Is the ocean floor a fractal?

The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed.     

Fractal Dimensions as Chaos Indicators

The correlation dimension D ₂ is used to develop a method of classification for phase space orbits. D ₂ depends only on the mutual distances of the orbits points, therefore the time development of the orbit is reflected in the time development of the correlation dimension approximants. It is shown, that this technique allows to investigate the dynamical properties of a phase space orbit, a classification of chaotic and regular orbits and a detection of sticky orbits.     

Geostatistical mapping of geomorphic variables in the presence of trend

Mapping geomorphic variables geostatistically, specifically by kriging, runs into difficulties when there is trend. The reason is that the variogram required for the kriging must be of residuals from any trend, which in turn cannot be estimated optimally by the usual method of trend surface analysis because the residuals are correlated. The difficulties can be overcome by the use of residual maximum likelihood (REML) to estimate both the trend and the variogram of the residuals simultaneously. We summarize the theory of REML as it applies to kriging in the presence of trend. We present the equations to show how estimates of the trend are combined with kriging of residuals to give empirical best linear unbiased predictions (E‐BLUPs). We then apply the method to estimate the height of the sub‐Upper‐Chalk surface beneath the Chiltern Hills of southeast England from 238 borehole data. The variogram of the REML residuals is substantially different from that computed by ordinary least squares (OLS) analysis. The map of the predicted surface is similar to that made from kriging with the OLS variogram. The variances, however, are substantially larger because (a) they derive from a variogram with a much larger sill and (b) they include the uncertainty of the estimate of the trend. Copyright © 2006 John Wiley & Sons, Ltd.     

A Reanalysis and Reinterpretation of Geodetic and Geological Evidence of Glacial-Isostatic Adjustment in the Churchill Region, Hudson Bay

We review the historical, geological, tide-gauge, GPS and gravimetric evidence advanced in favour of, or against, continuing land uplift around Hudson Bay, Canada. We also reanalyse the tide-gauge and GPS data for Churchill using longer time series than those available to previous investigators. The dependence of the mean rate of relative sea-level change obtained from the tide-gauge record on the length and mid-epoch of the observation interval considered is investigated by means of a newly developed linear-trend analysis diagram. For studying the shorter-period variability of the tide-gauge record, the wavelet transform is used. The mean rate of land uplift obtained from GPS is based on a new analysis using IGS solutions of GFZ. To include the post-glacial land uplift, sea-level indicators from the Churchill region representing the relative sea-level history during the past 8000 years are also used. Finally, the values of the four observables are jointly inverted in terms of mantle viscosity. The optimum values are ~3.2 × 10²⁰ Pa s and ~1.6 × 10²² Pa s for the upper- and lower-mantle viscosities, respectively.     

Geobotanical and biogeochemical reconnaissance of the ultramafics of Central Iran

In Iran, ultramafic rocks cover substantial areas at many locations in the country. These rocks consist predominantly of peridotite which has been serpentinized to some degree. Anarak and Nain are two ultramafic areas in Central Iran comprising about 180 and 270 km², respectively, located in a coloured melange zone. There is little information available regarding the geobotany and biogeochemistry of these areas. They have a dry climate, with low rainfall and high temperatures in summer which encourages mostly annual and perennial herbaceous types of plants. In this paper, we report a reconnaissance study of these two ultramafic areas of Iran. Soil analysis of total elements indicates that typical concentrations of Ni, Cr, Co, Mn, Fe, Mg and Ca are about 1500, 300, 75, 800, 45.000 150.000 and 2000 μg g^− 1, respectively. During this study 176 plant species were collected, belonging to 29 families. The species diversity at Anarak is more than at Nain, possibly due to microclimatic differences and a greater precipitation. The number of plants endemic to ultramafic soils of these two areas is very low. The herb Cleome heratensis (Capparaceae) appears to be an indicator of ultramafics in Central Iran. Populations of this plant cover quite extensive areas during summer and autumn when there is no rainfall. Analysis of the dry matter of the leaves of all plants collected did not reveal any hyperaccumulator of nickel or any other ‘serpentine’ metals. The ultramafic endemic plant C. heratensis contained low concentrations of all metals and thus it possesses exclusion mechanisms to restrict excessive metal uptake. The Mg/Ca ratio for some plants collected is high—up to 4.9. This initial survey suggests that a more complete investigation of the ultramafic areas of Iran would be valuable.     

不同方法下土壤重金属元素空问最大变异距离研究——以浙江上虞为例

从地质统计学和全域型空间自相关分析两种途径探讨浙江上虞市土壤重金属的空间变异情况。研究结果表明，空间分析法得到的上虞市重金属空间变程比地质统计学法得到的空间变程更为直观和稳定；但空间分析法的准确程度依赖于空间间隔的大小，不同的空间间隔计算量有很大的不同，随着间隔的逐渐减小，计算量成倍增加。地质统计学法能快速得到空间变程，还能推测空间变异程度，用优化的拟合模型得到的结果更为准确。     

黔西南炼山坡红土型金矿地质特征及找矿标志

简述了黔西南炼山坡红土型金矿的矿区地层与构造、分散流与次生晕的成果、矿体产出状态等矿床地质特征,并从成矿物质来源,地质构造,地形、地貌及古气候,红土化作用及元素的迁移与富集作用方面探讨其成矿地质条件,提出了找矿标志。     

桂西北地区锑矿地质特征及找矿标志探讨

桂西北地区是广西锑矿密集区,文章对区内锑矿床的地质特征、地球化学特征、矿体富集规律和找矿标志进行了分析和探讨。