Detecting Stochastic Behaviour and Scaling Laws in Time Series of Geomagnetic Daily Means

—We use advanced methods to extract quantitative time dynamics from geomagnetic signals. In particular we analyse daily geomagnetic time series measured at three stations in Norway. The dynamics of geomagnetic measurements has been investigated using autoregressive models. The procedure is based on two forecasting approaches: the global autoregressive approximation and the local autoregressive approximation. The first technique views the data as a realisation of a linear stochastic process, whereas the second considers them as a realisation of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a strong test to discriminate between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical system governing the phenomena is characterised by a stochastic dynamics, and the process could be described by numerous degrees of freedom. We also investigated the kind of stochasticity of the geomagnetic signals, analysing the power spectrum density. We identify a power law P(?)∝?^-α, with the scaling exponent α which is a typical fingerprint of irregular processes. In this analysis we use the Higuchi method, which presents an interesting relationship between the fractal dimension D and the spectral power law scaling index α.     

Complexity

It is difficult to define complexity in modeling. Complexity is often associated with uncertainty since modeling uncertainty is an intrinsically difficult task. However, modeling uncertainty does not require, necessarily, complex models, in the sense of a model requiring an unmanageable number of degrees of freedom to characterize the aquifer. The relationship between complexity, uncertainty, heterogeneity, and stochastic modeling is not simple. Aquifer models should be able to quantify the uncertainty of their predictions, which can be done using stochastic models that produce heterogeneous realizations of aquifer parameters. This is the type of complexity addressed in this article.     

地球系统模拟和混沌时间序列

地球系统是非线性的系统.为了模拟地球系统,我们就必须了解非线性科学的最新进展.本文从非线性科学角度论述了地球系统模拟中的几个关键问题,如尺度是分层次的,不同尺度之间存在着相似性及标度律,同时也存在差异性及非均匀性.为此还介绍了一些概念:吸引子、分维、信息和熵等.最后本文还说明如何从地球系统中所观测到的时间序列取得地球系统模拟所需要的信息.     

Statistical Variability and Tokunaga Branching of Aftershock Sequences Utilizing BASS Model Simulations

Aftershock statistics provide a wealth of data that can be used to better understand earthquake physics. Aftershocks satisfy scale-invariant Gutenberg–Richter (GR) frequency–magnitude statistics. They also satisfy Omori’s law for power-law seismicity rate decay and Båth’s law for maximum-magnitude scaling. The branching aftershock sequence (BASS) model, which is the scale-invariant limit of the epidemic-type aftershock sequence model (ETAS), uses these scaling laws to generate synthetic aftershock sequences. One objective of this paper is to show that the branching process in these models satisfies Tokunaga branching statistics. Tokunaga branching statistics were originally developed for drainage networks and have been subsequently shown to be valid in many other applications associated with complex phenomena. Specifically, these are characteristic of a universality class in statistical physics associated with diffusion-limited aggregation. We first present a deterministic version of the BASS model and show that it satisfies the Tokunaga side-branching statistics. We then show that a fully stochastic BASS simulation gives similar results. We also study foreshock statistics using our BASS simulations. We show that the frequency–magnitude statistics in BASS simulations scale as the exponential of the magnitude difference between the mainshock and the foreshock, inverse GR scaling. We also show that the rate of foreshock occurrence in BASS simulations decays inversely with the time difference between foreshock and mainshock, an inverse Omori scaling. Both inverse scaling laws have been previously introduced empirically to explain observed foreshock statistics. Observations have demonstrated both of these scaling relations to be valid, consistent with our simulations. ETAS simulations, in general, do not generate Båth’s law and do not generate inverse GR scaling.     

Optimal vibration abatement of mechanical systems

In this paper, a method is presented for forced vibration suppression of multi-degree-of-freedom systems with damping. The technique pursued in this investigation is based on applying control forces at a certain number of the system's degrees of freedom. The problem is organized as an unconstrained, non-linear optimization formulation so that the peak vibration amplitudes of a certain number of degrees of freedom would be minimized. An efficient mathematical programming algorithm is used to solve this optimization problem numerically. It will be shown that the scheme illustrated in this paper is remarkably effective in reducing the vibration of the system. In particular, the vibration amplitudes at selected degrees of freedom may be diminished substantially.     

