Continuum Fractal Mechanics of the Earth’s Crust

— In the cases when the Earth’s crust possesses self-similar structure its mechanical behaviour can be modelled by a continuous sequence of continua each determined by the size of the averaging volume element. It is shown that tensorial properties and integral state variables scale by power laws with exponents common for all components of the tensors. Thus the scaling is always isotropic with anisotropy accounted for by the prefactors. As an example, scaling laws for effective moduli of the Earth’s crust with self-similar cracking are derived for the cases of isotropic distribution of disk-like cracks and two mutually orthogonal sets of 2-D cracks. Real systems are not self-similar therefore the proposed approach is based on their approximation by self-similar systems. A necessary condition is formulated for such an approximation.     

Nutrient Budgets,Dynamics and Storm Effects in a Eutrophic,Stratified Baltic Lake

Between 1989 and 1998 the small eutrophic stratified Lake Belau was investigated intensively and multidisciplinarily. This article is a short, comprehensive summary and re‐evaluation of the hydrochemistry of the lake, with focus on nitrogen and phosphorus. In several aspects the lake can be regarded as a typical example of the glacial north German lakes. The 1960's and 1970's are characterised by heavy nutrient inputs and fast eutrophication. During the last two decades the external nutrient load, especially the phosphorus load into Lake Belau was significantly reduced. But phosphorus‐rich sediments and large areas with summerly anoxic sediment surface conditions cause intensive release of phosphorus from older deeper sediment layers. Annual budgets reveal that despite an average sediment accumulation of 3 mm a^?1 the lake has lost its function as net phosphorus sink and it is very likely that internal eutrophication by the sediments will keep the lake in its eutrophic state during the next decades. Despite that, monthly budgets of five vertical layers show that the main phosphorus supplier for the phosphorus depleted epilimnion during summer is the creek Alte Schwentine. The annual nitrogen budget indicates groundwater and interflow water as well as atmospheric input as additional important nitrogen sources. 36% (98 μmol m ^?2 h^?1 N) of all nitrogen input is lost to atmosphere mainly due to denitrification. The example of a heavy storm shows that about 10% of the annual nitrogen loss to the atmosphere can take place during a single day and in form of ammonia. The storm further made obvious that these unpredictable events can have strong impact on nutrient cycling and ecology in Lake Belau and the lake can become an unexpected nutrient source for downstream systems.     

水温分层型水库铁、锰垂直分布特征

贵阳市主要饮用水源地阿哈水库系水温分层型季节性缺氧水库,由于沉积物含高浓度Ｆｅ,Ｍｎ至使库水受到污染,经多年测定不同季节２０ｍ深垂直水柱结果表明,Ｆｅ,Ｍｎ分布随着季节变化,水库水温分层而变化,呈现明显的垂直分布规律,高浓度Ｆｅ,Ｍｎ主要出现在水温分层期水库中,下层,与库底缺氧,ＰＨ下降沉积物浓度Ｆｅ,Ｍｎ释放造成的二次污染等密切相关,从而为自来水厂实施优化分层取水和污染控制提供了依据。     

The oxygen cycle and a habitable Earth

As an important contributor to the habitability of our planet, the oxygen cycle is interconnected with the emergence and evolution of complex life and is also the basis to establish Earth system science. Investigating the global oxygen cycle provides valuable information on the evolution of the Earth system, the habitability of our planet in the geologic past, and the future of human life. Numerous investigations have expanded our knowledge of the oxygen cycle in the fields of geology,geochemistry, geobiology, and atmospheric science. However, these studies were conducted separately, which has led to onesided understandings of this critical scientific issue and an incomplete synthesis of the interactions between the different spheres of the Earth system. This review presents a five-sphere coupled model of the Earth system and clarifies the core position of the oxygen cycle in Earth system science. Based on previous research, this review comprehensively summarizes the evolution of the oxygen cycle in geological time, with a special focus on the Great Oxidation Event(GOE) and the mass extinctions, as well as the possible connections between the oxygen content and biological evolution. The possible links between the oxygen cycle and biodiversity in geologic history have profound implications for exploring the habitability of Earth in history and guiding the future of humanity. Since the Anthropocene, anthropogenic activities have gradually steered the Earth system away from its established trajectory and had a powerful impact on the oxygen cycle. The human-induced disturbance of the global oxygen cycle, if not controlled, could greatly reduce the habitability of our planet.     

Theory of Basin Scale Dynamics of a Stratified Rotating Fluid

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.     

一个令人振奋的新创举--地球镜

美国国家科学基金会地球科学部与科学团体正在谱写一曲新的和令人振奋的、称为地球镜的乐章,它由一些现代化的地震和大地测量仪台阵组成,多数台阵集中在太平洋活动的大地构造带上和美国西部的北美板块边界上.沿圣安德烈斯断层帕克菲尔德地段布设的地球深部观测系统也将是这个观测镜的一部分.     

