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1.
Analytical approach for the toroidal relaxation of viscoelastic earth   总被引：1，自引：0，他引：1  
This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.  相似文献   

2.
For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the complex-image expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields.  相似文献   

3.
The mode-matching method is used to obtain an exact analytical solution to the problem of B -polarization induction in two adjacent thin half-sheets, lying on a conducting layer that is terminated by a perfect conductor at finite depth. These components of the model represent, respectively, the Earth's conducting surface layers, crust, and mantle. In dimensionless variables, the model has three independent parameters, these being the two thin-sheet conductances and the layer thickness. The mode-matching solution obtained in this paper is shown to be identical lo that derived via the Wiener-Hopf method in a companion paper (Dawson 1996), and so provides additional verification of that solution. As was shown in the companion paper, the solution for the present model contains, as special limiting cases, those for three models considered earlier by various authors. The second part of the present paper addresses the solutions for the electric fields in the non-conducting half-space above the conductors, which represents the atmosphere. In the final part, sample numerical calculations are presented to illustrate the solution.  相似文献   

4.
We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.  相似文献   

5.
The Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo & Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.
Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series.  相似文献   

6.
We present an adaptive unstructured triangular grid finite element approach for effectively simulating plane-wave diffusive electromagnetic fields in 2-D conductivity structures.
The most striking advantage of irregular grids is their potential to incorporate arbitrary geometries including surface and seafloor topography. Adaptive mesh refinement strategies using an a posteriori error estimator yield most efficient numerical solutions since meshes are only refined where required.
We demonstrate the robustness of this approach by comparison with analytical solutions and previously published numerical simulations. Maximum errors may systematically be reduced to, for example, 0.8 per cent for the apparent resistivity and 0.2° in the phase.
An additional accuracy study of the thickness of the air layer in E-polarization suggests to keep a minimum thickness depending on lateral conductivity contrasts within the earth.
Furthermore, we point out the new quality and flexibility of our simulation technique by addressing two marine magnetotelluric applications. In the first case, we discuss topographic effects associated with a synthetic sinusoidal sea bottom model and in the second case, we show a close-to-reality scenario using real bathymetry data from the East Pacific Rise at 17°S.  相似文献   

7.
Summary. A new method is proposed for the geopotential field computation and gravitational attraction modelling. The usual method is to use a uniform density discrete numerical integration to represent either the gravitational potential or the gravitational attraction from a given density configuration. In this paper, an interpolation scheme is explained, using a piecewise continuous basis function to represent the arbitrarily varying density configuration in one, two and three dimensions. This new approach greatly simplifies the potential integrations and, in certain cases where symmetry exists, analytical evaluation of the integrals is also possible. Numerical tests and examples are given for a hypothetical salt dome, a vertical dyke with varying density structure and the hydrostatic ellipticity of earth model 1066B. The numerical error in this method is limited to the analytical approximation and interpolation errors in each case. This new approach can also be used as efficiently for other potential field studies.  相似文献   

8.
We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.  相似文献   

9.
The eikonal equation is the equation of the phase slowness surface for isotropic and anisotropic media. In general anisotropic media, there is no simple explicit expression for the phase slowness surface. An approximate expression of the eikonal equation may be obtained in weakly anisotropic media. In orthorhombic media, the approximate eikonal equation of the qP wave is the sum of an ellipsoidal form and a more complicated term. The ellipsoidal form corresponds to what we call ellipsoidal anisotropy. Ray equations written in the Hamiltonian formulation are characteristics of the eikonal equation. Ray perturbation theory may be used to compute changes in ray paths and physical attributes (traveltime, polarization, amplitude) due to changes in the medium with respect to a reference medium. Examples obtained in homogeneous orthorhombic media show that a reference medium with ellipsoidal anisotropy is a better choice to develop the perturbation approach than an isotropic reference medium. Models with strong anisotropy can be considered. The comparison with results obtained by an exact ray program shows a relative traveltime error of less than 0.5 per cent for a model with relatively strong anisotropy. We propose a finite element approach in which the medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, using a perturbation approach, analytical expressions for rays and traveltimes are obtained Ray tracing reduces to connecting these analytical solutions at the vertices of the cells.  相似文献   

10.
We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method.
  Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately.
  Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.  相似文献   

