned to geologic data in the form of a vertical variogram derived from cores and logs as well as fluid flow and transport data, such as tracer concentration history, by sequential application of simulated annealing (SA). Thus, the method incorporates elements of geostatistics within the framework of inverse modeling. For tracer-transport calculations, we have used a semianalytic transit-time algorithm which is fast, accurate, and free of numerical dispersion. For steady velocity fields, we introduce a transit-time function which demonstrates the relative importance of data from different sources. The approach is illustrated by application to a set of spatial permeability measurements and tracer data from an experiment in the Antolini Sandstone, an eolian outcrop from northern Arizona. The results clearly reveal the importance of tracer data in reproducing the correlated features (channels) of the permeability field and the scale effects of heterogeneity.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

重视和加强岩矿物性的测量研究

本文从物探科学技术的进步,勘查任务的发展变化、物探方法应用范畴的扩大和物性勘探等几个方面,论述了岩石和矿物物理性质测量、研究的重要性,指出：物性工作不可能毕其功于一役,并提出了五点建议：１．深入研究各类矿藏及其围岩（直至地面）物性的空间变化规律,为选择、研究合适的物探方法,提高物探效果,进一步探讨“直接”找矿问题,提供依据;２．这项工作可专门进行,但最好尽可能利用为其他目的而设计的钻井进行;３．物     

Using numerical modelling to evaluate tsunami hazard near the Kuril Island

A sequence of computer experiments is used to study questions concerning the tsunami problem as a quantitative estimate of tsunami danger, detailed geographical tsunami classification, determination of the parameters of critical tsunami waves, and the conditions of their development. We call a wave critical, if its impact on the coast is most hazardous.Using the Middle Kuril Island as an example, we present the results of a computer experiment which includes determining the wavefields on the shelf and estimating the effects connected with the deep-water Bussol and Diana Straits.Numerical simulation of tsunami waves of different sources permits the assessment of the extent of tsunami danger in different areas of the coastal zone of Simushir Island, depending on the location of the focus zone and their geometry.The major singularities of the wavefield arise in the zones of the deep-water straits. The distribution of the amplification factors is determined by both the global parameters of the wavefields and the local properties of individual harbours. The results obtained for a particular harbour in the northern part of Simushir Island, formed the basis for the quantitative estimate of tsunami danger for this area.     

Large eddy simulation of hydrocyclone—prediction of air-core diameter and shape

Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect.     

Fracture analysis in the south-western Corinth rift (Greece) and implications on fault hydraulic behavior

This paper reviews the data concerning the fracture network and the hydraulic characteristics of faults in an active zone of the Gulf of Corinth. Pressure gap measured through fault planes shows that in this area the active normal faults (Aigion, Helike) act, at least temporarily and locally, as transversal seal. The analysis of the carbonate cements in the fractures on both the hangingwall and the footwall of the faults also suggests that they have acted as local seals during the whole fault zone evolution. However, the pressure and the characteristics of the water samples measured in the wells indicate that meteoric water circulates from the highest part of the relief to the coast, which means it goes through the fault zones. Field quantitative analysis and core studies from the AIG-10 well have been performed to define both regional and fault-related fracture networks. Then laboratory thin section observations have been done to recognize the different fault rocks characterizing the fault zone components. These two kinds of approach give information on the permeability characteristics of the fault zone. To synthesize the data, a schematic conceptual 3D fluid flow modeling has been performed taking into account fault zone permeability architecture, sedimentation, fluid flow, fault vertical offset and meteoric water influx, as well as compaction water flow. This modeling allows us to fit all the data with a model where the fault segments act as a seal whereas the relays between these segments allow for the regional flow from the Peloponnese topographic highs to the coast.     

Modeling of the classification behavior of the diaphragms used in multi-chamber cement mills

A new approach has been developed for describing the classification that arises at the diaphragm in multi-chamber ball mills. Fourteen industrial scale cement mills have been sampled in this study and after mass balancing, model fits of the equipment were done. Successive mill product predictions for the sampled conditions were achieved, and requirements to build up an optimization capable model are discussed.