A primer on upscaling tools for porous media

Over the last few decades a number of powerful approaches have been developed to intelligently reduce the number of degrees of freedom in very complex heterogeneous environs, e.g. mathematical homogenization, mixture and hybrid mixture theory, spatial averaging, moment methods, central limit or Martingale methods, stochastic-convective approaches, various other Eulerian and Lagrangian perturbation schemes, projection operators, renormalization group techniques, variational approaches, space transformational methods, continuous time random walks, and etc. In this article we briefly review many of these approaches as applied to specific examples in the hydrologic sciences.     

Simulation of spatial and temporal properties of aftershocks by means of the fiber bundle model

The rupture processes of any heterogeneous material constitute a complex physical problem. Earthquake aftershocks show temporal and spatial behaviors which are consequence of the heterogeneous stress distribution and multiple rupturing following the main shock. This process is difficult to model deterministically due to the number of parameters and physical conditions, which are largely unknown. In order to shed light on the minimum requirements for the generation of aftershock clusters, in this study, we perform a simulation of the main features of such a complex process by means of a fiber bundle (FB) type model. The FB model has been widely used to analyze the fracture process in heterogeneous materials. It is a simple but powerful tool that allows modeling the main characteristics of a medium such as the brittle shallow crust of the earth. In this work, we incorporate spatial properties, such as the Coulomb stress change pattern, which help simulate observed characteristics of aftershock sequences. In particular, we introduce a parameter (P) that controls the probability of spatial distribution of initial loads. Also, we use a “conservation” parameter (π), which accounts for the load dissipation of the system, and demonstrate its influence on the simulated spatio-temporal patterns. Based on numerical results, we find that P has to be in the range 0.06 < P < 0.30, whilst π needs to be limited by a very narrow range (0.60 < π < 0.66) in order to reproduce aftershocks pattern characteristics which resemble those of observed sequences. This means that the system requires a small difference in the spatial distribution of initial stress, and a very particular fraction of load transfer in order to generate realistic aftershocks.     

A computational procedure for the implementation of equivalent linearization in finite element analysis

This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE‐analysis to evaluate non‐linear structural response under random excitation. A computational procedure is presented which requires the non‐linear part of the system to be subdivided into suitable sub‐domains (elements). Each element is independently linearized using only a minimum number of co‐ordinates. A local co‐ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non‐linear constitutive laws are defined by the local co‐ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE‐models. To illustrate the applicability of the procedure, two different non‐linear systems are analysed under bi‐directional earthquake excitation. Copyright © 2000 John Wiley & Sons, Ltd.     

Analytic scaling laws in planetary dynamo models

ABSTRACT

Numerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed.     

Frequency‐domain waveform modelling and inversion for coupled media using a symmetric impedance matrix

To simulate the seismic signals that are obtained in a marine environment, a coupled system of both acoustic and elastic wave equations is solved. The acoustic wave equation for the fluid region simulates the pressure field while minimizing the number of degrees of freedom of the impedance matrix, and the elastic wave equation for the solid region simulates several elastic events, such as shear waves and surface waves. Moreover, by combining this coupled approach with the waveform inversion technique, the elastic properties of the earth can be inverted using the pressure data obtained from the acoustic region. However, in contrast to the pure acoustic and elastic cases, the complex impedance matrix for the coupled media does not have a symmetric form because of the boundary (continuity) condition at the interface between the acoustic and elastic elements. In this study, we propose a manipulation scheme that makes the complex impedance matrix for acoustic–elastic coupled media to take a symmetric form. Using the proposed symmetric matrix, forward and backward wavefields are identical to those generated by the conventional approach; thus, we do not lose any accuracy in the waveform inversion results. However, to solve the modified symmetric matrix, LDLT factorization is used instead of LU factorization for a matrix of the same size; this method can mitigate issues related to severe memory insufficiency and long computation times, particularly for large‐scale problems.     

