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1.
Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.  相似文献   

2.
Summary. The transient and impulse responses (Green's function) for onedimensional wave propagation in a standard linear solid are calculated using a Laplace Transform method. The spectrum of relaxation times is chosen so as to model a constant Q medium within an absorption band covering a broad frequency range which may be chosen so as to include the seismic frequencies. The inverse transform may be evaluated asymptotically in the limit of very long propagation times using the saddle point method. For shorter propagation times the method of steepest descent may be modified so as to yield an accurate first motion approximation. The character of the small amplitude precursor to the large amplitude Visible' signal is investigated analytically. It is shown that the signal velocity is intermediate between the high-frequency ('unrelaxed') and the low-frequency ('relaxed') limits of the phase velocity.  相似文献   

3.
Summary. The Green's function, in a constant gradient medium, is derived for an explosive point source, in the frequency and the time domains. The analytical dynamic ray tracing (DRT) solution is rederived with conditions stated in Part I. The Gaussian beam (GB) solution is investigated. New beam parameters and conditions are defined. Comparisons between exact and approximate solutions are undertaken.
For both methods, DRT and GB, conditions of validity are explicit and quantitative. An accuracy criterion is defined in the time domain, and measures a global relative error. The range of validity is expressed in the form of two inequalities for the dynamic ray tracing method and of five inequalities for the Gaussian beam method. Results remain accurate at ray turning points. For the types of medium considered, the breakdown of the dynamic ray tracing method is smoother and better behaved than that of Gaussian beams. As examples, a vertical seismic profiling configuration, and a shallow earthquake are modelled, using Gaussian beams.  相似文献   

4.
官厅水库妫水地区土壤侵蚀较为严重。为控制妫水地区的土壤流失非点源污染,本文建立了一个参数较少、便于应用的分布式土壤侵蚀和泥沙输移子模型。该模型由USLE模型和泥沙输移模型组成。首先,本研究确定了USLE中各因子的计算公式,用该模型计算土壤流失。然后,将流域概化为河网,利用曾提出的应用于经Laplace变换和逆变换求得的一维水质迁移转化方程的解中的面积汇污系数和S曲线之间的关系,推导得到了分布式泥沙输移模型。最后,从妫水河流域土壤图、土地利用图中提取地理信息,以DEM为依据,研究了该模型在妫水河流域的应用。结果表明,该模型不仅可用于研究非点源泥沙污染,而且可用于研究流域内土壤侵蚀的空间分布,为实现农业最佳管理提供科学依据。妫水流域土壤流失主要来自坡度较大、地表植被覆盖差的丘陵和山地,控制土壤流失应该将重点放在该流域内的丘陵和山地上。  相似文献   

5.
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   

6.
A general correspondence principle is presented that relates any time-domain electromagnetic diffusion field to an electromagnetic wavefield in a 'corresponding' configuration. The principle applies to arbitrarily inhomogeneous and anisotropic media and arbitrary transmitters and receivers. For the correspondence between the two types of electromagnetic fields to hold, the electric conductivity in the diffusive case and the permittivity in the wavefield case should have the same spatial variation, while the permeability distributions in space in the two cases are to be identical. Essential steps in the derivation of the correspondence principle are the use of the time Laplace transformation of causal signals, taken at real, positive values of the transform parameter, the Schouten-Van der Pol theorem in the theory of the Laplace transformation, and the reliance upon Lerch's theorem of the uniqueness of the interrelation between causal field quantities and their time-Laplace-transform representations at real, positive values of the transform parameter. Correspondence is then established between the tensorial Green's functions in the two cases, where the Green's functions are the point-receiver responses (either electric or magnetic field) to point-transmitter excitations (either electric- or magnetic-current source).
Through the correspondence principle, all transient electromagnetic wavefields (where losses are neglected) have as a counterpart a transient diffusive electromagnetic field (where the electric displacement current is neglected). The interrelation yields the tool to compare quantitatively the potentialities of the two types of fields in transient electromagnetic geophysical prospecting.
Finally, a general medium-parameter scaling law for time-domain electromagnetic wavefields is presented.  相似文献   

7.
Summary. A simple dynamic model, based on the geometry of mantle divergence and thermal parameters controlling equilibrium size of the axial magma chamber, explains the variation in topography along mid-ocean ridges. Among morphological characters accounted for are: (1) the change from axial-valley to axial-high type ridge crests with increasing spreading rate, (2) the localized occurrence of deeps at ridge-transform intersections, and (3) the correlation of average transform spacing with spreading rate. The model also yields an explanation for anomalous ridge topography associated with oceanic hot spots. Incorporation of smaller-scale bathymetric and ophiolite data into this scheme permits construction of a comprehensive model of ocean crust accretion.  相似文献   