11.
Summary. The Wiener—Hopf technique is used to obtain an exact analytical solution for the problem of H -polarization induction over the edge of a perfectly conducting thin sheet, representing an ocean, electrically connected to a perfectly conducting mantle through a slab of finite conductivity and thickness, which represents the Earths crust. It is shown that the induced currents resulting from this type of induction process are drawn up into the sea from the cust and mantle with the greatest concentration of current near the ocean edge. The surface impedance over the land surface, is calculated for various mantle depths and is shown to increase sharply as the coastline is approached. The magnetic field along the ocean floor is also plotted as a function of distance from the coastline, and the results are found to agree very well with those calculated previously by approximate and numerical methods.  相似文献   

12.
The development of interoperable environmental process models is widely supported by both the research community and government agencies. This paper discusses a conceptual framework to guide the delineation of process components, the basic unit of interoperable models. The concepts of semantic reference system and dual hierarchy are explored to establish the conceptual framework. Based on this discussion, the Formal Concept Analysis is used as an analytical approach to decompose and fuse existing environmental process models in order to identify environmental process components. For purposes of discussion, a hydrological process, surface runoff, is used throughout the paper as an example of an environmental process to support the conceptual discussion and to illustrate the application of the conceptual framework and analytical approach.  相似文献   

13.
The characteristics of a reflected spherical wave at a free surface are investigated by numerical methods; in particular, the polarization angles and amplitude coefficients of a reflected spherical wave are studied. The classical case of the reflection of a plane P wave from a free surface is revisited in order to establish our terminology, and the classical results are recast in a way which is more suited for the study undertaken. The polarization angle of a plane P wave, for a given angle of incidence, is shown to be 90° minus twice the angle of reflection of the reflected S wave. For a Poisson's ratio less than 1/3, there is a non-normal incident angle for which both amplification coefficients are 2 precisely; for this incident angle the direction of the particle motion at the free surface is also the direction of the incident wave. For a wave emanating from a spherical source, the polarization angle, for all angles of incidence, is always less than, or equal to, the polarization angle of a plane P wave. The vector amplification coefficient of a spherical wave, for all angles of incidence, is always greater than the vector amplification coefficient of a plane P wave. As expected, the results for a spherical wave approach the results for a plane P wave in the far field. Furthermore, there was a good agreement between the theoretical modelling and the numerical modelling using the dynamic finite element method (DFEM).  相似文献   

14.
Participatory approaches elicit information from multiple stakeholders while planning and implementing resource management systems. Such elicited information is often associated with significant variability. Public participation geographical information science (GIS) (PP-GIS) solutions can reduce this variability by helping stakeholders to measure the factors involved and provide the elicited information. We propose a ‘Quality Function Deployment’-based participatory framework for developing such PP-GIS solutions. It is demonstrated using a case study to enhance an existing PP-GIS into a solution for rainwater harvesting systems in Indian villages. The novelty of the proposed framework is that it identifies metrics and carries out comparative analysis of three existing solutions: participatory rural appraisal, participatory mapping and PP-GIS. In the case study, PP-GIS scored less than participatory mapping as it scored less on usability and affordability. To improve PP-GIS in these aspects, an easy-to-use mobile and web based, free and open source PP-GIS solution, Watershed GIS, was developed. It scored better than the three existing solutions and its usage resulted in substantial reduction of variability in criteria values and thus better ranking of alternatives, with the average coefficient of variation decreasing from 0.12 to 0.05.  相似文献   

15.
b
In this paper, we apply the boundary element method (BEM) to the 2-D steady state heat flow problem of what would be the perturbation to the regional temperature gradient, and hence heat flow density, determined from temperatures measured in a borehole that passes close to, but does not penetrate, a body of anomalous thermal properties. This type of problem with an infinity boundary is particularly well suited to the BEM.
The results have been compared with those obtained from analytical solutions for bodies of simple shape; it is found that for the worst case of a close approach to a boundary of small radius of curvature, a numerical modelling error of less than 1 per cent can still be obtained provided the length of each element is less than the shortest distance between the calculation point and the object.  相似文献   

