Determination of the phase projection of a dynamic system from strain field observations

The paper analyzes the possibility of extracting a geophysical field component from a time series considered as a phase projection of a dynamic system. Based on model calculations, the method of averaging of phase trajectories is shown to be applicable for the recovery of time variations of a dynamic system and more reliable determination of its quantitative characteristics if the variations are superimposed by a high-dimension process (a purely random process) and a low-dimension process (linear interpolation). The analysis of the extraction of dynamic system variations from strain records obtained at various points of seismically active regions of China provided the following estimates of dynamic parameters: the phase space dimension is m = 5–7, and the correlation dimension varies, depending on the observation point, within the range d ₂ = 2.6–3.5.     

Parameters of the response of the volumetric strain field to the external acting processes

It is necessary to widen the registration amplitude range by controlling the influence factors on different time scales in order to analyze the properties of the dynamic system, forming the observed data of different-nature geophysical fields. The data on the volumetric strain variations, obtained in the scope of the PBO project (Parkfield, California), make it possible to construct the correct regression model for the external influence tidal and baric factors, as well as for the precipitation factor. The specific features of separation of the deformation components caused by the external sources, including the relation between the baric and tidal influences and the additional component reflecting the deformation process internal dynamics, are considered. The precipitation cumulative series has been considered in order to remove seasonal variations in the time range T ≤ 10 days. The estimated error of the amplitudes, determined based on the proposed component method, proved to be close to the initial data accuracy. An inhomogeneous complex structure of the geological environment in the zone adjacent to the San Andreas fault could be responsible for the difference in the character of the deformation processes and the response to the external influences at the considered observation points.     

Results of cosmic ray monitoring with a multichannel complex

We describe a method for monitoring geophysical (atmospheric and magnetospheric) parameters on the basis of cosmic rays (CR). The method is based on the principle of multichannel synchronous recording of all secondary components of CR in the energy range from a few to 200 GeV. The geophysical parameters are found from solving a system of equations for CR variations. The results of CR monitoring using a multichannel observation complex for the period from January, 2004 are considered.     

纬向平均区域臭氧层动力学系统的反演及其研究

根据观测的O3总量场序列资料反演区域系统的非线性演化方程,采用自然正交分解方法,由空间函数构造相空间正交基,将时间函数（主成分）嵌入对应于系统状态变量,计算得到O3层系统的分数维D2＝2．9,说明它属于低自由度的混饨动力学系统．主成分的时间尺度层次特征,反映了O3层的各种动力行为,它们是动力学系统再现的集合,用于反演动力学方程可描述不同层次扰动的约束及相互作用的性质,刻画出系统的演化形态．为研究系统成分的内在关系,在三维和四维相空间中分别建立动力学方程。通过对比分析,两者描述O3层动力行为的差异表现在较低层次的系统成分中,表明在系统成分相互作用过程中高层次对低层次信息的不完全确定性。     

Petrophysics and mineral exploration: a workflow for data analysis and a new interpretation framework

As mineral exploration seeks deeper targets, there will be a greater reliance on geophysical data and a better understanding of the geological meaning of the responses will be required, and this must be achieved with less geological control from drilling. Also, exploring based on the mineral system concept requires particular understanding of geophysical responses associated with altered rocks. Where petrophysical datasets of adequate sample size and measurement quality are available, physical properties show complex variations, reflecting the combined effects of various geological processes. Large datasets, analysed as populations, are required to understand the variations. We recommend the display of petrophysical data as frequency histograms because the nature of the data distribution is easily seen with this form of display. A petrophysical dataset commonly contains a combination of overlapping sub-populations, influenced by different geological factors. To understand the geological controls on physical properties in hard rock environments, it is necessary to analyse the petrophysical data not only in terms of the properties of different rock types. It is also necessary to consider the effects of processes such as alteration, weathering, metamorphism and strain, and variables such as porosity and stratigraphy. To address this complexity requires that much more supporting geological information be acquired than in current practice. The widespread availability of field portable instruments means quantitative geochemical and mineralogical data can now be readily acquired, making it unnecessary to rely primarily on categorical rock classification schemes. The petrophysical data can be combined with geochemical, petrological and mineralogical data to derive explanations for observed physical property variations based not only on rigorous rock classification methods, but also in combination with quantitative estimates of alteration and weathering. To understand how geological processes will affect different physical properties, it is useful to define three end-member forms of behaviour. Bulk behaviour depends on the physical properties of the dominant mineral components. Density and, to a lesser extent, seismic velocity show such behaviour. Grain and texture behaviour occur when minor components of the rock are the dominate controls on its physical properties. Grain size and shape control grain properties, and for texture properties the relative positions of these grains are also important. Magnetic and electrical properties behave in this fashion. Thinking in terms of how geological processes change the key characteristics of the major and minor mineralogical components allows the resulting changes in physical properties to be understood and anticipated.     

