共查询到20条相似文献，搜索用时 109 毫秒
1.
Simon A. Mathias 《Ground water》2010,48(3):438-441
When seeking to predict plume geometry resulting from fluid injection through partially penetrating wells, it is common to assume a steady-state spherically diverging flow field. In reality, the flow field is transient. The steady-flow assumption is likely to cause overestimation of injection plume radius since the accommodation of fluid by increases in porosity and fluid density is ignored. In this paper, a transient solution is developed, resulting in a nonlinear ordinary differential equation expressing plume radius as a function of time. It is shown that the problem can be fully described by one type curve. A critical time, tc, is identified at which the percentage error of the steady-state flow solution compared to the fully dynamic problem is less than 1%. Only for large injection rates and low permeabilities, does tc become greater than 1 h. Nevertheless, an improved approximate solution is obtained by a simple linearization procedure. The critical time, tc for the new approximate solution is 0.3% of that required for the steady-state flow solution. 相似文献
2.
YU Jinhai & ZHANG Chuanding . Institute of Geodesy Geophysics of Chinese Academy of Sciences Wuhan China . Zhengzhou Information Engineering University Zhengzhou China 《中国科学D辑(英文版)》2005,48(3):398-405
Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy… 相似文献
3.
In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)2, where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C1 or C ≥ C1, where C1 is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C1 as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C. 相似文献
4.
Sarva Jit Singh 《Pure and Applied Geophysics》1967,67(1):83-94
Summary The problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c
0(1 +m z) wherem is a constant andc
0 is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem. 相似文献
5.
Abstract The problem of the removal of the degeneracy of the patterns of convective motion in a spherically symmetric fluid shell by the effects of rotation is considered. It is shown that the axisymmetric solution is preferred in sufficiently thick shells where the minimum Rayleigh number corresponds to degree l = 1 of the spherical harmonics. In all cases with l > 1 the solution described by sectional spherical harmonics Yl l (θ,φ) is preferred. 相似文献
6.
An inverse problem is one in which the parameters of a model are determined from measured seismic data. Important to the solution of inverse problems is the issue of whether or not a solution exists. In this paper we show, in a constructive manner, that a solution does exist to the specific inverse problem of determining the parameters of a horizontally stratified, lossless, isotropic and homogeneous layered system that is excited by a non-normal incidence (NNI) plane wave. Mode conversion between P- and S-waves is included. We develop a seven-step layer-recursive procedure for determining all of the parameters for layer j. These parameters are P-wave and S-wave velocities and angles of incidence, density, thickness, traveltimes, and reflection- and transmission-coefficient matrices. Downward continuation of data from the top of one layer to the top of the next lower layer is an important step in our procedure, just as it is in normal incidence (NI) inversion. We show that, in order to compute all parameters of layer j, we need to (and can) compute some parameters for layer j+ 1. This is a non-causal phenomenon that seems to be necessary in NNI inversion but is not present in NI inversion. 相似文献
7.
A. J. W. DUIJNDAM 《Geophysical Prospecting》1988,36(8):899-918
A parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters. The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non-linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two-parameter inverse problem. 相似文献
8.
J. H. Cushman B. X. Hu 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(4):297-302
A recursive perturbation solution to the eulerian transport problem for a conservative solute in a random conductivity field
is reported. The stochastic concentration is given to arbitrary order inσ
ν, the variance of fluctuating velocity. The result gives the stochastic concentration as a perturbation to the deterministic
concentration for constant mean flow. The closed form solution is easy to implement numerically via FFT. 相似文献
9.
David E. Dougherty 《Advances in water resources》1985,8(4):201-209
An unconditionally stable explicit time integrator has recently been developed for parabolic systems of equations. This rational Runge Kutta (RRK) method, proposed by Wambecq1 and Hairer2, has been applied by Liu et al.3 to linear heat conduction problems in a time-partitioned solution context. An important practical question is whether the method has application for the solution of (nearly) hyperbolic equations as well.In this paper the RRK method is applied to a nonlinear heat conduction problem, the advection-diffusion equation, and the hyperbolic Buckley-Leverett problem. The method is, indeed, found to be unconditionally stable for the linear heat conduction problem and performs satisfactorily for the nonlinear heat flow case. A heuristic limitation on the utility of RRK for the advection-diffusion equation arises in the Courant number; for the second-order accurate one-step two-stage RRK method, a limiting Courant number of 2 applies. First order upwinding is not as effective when used with RRK as with Euler one-step methods. The method is found to perform poorly for the Buckley-Leverett problem. 相似文献
10.