Aftershock Statistics

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Båths law for the magnitude of the largest aftershock, and (3) the modified Omoris law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Båths law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omoris law.     

有限断层震源全局参数定标律的稳定性

根据eQuake-RC网站及相关文献,建立了383个地震全局参数的数据集,与二十多年中3篇参考文献先后发表的震源全局参数及其定标律统计结果比较,讨论了定标律的稳定性。虽然数据量大大增加,尤其是高震级数据增加更显著,震级范围扩大,不同年代的全局参数与矩震级域数据点的分布大多重叠,新补充的数据往往分布在以往数据分布的延伸方向上。区分两类地震、三种破裂类型、五(三)个震级段统计全局参数定标律,与3篇参考文献的结果比较,期望值两两相对差别的特征相近,统计标准差有所减小,说明随数据增加全局参数定标律结果变化不大,总体趋于稳定。分4组比较、分析数据分布的区域特征,没有发现系统性差别,说明全球数据是可以一起统计的。板内地震和俯冲带地震分组的结果表明,震级范围不同,高震级段数据分布存在明显差异,宜分开统计。     

用广义协调元分析复合式多层无孔和开孔矩形薄板的振动

复合式多层无孔和开孔矩形薄板是桥梁结构和建筑等结构中的最重要的组成部分。当研究它们的振动问题时,用解析法求解自振频率十分困难,而采用通用的有限元法求解自由度数目多,收敛也比较慢。本文利用三角形薄板广义协调元分析了复合式多层四边简支、四边固定无孔和开孔矩形薄板的自由振动,求出了前几阶频率系数,其结果与用ANSYS软件算出的结果基本接近,当为单层无孔和开孔板时,与文献[8]的结果完全相同,且与文献[10]的解析解吻合较好,证明了本文理论推导及程序编制的正确性,表明广义协调元与有限元相比具有自由度少、精度高、程序简便以及收敛快等优点。     

Temporal scaling in river flow: can it be chaotic? / L’invariance d’échelle de l’écoulement fluvial peut-elle être chaotique?

Abstract

Abstract Identification of the presence of scaling in the river flow process has been a challenging problem in hydrology. Studies conducted thus far have viewed this problem essentially from a stochastic perspective, because the river flow process has traditionally been assumed to be a result of a very large number of variables. However, recent studies employing nonlinear deterministic and chaotic dynamic concepts have reported that the river flow process could also be the outcome of a deterministic system with only a few dominant variables. In the wake of such reports, a preliminary attempt is made in this study to investigate the type of scaling behaviour in the river flow process (i.e. chaotic or stochastic). The investigation is limited only to temporal scaling. Flow data of three different scales (daily, 5-day and 7-day) observed in each of three rivers in the USA: the Kentucky River in Kentucky, the Merced River in California and the Stillaguamish River in Washington, are analysed. It is assumed that the dynamic behaviour of the river flow process at these individual scales provides clues about the scaling behaviour between these scales. The correlation dimension is used as an indicator to distinguish between chaotic and stochastic behaviours. The results are mixed with regard to the type of flow behaviour at individual scales and, hence, to the type of scaling behaviour, as some data sets show chaotic behaviour while others show stochastic behaviour. They suggest that characterization (chaotic or stochastic) of river flow should be a necessary first step in any scaling study, as it could provide important information on the appropriate approach for data transformation purposes.     

Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation

Surface wave dispersion curve inversion is a challenging problem for linear inversion procedures due to its highly non-linear nature and to the large numbers of local minima and maxima of the objective function (multi-modality). In order to improve the reliability of the inversion results, we implemented and tested a two-step inversion scheme based on Genetic Algorithms (GAs). The proposed scheme performs several preliminary “parallel” runs (first step) and a final global run using the previously-determined fittest models as starting population.In this work we focus on the inversion of shear-wave velocity and layer thickness while fixing compressional-wave velocity and density according to user-defined Poisson's ratios and velocity–density relationship respectively. The procedure can nonetheless perform the inversion under different degrees of regularization, depending on the a priori information and the desired degree of freedom of the system.Thanks to the large number of considered models, in addition to the fittest model, a mean model and its accuracy are evaluated by means of a statistical approach based on the estimation of the Marginal Posterior Probability Density (MPPD).We tested the proposed GA-based inversion scheme on three synthetic models reproducing a complex structure with low-to-moderate velocity cover (also including a low-velocity channel) lying over hard bedrock. For all the considered cases the bedrock velocity and depth were properly identified, and velocity inversion was reconstructed with minor uncertainties.The performed tests also investigate the influence of the first higher mode, the reduction of the frequency range of the considered dispersion curve as well as the use of different number of strata. While a limited frequency range of the dispersion curve (maximum frequency reduced from 80 to 40 Hz) does not seem to significantly limit the accuracy of the retrieved model, the adoption of the correct number of strata and the addition of the first higher mode help better focus the final solution.In conclusion, the proposed approach represents an improvement of a purely GA-based optimization scheme and the MPPD-based mean model typically offers a more significant and precise solution than the fittest one.Results of the inversion performed on a field data set were validated by borehole stratigraphy.     

Application of bioassays in toxicological hazard, risk and impact assessments of dredged sediments

Given the potential environmental consequences of dumped dredged harbour sediments it is vital to establish the potential risks from exposure before disposal at sea. Currently, European legislation for disposal of contaminated sediments at sea is based on chemical analysis of a limited number of well-known contaminants for which maximum acceptable concentrations, action levels (ALs), have been set. The present paper addresses the issue of the applicability of in vitro and in vivo bioassays for hazard, risk and local impact assessment of dredged polluted sediments to be disposed of at sea. It discusses how and to what extent selected bioassays can fill in the gaps left open by chemical analysis and the way in which the bioassays may contribute to the present licensing system for disposal. Three different purposes for application were distinguished: the most basic application (A) is a rapid determination of the hazard (potential toxicity) of dredged sediments which is then compared to ALs in a licensing system. As with chemical analysis on whole sediment extracts, the bioavailability of the chemicals is not taken into account. As in vitro assays with sediment extracts are not sensitive to matrix effects, a selection of specific in vitro bioassays can be suitable fast and standardized additions for the licensing system. When the outcome of (A) does not convincingly demonstrate whether the sediment is clean enough or too polluted, further bioanalysis can help the decision making process (B). More aspects of the mostly unknown complex chemical mixtures are taken into account, including the bioavailability and chronic toxicity focusing on ecologically relevant endpoints. The ecotoxicological pressure imposed by the dredged sediments can be quantified as the potentially affected fraction (PAF) based on chemical or biological analysis of levels of contaminants in sediment or biota. To validate the predicted risk, the actual impact of dumped harbour sediments on local ecosystems (C) can be determined using a dedicated set of in vitro and in vivo bioassays as well as bio-indicators selected based on the information obtained from (A) and (B) and on the characteristics of the local ecosystem. Conversely, the local sediment impact assessment (C) can direct fine-tuning of the selection of chemical and bioassay analyses and for setting safe levels in the licensing system. It is concluded that in vitro and in vivo bioassays and biological indicators are useful tools in the process of hazard, ecotoxicological risk and impact assessment of dredged harbour sediments, provided they are consciously chosen and quality criteria for assay performance are defined.     

医用CT在三维椭球颗粒随机堆积结构研究中的应用

颗粒随机堆积问题是物理和工程领域的热门问题。椭球颗粒随机堆积体系作为球形体系的拓展,增加了旋转自由度,从而表现出更复杂的性质,由于椭球颗粒比球形颗粒更类似于自然界中普遍存在的非规则颗粒,因此其研究具有重要的实用价值。研究三维颗粒堆积结构问题一般需要CT成像技术,本文介绍了如何利用医用CT对三维椭球随机堆积体系进行成像研究的技术细节,包括如何通过图像处理的方法获取椭球颗粒的空间位置、取向和体积,如何利用接触数标度函数拟合的方法得到近邻颗粒间的接触信息等。本文的研究内容和方法为利用各种X射线CT成像方法研究三维颗粒体系提供了技术参考。      