Dimension of the phase space of a dynamic system from geophysical data

The possibility of determining parameters of complex geophysical processes is considered in terms of nonlinear dynamics. In accordance with modern approaches in the theory of nonlinear dynamic systems, the number of independent parameters controlling the behavior of a nonlinear system can be estimated from the available time realization of only one of these parameters. Model calculations showed that the dimension of the phase space of a dynamic system can be estimated from a sample of one variable. Experimental data on variations in the apparent electric resistivity (AER) and the relative vertical movement of the surface (RVMS) in a seismically active region are analyzed and the dimension of the dynamic system determining its behavior in the phase space is estimated. The resulting estimates of the embedding dimension m = 7?8 for AER variations and m = 6 for RVMS variations possibly characterize the complexity of the dynamic system describing the given fields. The method presented in the paper is also applied to the analysis of the degree of connectivity of different dynamic systems and their parameters. By the connectivity we mean the number of independent parameters simultaneously involved in the formation of the dynamic behavior of various physical fields. The model estimates demonstrate the possibility of such an approach. It is shown that variations in the AER in perpendicular directions are described by a general system of dynamic equations, whereas dynamic systems controlling the AER field and the RVMSs are interconnected only partially. The resulting dimension m = 12 estimated for the AER-RVMS system provides an estimate for the number of common controlling parameters: n = (8 + 6)?12 = 2. The methods and results presented in the paper are applicable to the construction of models of complex geophysical processes and the development and the development of new approaches and methods of identification of prognostic characteristics for the behavior of physical fields of various origins.     

Nonlinear dynamics of level variations in the Caspian Sea

Caspian Sea level variations, which have several equilibrium states, are studied by the methods of the theory of nonlinear dynamic systems. Normal monthly values of sea level according to data collected at Makhachkala gauge from 1900 to 2000 are considered. The diagnostic characteristics of dynamic chaos are used to show that sea level variations have some properties of series with chaotic behavior. A model of level variations in the Caspian Sea, comprising a system of water balance equations for the sea basin, the dynamics of river runoff, and water balance of the sea itself, is proposed. Equation of a nonlinear oscillator is derived and shown to have solutions with chaotic regimes at some combinations of parameters.     

Wavelet-Aggregated Signal in Earthquake Prediction

The concept of aggregated signal is introduced. Quantitatively, an aggregated signal can be defined as the scalar signal: it accumulates in its own variations only those spectral components that are presented simultaneously in each scalar time series of the multidimensional signal to be analyzed. Moreover, an algorithm of aggregation is proposed to suppress the spectral components that are present in any of the scalar components but absent in others (these components can be called local disturbance signals, for instance of technogenic nature). The main purpose of constructing the aggregated signal is to make clearer the common tendency of low-frequency data-flow in geophysical networks, which indicates an increase in collective behavior.It is known that almost all models of the process of earthquake preparation have pointed out an increase in collective behavior of components of geophysical fields in the region of preparation when the coming geocatastrophe has entered its long- and mid-term stages. Long     

地球物理信号能量(密度)多维分形及应用

地球物理信号代表的地质地球物理过程在多种尺度上和尺度之间表现为自相似性（self-affinity)或尺度无关性（Scale Invariant)，称为地球物理信号的分形性质，多个分形地球物理信号叠加在一起表现为多维分形特征，研究多维分形地球物理信号的能量或能量密度特征，可以进行时间或空间地球物理信号的校正、奇异性研究分析，或进行不同地球物理动力学过程的分解，本文描述了地球物理时间（空间）信号的多维分形过程和功率谱密度（能量密度）与波数以及重磁场能谱密度及面积（能量）与能谱密度的多维分形关系，并用地球物理测井与重磁资料作了试算。     

强震地面运动的混沌特性分析

引入非线性动力学理论和混沌时间序列分析方法考察强震地面运动加速度时程的非线性特征。首先采用功率谱分析法、主成份分析法和Cao方法定性判断地震动加速度时程具有混沌特性,然后应用混沌时间序列分析方法定量计算了30条地震动加速度时程的三个非线性特征参数。计算表明,这些地震动时程的关联维数为2．0～4．0的分数维,Kolmogorov熵K2为大于零的有限正值,最大Lyapunov指数在o～i．0之间。结果说明,强震地面运动具有混沌特性,地震动的高度不规则和复杂性是地震过程强非线性的反映。     