8.
李海龙 《盐湖研究》1995,3(3):70-73
定常态渠道法采集地下卤水［１］的过程可由一类拟线性椭圆型方程的定解问题来描述，该定解问题在区域内部的曲线（集卤渠）上满足等值面边界条件。在适当假设下该定解问题可简化为求一线性定解问题的非负解。本文给出了该非负解存在唯一的充分条件。  相似文献   

9.
Summary. The Radon transform or slant stack is becoming a widely used technique for analysing high-quality reflection and refraction data. The transform normally used is applicable to data from a line source in a plane model, that is, one Cartesian coordinate. The theoretical basis for the Radon transform pair for one Cartesian coordinate has appeared in the seismological literature. For a point source in plane or spherical geometry, or a line source in cylindrical geometry only the Radon transform for the direct problem (computation of synthetic seismograms) has been published. To analyse data an approximate inverse transform has been used. In this research note, the exact forms of the generalized Radon transform pairs are completed for a point source in plane or spherical geometry, and for a line source in cylindrical geometry. The differences will be important if the waveforms are being interpreted, and are most significant for near-vertical reflections—the type of data most commonly slant stacked.  相似文献   

10.
We present a new numerical method to describe the internal dynamics of planetary mantles through the coupling of a dynamic model with the prediction of geoid and surface topography. Our tool is based on the simulation of thermal convection with variable viscosity in a spherical shell with a finite-volume formulation. The grid mesh is based on the 'cubed sphere' technique that divides the shell into six identical blocks. An investigation of various numerical advection schemes is proposed: we opted for a high-resolution, flux-limiter method. Benchmarks of thermal convection are then presented on steady-state tetrahedral and cubic solutions and time-dependent cases with a good agreement with the few recent programs developed to solve this problem.
A dimensionless framework is proposed for the calculation of geoid and topography introducing two dimensionless numbers: such a formulation provides a good basis for the systematic study of the geoid and surface dynamic topography associated to the convection calculations. The evaluation of geoid and surface dynamic topography from the gridded data is performed in the spectral domain. The flow solver is then tested extensively against a precise spectral program, producing response functions for geoid as well as bottom and surface topographies. For a grid mesh of a reasonable size (6 × 64 × 64 × 64) a very good agreement (to within ∼1 per cent) is found up to spherical harmonic degree 15.  相似文献   

11.
As an alternative to finite element or finite difference modelling, analytical solutions are derived by the method of Laplace transformation and numerical results obtained for several models of the bottom hole temperature stabilization. Included in the models are the finite circulation time, the thermal property contrast between the borehole mud and the surrounding formation, and the presence of radial or lateral fluid flow in the formation, all of which are found to have significant effects on the dissipation of the thermal disturbance induced by drilling.
The mud circulation is considered to have the effect of either maintaining the borehole mud at a constant temperature or supplying a constant amount of heat per unit length per unit time to the borehole. For small circulation times, the former reduces to the 'zero circulation' model in which the mud circulation creates an instantaneous temperature anomaly at the hole bottom; for small borehole radii, the latter reduces to the line source model and the traditional 'Homer plot'.
For typical drilling operations in which the bottom hole temperatures are measured several hours to several tens of hours after the hole is shut in, the new models generally predict higher equilibrium formation temperatures than does the Horner plot. However, predictions from the various models converge if the BHTs are taken after the hole has been shut in for a period which is greater than about five times the circulation period.  相似文献   

12.
The vibration of a fluid-filled crack is considered to be one of the most plausible source mechanisms for the long-period events and volcanic tremors occurring around volcanoes. As a tool for the quantitative interpretation of source process of such volcanic seismic signals, we propose a method to numerically simulate the dynamic response of a fluid-filled crack. In this method, we formulate the motions of the fluid inside and the elastic solid outside of the crack, using boundary integrals in the frequency domain and solve the dynamic interactions between the fluid and the elastic solid using the point collocation method. The present method is more efficient compared with the time-domain finite difference method, which has been used in simulations of a fluid-filled crack and enables us to study the dynamics of a fluid-filled crack over a wide range of physical parameters. The method also allows us direct calculation of the attenuation quality factor of the crack resonance, which is an indispensable parameter for estimating the properties of the fluid inside the crack. The method is also designed to be flexible to many applications, which may be encountered in volcano seismology, and thus, extensions of the method to more complicated problems are promising.  相似文献   

13.
The seafloor topography of a slow-spreading ridge shows a number of well-documented regularities at the ridge segment scale as the result of the complex interplay between ridge-axis magmatic and tectonic processes. This paper describes the results of a detailed analysis of the seafloor topography of the Mid-Atlantic Ridge near the Atlantis transform, where marine gravity data provide independent, although non-unique, constraints on subseafloor density structure. Using a combined topography and gravity data set, we identified the specific contributions of subseafloor density structure to the seafloor topography. We show that the observed along-axis deepening (0.3–0.8 km) from the midpoint of a ridge segment towards the non-transform offsets in the study area can be explained by the vertical deflection of a zero-age plate in response to along-axis crustal thickness variations. However, this effect can only account for 50–60 per cent of the observed 1.5–1.7 km deepening towards the Atlantis transform, suggesting the presence of significant stresses in the lithosphere near a transform. Results of plate flexural calculations also predict a more elevated rift flank at the inside corner of the ridge–transform intersection than at the conjugate outside corner. Such an asymmetry in rift flank topography is calculated to be greatest near a transform fault with a significant volume of deep transform valley and when adjacent plates across the transform fault are mechanically decoupled or only weakly coupled. Together these results illustrate the complex interplay between various tectonic processes at a slow-spreading ridge.  相似文献   