Response spectrum-oriented pulse identification and magnitude scaling of forward directivity pulses in near-fault ground motions

This paper presents a novel approach to identify the pulse-like motions in earthquake recordings that dominate the maximum structural responses over a wide period range. The identification method is based on the congruence relationship between the response spectrum and the dimensionless П-response spectrum established in this study through straightforward dimensional arguments of linear and bilinear SDOF oscillators subject to pulse-like ground motions. By evaluating the geometric match and dislocations of the П-response spectrum of a given waveform with the dimensional response spectrum in bi-logarithm plotting, one can identify the simple pulses and their parameters that match simultaneously the kinematic characteristics and the response spectrum of earthquake recordings that exhibit pulse-like features. The developed pulse identification method has been implemented in a computer program and applied successfully to detect the pulse-like motions in the PEER NGA strong motion database. Both velocity and acceleration pulses potentially due to forward directivity effects in near fault regions are identified. The identified velocity pulses show strong correlation with the seismological parameters. They are subsequently used in regression analysis to derive the empirical scaling laws that relate the directivity pulse parameters to the earthquake magnitude and rupture distance. The study confirms some magnitude scaling laws in literature and demonstrates the accuracy and efficiency of the proposed pulse identification method.     

Upscaling geochemical reaction rates using pore-scale network modeling

Geochemical reaction rate laws are often measured using crushed minerals in well-mixed laboratory systems that are designed to eliminate mass transport limitations. Such rate laws are often used directly in reactive transport models to predict the reaction and transport of chemical species in consolidated porous media found in subsurface environments. Due to the inherent heterogeneities of porous media, such use of lab-measured rate laws may introduce errors, leading to a need to develop methods for upscaling reaction rates. In this work, we present a methodology for using pore-scale network modeling to investigate scaling effects in geochemical reaction rates. The reactive transport processes are simulated at the pore scale, accounting for heterogeneities of both physical and mineral properties. Mass balance principles are then used to calculate reaction rates at the continuum scale. To examine the scaling behavior of reaction kinetics, these continuum-scale rates from the network model are compared to the rates calculated by directly using laboratory-measured reaction rate laws and ignoring pore-scale heterogeneities. In this work, this methodology is demonstrated by upscaling anorthite and kaolinite reaction rates under simulation conditions relevant to geological CO₂ sequestration. Simulation results show that under conditions with CO₂ present at high concentrations, pore-scale concentrations of reactive species and reaction rates vary spatially by orders of magnitude, and the scaling effect is significant. With a much smaller CO₂ concentration, the scaling effect is relatively small. These results indicate that the increased acidity associated with geological sequestration can generate conditions for which proper scaling tools are yet to be developed. This work demonstrates the use of pore-scale network modeling as a valuable research tool for examining upscaling of geochemical kinetics. The pore-scale model allows the effects of pore-scale heterogeneities to be integrated into system behavior at multiple scales, thereby identifying important factors that contribute to the scaling effect.     

Optimum segmentation of simple objects in high-resolution remote sensing imagery in coastal areas

The optimum segmentation of ground objects in a landscape is essential for interpretation of high-resolution remotely sensed imagery and detection of objects; and it is also a technical foundation to efficiently use spatial information in remote sensing imagery. Landscapes are complex system composed of a large number of heterogeneous components. There are many explicit homogeneous image objects that have similar spectral character and yet differ from surrounding objects in high-resolution remote sensing imagery. Thereby, a new concept of Distinctive Feature of fractal is put forward and used in deriving Distinctive Feature curve of fractal evolution in multiscale segmentation. Through distinguishing the extremum condition of Distinctive Feature curve and the inclusion relationship of fractals in multiscale representation the Scalar Order is built. This can help to determinate the optimum scale in image segmentation for simple-objects, and the potential meaningful image-object fitting the intrinsic scale of the dominant landscape object can be obtained. Based on the application in high-resolution remote sensing imagery in coastal areas, a satisfactory result was acquired.