美国中东部地震台阵波场的三分量波形梯度

波形梯度法是一种全新的台阵数据处理技术,该方法利用子台阵中的波形差异可以得到一些基本的地震波传播参数.本文首次将其应用于美国中东部地震台阵面波的三分量研究当中.首先通过垂向分量的面波进行波形梯度分析,得到垂直分量面波的相速度、传播方向、几何扩散和辐射花样.再通过垂向分量得到的传播方向进行坐标旋转,从而得到了径向分量以及切向分量的面波,再将其应用于波形梯度分析,分别得到径向分量以及切向分量面波的相速度、传播方向、几何扩散和辐射花样.利用2012年8月27日发生在中美洲西海岸地震事件的三分量地震数据的面波波形得到的结果显示,在相同周期,研究区域的三个分量面波的相速度分布横向差异显著.切向分量面波的相速度分布特征差异较大,可能是由于径向各向异性造成的.三个分量的传播方向变化都不大,且切向分量的传播方向变化大于垂直分量与径向分量,说明地震波的切线分量在传播过程中受到的影响更大,同时还可以看出传播方向的变化呈现出条带状的特征.几何扩散和辐射花样都是与地震波的振幅项有关的信息,三个分量的几何扩散特征基本一致.但是由于切向分量传播方向变化相对较大,可能导致了切向分量面波的辐射花样有所差异.     

空间自相似性与地球物理和地球化学场的分解方法

场的分解是应用勘查地球物理和地球化学数据所必不可少的数理处理工作，这项工作往往是为了分解不同的场来研究和了解不同的地质以及相应的地质过程，比如划分不同岩石类型以及识别和圈定矿化蚀变睡.闰定地质过程所产生的同类型的地质体并不简单地对应于相同的场值和频率，场的分布特征往往还与地质体的几何形态，。埋藏深度以及与其周围地质体的相对差异有关。然而，由于地质过程往往具有多期次和空间相关性等特点，所产生的地质体或者相应的场往往会呈现空间自相似性或统计自相似性。这种自相似性可以帮助分解不同地质过程所产生的同类地质体，文中所介绍的多重分形（multifractal)滤波方法（S－A）根据场的能谱分布的不同空间自相似性形成不规则甚至分形滤波器，并将场分解为不同同的组份，如局部异常和背景场，应用该方法对多处地球化学和地球物理场的处理结果表明，该方法对区分与矿有关的局部异常与背景场是很有效的，对加拿大NOVA SCOTIA省西南部航空放射性铀钍钾（U-Tn-K)数据处理所分解的异常对反映岩体中与铀－钨－锡（U－W－Sn)矿化有关的围岩饰变具有明显的效果。     

The gravitational potential and its derivatives of a right rectangular prism with depth-dependent density following an n-th degree polynomial

The direct gravity problem and its solution belong to the basis of the gravimetry. The solutions of this problem are well known for wide class of the source bodies with the constant density contrast. The non-uniform density approximation leads to the relatively complicated mathematical formalism. The analytical solutions for this type of sources are rare and currently these bodies are very useful in the gravimetrical modeling. The solution for the vertical component of the gravitational attraction vector for the 3D right rectangular prism is known in the geophysical literature for the density variations described by the 3-rd degree polynomial. We generalized this solution for an n-th degree, not only for the vertical component, but for the horizontal components, the second-order derivatives and the potential as well. The 2D modifications of all given formulae are presented, too. The presented general solutions, which involve a hypergeometric functions, can be used as they are, or as an auxiliary tool to derive desired solution for the given degree of the density polynomial as a sum of the elementary functions. The pros-and-cons of these approaches (the complexity of the programming codes, runtimes) are discussed, too.     

Influence of water pressure dynamics and fluid flow on the streaming‐potential response for unsaturated conditions

Streaming‐potentials are produced by electrokinetic effects in relation to fluid flow and are used for geophysical prospecting. The aim of this study is to model streaming potential measurements for unsaturated conditions using an empirical approach. A conceptual model is applied to streaming potential measurements obtained from two drainage experiments in sand. The streaming potential data presented here show a non‐monotonous behaviour with increasing water saturation, following a pattern that cannot be predicted by existing models. A model involving quasi‐static and dynamic components is proposed to reproduce the streaming potential measurements. The dynamic component is based on the first time derivative of the driving pore pressure. The influence of this component is investigated with respect to fluid velocity, which is very different between the two experiments. The results demonstrate that the dynamic component is predominant at the onset of drainage in experiments with the slowest water flow. On the other hand, its influence appears to vanish with increasing drainage velocity. Our results suggest that fluid flow and water distribution at the pore scale have an important influence on the streaming potential response for unsaturated conditions. We propose to explain this specific streaming potential response in terms of the behaviour of both rock/water interface and water/air interfaces created during desaturation processes. The water/air interfaces are negatively charged, as also observed in the case of water/rock interfaces. Both the surface area and the flow velocity across these interfaces are thought to contribute to the non‐monotonous behaviour of the streaming potential coefficient as well as the variations in its amplitude. The non‐monotonous behaviour of air/water interfaces created during the flow was highlighted as it was measured and modelled by studies published in the literature. The streaming potential coefficient can increase to about 10 to 40 when water saturation decreases. Such an increase is possible if the amount of water/air interfaces is increased in sufficient amount, which can be the case.     