14.
Summary. Factors influencing the seismic response characteristics of marine profiling systems are reviewed. The single frequency case is used to illustrate the influence of different frequencies on the response, as well as the towing depths of the source and receiver, and the geometry of a linear receiving array. The more realistic case of band-limited source waveforms is considered, using frequency spectra calculated from theoretically derived airgun signals. The results show that the number and shape of sidelobes of the profiling system response, as well as the filtering characteristics for reflections arising from reflectors in the vertical plane perpendicular to the axis of the receiver array are determined by the depths of the source and receiver and the relative amplitudes of the frequencies in the source waveform. These factors, along with the configuration of the hydrophone elements in the receiver array, determine the frequency and amplitude attenuation of reflections in the vertical plane containing the receiver array.
The filtering characteristics of the system both in and out of the vertical plane containing the receiver array are discussed, with implications for discriminating between off-axis and in-plane reflections. A plan view of the response of the system is constructed in the time domain for various profiling configurations and sources of different frequency content at a given time. This example shows how useful the resulting pictures are for optimizing acquisition parameters in profiling experiments.  相似文献   

15.
New remote sensing techniques, such as airborne laser scanning (LiDAR), have led to a dramatic increase in terrain information, providing new opportunities for landform analysis. A major advance in using LiDAR‐derived high‐resolution topography (HRT) is the capability to provide an accurate and detailed terrain morphology. This study aims to use LiDAR HRT to identify palaeochannels of the Manawatu River (New Zealand) using an automated procedure based on the statistical analysis of landform curvature. The approach can provide rapid assessment and classification of floodplain topography. The proposed analysis is crucial, especially for intensively used floodplains requiring effective flood management and mitigation.  相似文献   

16.
Summary. Simple and convenient formulae are derived which describe the transformation of a multipolar expansion under an arbitrary proper rotation of the reference frame. When combined with the corresponding formulae for a translation, these results show how multipolar representations of source fields transform under any proper displacement of the reference frame. Particular emphasis is placed on the seismic source problem; however, these results find applications in many other physical problems.  相似文献   

17.
Planetary topography can either be modelled as a load supported by the lithosphere, or as a dynamic effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However, local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this paper, we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. While being constrained by the static assumption, degree-one loads can deform the shell and generate stresses. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.  相似文献   

18.
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   

19.
Summary. The usual asymptotic methods used to correct the high-frequency solutions of the wave equation are unsatisfactory as they do not give the low-frequency, partial reflections expected from a region of high velocity gradient. A new iterative solution is obtained which uses the first term of the Langer asymptotic expansion as the zeroth iterate. This satisfactorily gives the partial reflections from a region of high velocity gradient, even when they are generated near the turning point of the ray. Although the results are somewhat complicated in the frequency domain, in the time domain all types of wave interaction are described by six universal time functions. For any problem, these functions are scaled in time according to the depth of the interaction, and in strength according to the magnitude of the coupling parameter. Numerical results and approximations are given for these functions. Coupling parameters are investigated for acoustic and elastic waves in a plane model, and acoustic and elastic-gravitational waves in a spherical model. The same universal time functions allow the excitation of elastic waves to be studied when the source is in a region of high velocity gradient or is near the wave's turning point. Results are given for a moment tensor, point source in plane and spherical models.  相似文献   

20.
summary . A formulation is given for the seismic-wave scattering by a rough solid—liquid interface, in analogy to results derived for a solid—solid interface and a heterogeneous volume. Using Kennett's approach and the reciprocity theorem, the scattering is formulated as the excitation by an equivalent dislocation. Using interface parameters relevant to the core—mantle boundary (CMB), computational results for several types of body-wave scattering are given and compared to scattering by a heterogeneous volume. In an application to the generation of PKP precursors it is concluded that, whereas some data groups point to heterogeneity (which may not be small) in the lower mantle above CMB, in other cases a rough CMB may be considered equally feasible. Scattering at the source or receiver side of the core by both a slightly rough CMB (radial variations up to a few hundred metres) and a slightly heterogeneous lower mantle (relative variations in physical parameters up to a few per cent) produces the energy level that is observed in most of the PKP precursors; also the relevant scale lengths of variation are about the same ie both mechanisms (10–20 km with possibly somewhat higher values at relatively long epicentral distances).  相似文献   

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