16.
We examine the issue concerning the determination of the line of demarcation between geomorphology and the related Earth sciences which is associated with elementarization of continual topographic surface of the planet’s relief. We present our view of the progression along this direction that relies on the theory of the system-morphological foundation of Earth sciences. We established the existence of the synenergy effect in the use of the system-morphological approach in all particular geographical sciences: in microclimatology, it provides a means of referencing microclimates and “local climates” to topographic features; in soil science, it revitalizes the notion of an elementary soil area thus simplifying the process of soil mapping. In geobotany and biogeocenology, this approach helps to make results from studying phytocenose productivity and from dendroindication investigations more representative. We determined a direct practical importance of landscape geophysics and assessments of the significance of geotopes on land surface as well as on the bottom of the World Ocean and beneath mainland glaciers. It is suggested that the system-morphological approach be used in the interests of a further development not only of traditional analytical geomorphology but also its new, synthetic direction that relates geomorphology with social sciences. It is established that in such a case the symmetry tools can be sued to define the relief as the set of locations with anthropogenic objects, processes and phenomena.  相似文献   

17.
While the business intelligence sector, involving data warehouses and online analytical processing (OLAP) technologies, is experiencing strong growth in the IT marketplace, relatively little attention has been devoted to the problem of utilizing such tools in conjunction with GIS. This study contributes to the development of this research area by examining the issues involved in the design and implementation of an integrated data warehouse and GIS system that delivers analytical OLAP and mapping results in real‐time across the Web. The case study chosen utilizes individual records from the US 1880 population census, which have recently been made available by the North Atlantic Population Project. Although historical datasets of this kind present a number of challenges for data warehousing, the results indicate that the integrated approach adopted offers a much more flexible and powerful analytical methodology for this kind of large social science dataset than has hitherto been available.  相似文献   

18.
We present an improved method for computing polarization attributes of particle motion from multicomponent seismic recordings in the time–frequency domain by using the continuous wavelet transform. This method is based on the analysis of the covariance matrix. We use an approximate analytical formula to compute the elements of the covariance matrix for a time window which is derived from an averaged instantaneous frequency of the multicomponent record. The length of the time-window is automatically and adaptively set to match the dominant period of the analysing wavelet at each time–frequency point. Then the eigenparameters are estimated for each time–frequency point without interpolation. With these key features, our method provides a suitable approach for polarization analysis of dispersive signals or overlapping seismic arrivals in multicomponent seismic data. For polarization analysis in the time domain, we show that the proposed method is consistent with existing polarization analysis methods. We apply the method to real data sets from exploration and earthquake seismology to illustrate some filtering applications and wave type characterizations.  相似文献   

19.
Assessing urban vulnerability to natural hazards such as earthquakes can be regarded as an ill-structured problem (i.e. a problem for which there is no unique, identifiable, objectively optimal solution). A review of the literature indicates a number of contrasting definitions of what vulnerability means, as well as numerous conflicting perspectives on what should or should not be included within the broad assessment of vulnerability in cities. This paper reports on the findings from a project in which a GIS methodology has been developed to assess urban vulnerability through a spatial analytical procedure. First, we highlight the deficiencies of current GIS approaches to urban vulnerability analysis and discuss the ill-structured nature of the vulnerability problem. We then propose a working definition for vulnerability assessment in which vulnerability is thought of as a spatial decision problem under the conditions of uncertainty. Next, we present a methodology to incorporate this definition into a GIS framework that combines elements from the techniques of spatial multicriteria analysis and fuzzy logic. The application of this methodology is then illustrated with a case study from Los Angeles County. The results suggest that the proposed methodology may provide a new approach for analyzing vulnerability that can add to our understanding of human/hazards interaction.  相似文献   

20.
The interpretation of geodetic data in volcanic areas is usually based on analytical deformation models. Although numerical finite element (FE) modelling allows realistic features such as topography and crustal heterogeneities to be included, the technique is not computationally convenient for solving inverse problems using classical methods. In this paper, we develop a general tool to perform inversions of geodetic data by means of 3-D FE models. The forward model is a library of numerical displacement solutions, where each entry of the library is the surface displacement due to a single stress component applied to an element of the grid. The final solution is a weighted combination of the six stress components applied to a single element-source. The pre-computed forward models are implemented in a global search algorithm, followed by an appraisal of the sampled solutions. After providing extended testing, we apply the method to model the 1993–1997 inflation phase at Mt Etna, documented by GPS and EDM measurements. We consider four different forward libraries, computed in models characterized by homogeneous/heterogeneous medium and flat/topographic free surface. Our results suggest that the elastic heterogeneities of the medium can significantly alter the position of the inferred source, while the topography has minor effect.  相似文献   

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