Interpretation of VLF Resistivity Data for Ground Water Contamination Surveys

Very low frequency (VLF) military communications systems provide a primary field that can be used for shallow geophysical surveys to locate ground water contamination and vertical geologic contacts. Useful properties that can be easily obtained from the interaction of the earth and the primary field are the magnitude of the vertical secondary magnetic field, the surface impedence, and the phase angle between the electrical and magnetic horizontal components. The variations in the secondary magnetic field can be related to vertical geologic contacts, such as the edges of landfill trenches. The surface impedence yields an apparent terrain conductivity, which can be used to locate low-resistivity anomalies often associated with contaminated ground water. The phase angle gives information on vertical variations in resistivity, phase angles less than 45° indicating increasing resistivity with depth. The depth of penetration of the VLF field is about one skin depth. For a frequency of 20 kHz, the skin depth in meters is approximately equal to 3.67 where p is terrain resistivity in ohmmeters.     

Seismic response of floor-anchored nonstructural components fastened with yielding elements

Failure of nonstructural components during an earthquake can lead to structure functionality loss, cause widespread property damage, and pose a life-safety threat to the occupants. Current code provisions for floor-anchored components aim to minimize the life safety threat by specifying lateral force demands and anchoring requirements. These code requirements are based on a simplified equation that does not fully consider the contribution of the attachment to the overall component dynamic response. Previous results from shaking-table tests of anchored components suggest that the component attachment is an important parameter that determines its dynamic properties. For this study, a nonstructural experimental model was attached via several attachment designs to a concrete slab and tested on a shaking table to evaluate this contribution. The attachments were dimensioned based on a capacity design approach, such that they would be the weakest element in the force path while providing a yielding mechanism. The attachment designs provide different plastic mechanisms that control the displacement ductility in the response of the component. This paper focuses on the contribution of the attachment to the dynamic response and seismic force demand on the component. The experimental results demonstrate that the selected attachment properties govern the boundary conditions of the nonstructural component and strongly influence its dynamic response. The more flexible attachments sustained large deformations, leading to tensile membrane action and enhanced tensile strength in the attachments. Consequently, the ductile attachments did not result in reduced seismic loads in the nonstructural components.     

Characteristics of a Dynamic System of Geophysical Fields on Different Time Scales

Izvestiya, Physics of the Solid Earth - The paper presents the results of estimating the parameters of the dynamic systems of observed variations in different types of geophysical fields based on...     

On estimation of high frequency geophysical signals in Earth rotation by complex demodulation

Polar motion and UT1 contain small geophysical signals (<0.1 milliarcsecond) driven by the daily cycle in the solar heating. These signals are either irregular or quasi-harmonic therefore need to be expressed by the time series and studied using the time domain techniques. This work is focused on the complex demodulation method which seems to be particularly useful for studying high frequency geophysical signals in Earth rotation. After general introduction of the method and its properties, we describe its application for modeling diurnal and subdiurnal components of polar motion and UT1 and of the corresponding excitation functions. We also derive dynamical equations which can be used for direct comparison of the signals demodulated from the Earth rotation and geophysical excitation data.     

Characterization of Individual Rock Magnetic Components by Analysis of Remanence Curves, 1. Unmixing Natural Sediments

Natural sediments are a complex mixture of magnetic minerals with different origins and different geochemical history, each of which is called a magnetic component. Magnetic components practically never occur in isolated form, and their characterization using bulk magnetic measurements relies on the individuation of the systematic variation of some parameters within a large group of samples. These variations can be interpreted either as a mixing trend or as the result of natural processes, which affect the physical and chemical properties of the magnetic particles. An alternative approach is offered by the analysis of magnetization curves using model functions, which are supposed to represent the magnetic properties of individual components. The success of this approach relies on (1) the choice of model functions that can reproduce the natural properties of a component with sufficient accuracy by varying a minimum number of parameters and (2) on very precise and accurate measurements, which are necessary to overcome the extreme sensitivity of the method to noise. In this paper, the analysis of remanent magnetization curves proposed by Egli (2003) is applied to a large set of representative sediments from the most variable environments and to a set of artificial magnetite samples. Despite the variety of materials and natural processes involved in the formation of these sediments, seven groups of magnetic components with well-defined and consistent properties could be identified. It has been found that both lacustrine and marine sediments contain two magnetically distinct groups of magnetosomes, which react differently to changes of the redox potential. The effects of some natural processes, such as weathering, reductive dissolution and transport could be observed on the individual components.