We consider how to treat a finite-dimensional linear inverse problem when the form of the forward problem is known exactly, but is dependent upon some parameters whose exact value is uncertain and which enter the forward problem multiplicatively. We show one way to proceed when the uncertainty is treatable in a statistical manner. Predicting the secular variation ∂tB(t) produced by a particular fluid flow V at the core-mantle boundary (when magnetic diffusion is ignored) is one such example, because the results depend on the main magnetic field B(t) originating in the core which is improperly known because of contamination by the crustal magnetic field. This infinite-dimensional inverse problem is often solved by projection on to a finite-dimensional basis, and the resulting parameters found by a maximum likelihood technique. If the main field is contaminated with errors from a Gaussian distribution, this paper describes how the maximum likelihood solution can take this into account, and we show the probability density function that must be maximised in this case. We give an example of the effects for a simple model system, and suggest possible areas of application. 相似文献
11.
Antonín Zeman 《Studia Geophysica et Geodaetica》1991,35(2):75-80
Summary The problem of the constant part of the tidal field is still topical in view of the recommendations of IAG[1, 2] to eliminate the tidal effect of external masses from all geodetic measurements under preservation of the effect of the time-constant tidal deformation of the Earth. The paper discusses the consequences of accepting this recommendation for normal heights, and suggests a solution based on the new definition of the normal gravity field[3]. 相似文献
12.
13.
The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J
2 and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W
o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers. 相似文献
14.
The optimal scaling problem for the time t(L × L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L × L) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our
theoretical deductions are corroborated by California seismicity with magnitude M ≥ 2. In other words, the population of waiting time distributions for L = 10–100 km provides positive information on the multifractal nature of seismicity, which impedes the population to be converted
into a unified law by scaling. This study is a follow-up of our analysis of power/unified laws for seismicity (see Pure and
Applied Geophysics 162 (2005), 1135 and GJI 162 (2005), 899). 相似文献
15.
Abstract The stability of a plane parallel shear flow with the profile U(z) = tanh z is considered in a rotating system with the axis of rotation in the z-direction. The establishment of the basic flow requires a baroclinic state, but baroclinic effects are suppressed in the stability analysis by assuming a limit of high thermal conductivity. It is shown that the strongest growing disturbance changes from a purely transverse form in the limit of vanishing rotation rate to a nearly longitudinal form as the angular velocity of rotation increases. An analytical solution of the stability equation is obtained for vanishing growth rates of the transverse form of the instability. But, in general, the solution of the problem requires numerical integrations which demonstrate that the preferred direction of the wave vector of the instability is towards the left of the direction of the mean flow. 相似文献
16.
Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5]. 相似文献
17.
Numerical electromagnetic modeling by the finite-difference or finite-element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial-and-error. 相似文献
18.
Alexander Ruzmaikin Anvar Shukurov Dmitry Sokoloff Sergey Starchenko 《地球物理与天体物理流体动力学》2013,107(1-3):125-139
Abstract We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema. The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified. Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability using comparisons with complementary asymptotic expansions and numerical simulations. In particular, this justifies application of the MEGA solutions to estimation of the generation threshold. 相似文献
19.
C. H. Chapman 《Pure and Applied Geophysics》1972,94(1):233-247
Summary In a recent paper,Gupta [5]2) re-examined the significance of leaking modes in Lamb's problem (Lamb [7]). In this paper, we present a brief review of the exact Cagniard-de Hoop solution to this problem, and use these results to examine the question of the leaking mode in more detail. The leaking mode may either cause a separate arrival,P, or influence the shape of other arrivals e.g.SpS. We have attempted to clarify and extend previous results and correct misconceptions which have appeared elsewhere and, therefore, most of this discussion is tutorial in nature. 相似文献
20.
Ivan N. Totomanov 《Journal of Geodynamics》1987,8(2-4)
An experiment is described dealing with the detailed mapping of the vertical velocity V of recent crustal movements in the central Danubian riverside region of the Moesian platform in Northern Bulgaria. The error in V being significant here, the problem of statistical control on the reliability of the initial data and results of such studies is investigated; this question is also relevant for other platform regions in Eastern and Central Europe. With the aim of assessing the significance of a movement, the sampling distribution of V is used. The problem is reduced to a checking of a standard statistical hypothesis and to a probabilistic characterization of V. In order to estimate the statistical significance of the relative velocity δV between neighbouring benchmarks, the distribution of the module G of the horizontal gradient of V is studied. An agreement between the sampling distribution obtained and the theoretical Weibull distribution is established. A sufficiently high probability P>86% is determined for the significance of δV in this region and an optimal interval of the isobases is suggested. The experiment itself embraces three variant solutions: independent mapping of V, independent mapping of G, and mapping of V with respect to G. The analysis and comparison of the results obtained demonstrate the high efficiency of the third solution. 相似文献