Estimation of Q p and Q s of Kinnaur Himalaya

The attenuation characteristics of the Kinnaur area of the North West Himalayas were studied using local earthquakes that occurred during 2008–2009. Most of the analyzed events are from the vicinity of the Panjal Thrust (PT) and South Tibetan Detachment Thrust, which are well-defined tectonic discontinuities in the Himalayas. The frequency-dependent attenuation of P and S waves was estimated using the extended coda normalization method. Data from 64 local earthquakes recorded at 10 broadband stations were used. The coda normalization of the spectral amplitudes of P and S waves was done at central frequencies of 1.5, 3, 6, 9, and 12 Hz. Q _p increases from about 58 at 1.5 Hz to 706 at 12 Hz, and Q _s increases from 105 at 1.5 Hz to 1,207 at 12 Hz. The results show that the quality factors for both P and S waves (Q _p and Q _s) increase as a function of frequency according to the relation Q?=?Q _o f ⁿ , where Q _o is the corresponding Q value at 1 Hz frequency and “n” is the frequency relation parameter. We obtained Q _p?=?(47?±?2)f ^(1.04±0.04) and Q _s?=?(86?±?4)f ^(0.96±0.03) by fitting power law dependency model for the estimated values of the entire study region. The Q ₀ and n values show that the region is seismically very active and the crust is highly heterogeneous. There was no systematic variation of values of Q _p and Q _s at different frequencies from one tectonic unit to another. As a consequence, average values of these parameters were obtained for each frequency for the entire region, and these were used for interpretation and for comparison with worldwide data. Q _p values lie within the range of values observed for some tectonically active regions of the world, whereas Q _s values were the lowest among the values compared for different parts of the world. Q _s/Q _p values were >1 for the entire range of frequencies studied. All these factors indicate that the crust is highly heterogeneous in the study region. The high Q _s/Q _p values also indicate that the region is partially saturated with fluids.     

Ptolemy, Babylon and the rotation of the Earth

John Steele finds that Ptolemy was right to believe that Babylonian observers saw the eclipse of 23 December 383 BC – which poses a problem that can be solved by invoking a large clock error or unusual atmospheric conditions.     

Tri-axiality of the Earth,the Moon and Mars

Summary Parameters defining the tri-axiality of the Earth, the Moon and Mars are discussed and up-to-date values recommended, as recently computed and submitted to the XVIIth IAG General Assembly (Canberra, December 1979).     

自重可压缩层状球体地球模型下地震变形算法的优化研究

本文利用龙格库塔法求解球坐标系下微分方程组, 基于自重、可压缩和连续分层地球模型研究地震引起的地球变形, 优化相关算法.首先对传统的两次同向积分法进行调整, 对微分方程的齐次部分进行两次相向积分, 分别由地心向上积分至震源和由地表向下积分至震源.接着利用震源间断条件求解震源上方和震源下方通解的组合系数, 得到微分方程组的解矢量.基于该积分方法可以避免高阶微分方程组求解中精度丢失的问题.接着与均质地球模型下微分方程组解析解的比较, 发现自重效应对走滑震源低阶求解结果的影响较大, 对垂直引张震源变形解y₄的影响超过100阶.最后比较了均质地球模型和层状地球模型下高阶求解结果, 发现两者的比值趋于稳定, 当均质地球模型参数设置为震源所在层参数时, 并且变形深度和震源处于模型同一层, 两种地球模型下高阶变形解的比值趋于1.基于该发现, 结合均质地球模型下渐近解, 可解决实际分层地球模型下震源附近地震变形发散的问题.

     

Fractal Seismicity and Seismic Risk

Izvestiya, Physics of the Solid Earth - Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches...     

Observing,Modeling, and Interpreting Magnetic Fields of the Solid Earth

Many Earth system processes generate magnetic fields, either primary magnetic fields or in response to other magnetic fields. The largest of these magnetic fields is due to the dynamo in the Earth’s core, and can be approximated by a geocentric axial dipole that has decayed by nearly 10% during the last 150 years. This is an order of magnitude faster than its natural decay time, a reflection of the growth of patches of reverse flux at the core–mantle boundary. The velocity of the North magnetic pole reached some 40 km/yr in 2001. This velocity is the highest recorded so far in the last two centuries. The second largest magnetic field in the solid Earth is caused by induced and remanent magnetization within the crust. Controlled in part by the thermo-mechanical properties of the crust, these fields contain signatures of tectonic processes currently active, and those active in the distant past. Recent work has included an estimate of the surface heat flux under the Antarctic ice cap. In order to understand the recent changes in the Earth’s magnetic field, new high-quality measurements are needed to continue those being made by Ørsted (launched in 1999), CHAMP and the Ørsted-2 experiment onboard SAC-C (both launched in 2000). The present paper is motivated by the advent of space surveys of the geomagnetic field, and illustrates how our way of observing, modeling, and interpreting the Earth’s magnetic field has changed in recent years due to the new magnetic satellite measurements.     

Upscaling: Effective Medium Theory, Numerical Methods and the Fractal Dream

Upscaling is a major issue regarding mechanical and transport properties of rocks. This paper examines three issues relative to upscaling. The first one is a brief overview of Effective Medium Theory (EMT), which is a key tool to predict average rock properties at a macroscopic scale in the case of a statistically homogeneous medium. EMT is of particular interest in the calculation of elastic properties. As discussed in this paper, EMT can thus provide a possible way to perform upscaling, although it is by no means the only one, and in particular it is irrelevant if the medium does not adhere to statistical homogeneity. This last circumstance is examined in part two of the paper. We focus on the example of constructing a hydrocarbon reservoir model. Such a construction is a required step in the process of making reasonable predictions for oil production. Taking into account rock permeability, lithological units and various structural discontinuities at different scales is part of this construction. The result is that stochastic reservoir models are built that rely on various numerical upscaling methods. These methods are reviewed. They provide techniques which make it possible to deal with upscaling on a general basis. Finally, a last case in which upscaling is trivial is considered in the third part of the paper. This is the fractal case. Fractal models have become popular precisely because they are free of the assumption of statistical homogeneity and yet do not involve numerical methods. It is suggested that using a physical criterion as a means to discriminate whether fractality is a dream or reality would be more satisfactory than relying on a limited data set alone.