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1.
The underpressure observed in the glacial valley Adventdalen at Svalbard is studied numerically with a basin model and analytically with a compartment model. The pressure equation used in the basin model, which accounts for underpressure generation, is derived from mass conservation of pore fluid and solid, in addition to constitutive equations. The compartment model is derived as a similar pressure equation, which is based on a simplified representation of the basin geometry. It is used to derive analytical expressions for the underpressure (overpressure) from a series of unloading (loading) intervals. The compartment model gives a characteristic time for underpressure generation of each interval, which tells when the pressure state is transient or stationary. The transient pressure is linear in time for short‐time spans compared to the characteristic time, and then it is proportional to the weight removed from the surface. We compare different contributions to the underpressure generation and find that porosity rebound from unloading is more important than the decompression of the pore fluid during unloading and the thermal contraction of the pore fluid during cooling of the subsurface. Our modelling shows that the unloading from the last deglaciation can explain the present day underpressure. The basin model simulates the subsurface pressure resulting from erosion and unloading in addition to the fluid flow driven by the topography. Basin modelling indicates that the mountains surrounding the valley are more important for the topographic‐driven flow in the aquifer than the recharging in the neighbour valley. The compartment model turns out to be useful to estimate the orders of magnitude for system properties like seal and aquifer permeabilities and decompaction coefficients, despite its geometric simplicity. We estimate that the DeGeerdalen aquifer cannot have a permeability that is higher than 1 · 10?18 m2, as otherwise, the fluid flow in the aquifer becomes dominated by topographic‐driven flow. The upper value for the seal permeability is estimated to be 1 · 10?20 m2, as higher values preclude the generation and preservation of underpressure. The porosity rebound is estimated to be <0.1% during the last deglaciation using a decompaction coefficient αr = 1 · 10?9 Pa?1.  相似文献   

2.
Summary . A two-space singular perturbation technique is employed to derive approximate governing equations for flow of a viscous heat-conducting fluid through a rigid porous solid. It is assumed that buoyancy forces are significant, and it is shown that standard approximations used in the study of flow through a porous medium are valid provided that Gr ≫ 1, where Gr is a Grashof number calculated using a typical pore radius as the length scale. Results previously derived in the literature for flow through an isotropic random array of spherical particles are used to show how the permeability and conductivity tensors can be calculated for a problem of interest in planetary science.  相似文献   

3.
A conservative staggered-grid finite difference method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994 ) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H , and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model ( Kuvshinov & Pankratov 1994 ), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres ( Martinec 1998 ).  相似文献   

4.
Volcanic rocks forming sills, dykes or lava flows may display a magnetic anisotropy derived from the viscous flow during their emplacement. We model a sill as a steady-state flow of a Bingham fluid, driven by a pressure gradient in a horizontal conduit. The magma velocity as a function of depth is calculated from the motion and constitutive equations. Vorticity and strain rate are determined for a reference system moving with the fluid. The angular velocity and the orientation of an ellipsoidal magnetic grain immersed in the fluid are calculated as functions of time or strain. Magnetic susceptibility is then calculated for a large number of grains with a uniform distribution of initial orientations. It is shown that the magnetic lineation oscillates in the vertical plane through the magma flow direction, and that the magnetic foliation plane changes periodically from horizontal to vertical. The results are compared with the magnetic fabric of Ferrar dolerite sills (Victoria Land, East Antarctica) derived from low-field susceptibility measurements.  相似文献   

5.
It is shown that the block LU decomposition of the transfer and scattering matrix convert these matrices into each other. This allows to introduce a generalization of the Kennett reflectivity method, which is applicable to arbitrary systems of linear differential equations. The introduced method is convenient to analyse equilibria, where the governing matrix is degenerate. The resulting algorithm is compact and numerically stable. To illustrate the concept, we consider elastic equilibrium of a layered medium. We also derive closed-form expressions for a quasi-stationary poroelastic case taking into account solid–fluid and electrokinetic coupling.  相似文献   

6.
Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.  相似文献   

7.
稳定渠道几何形态解析   总被引：1，自引：0，他引：1  
孙志林 《地理研究》1992,11(4):20-27
本文基于临界理论,同时引入合理的水流切应力表达式,建立起稳定渠道断面形态微分方程,据此获得断面曲线、过水面积及湿周的全部分析解。在此基础上,结合现有基本力学方程,严格从理论上导出稳定渠道的河相关系,并用实测资料作初步验证,结果较为满意。还运用积分中值定理给出断面宽度的另一形式的分析解,以便于水力计算中应用。  相似文献   

8.
The gravitational compaction of sediments is an important process in forward basin modelling. This paper presents a mathematical model for the one-dimensional compaction of an accreting layer of argillaceous sediments. Realistic constitutive laws for the clay compressibility and the clay permeability, based on soil mechanics tests, were incorporated into the model. The governing equations were put in dimensionless form and the extent of abnormal pore fluid pressure development was found to depend on the sedimentation parameter, a dimensionless group representing the ratio of the sediment hydraulic conductivity to the sediment accumulation rate. The effects of clay compressibility were studied and highly colloidal clays such as montmorillonite developed higher overpressures than less compressible materials. The results also showed that overpressuring developed in shales for cases in which the clay permeability did not go to zero in the limit of zero porosity. Linear models based on simplifying assumptions inappropriate for sedimentary basins were found to give significantly different estimates for the conditions leading to overpressuring. Using reasonable parameters, the model adequately reproduced porosity and pore pressure profiles measured in the sand-shale sequences of the South Caspian Sea.  相似文献   

9.
Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E y ) and magnetic ( H x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area.  相似文献   

10.
粘性泥石流阻力和运动方程验证分析   总被引：6，自引：2，他引：4  
周必凡 《山地学报》1999,17(1):55-58
现有的粘性泥石流阻力方程可以大致归纳为三类：一类是将泥石流视为固液两相流,通过理论分析建立的泥石流阻力运动方程;二类是认为粘性泥石流符合宾汉姆流体阻力方程;三类是依据泥石流体具有基本符合库伦公式的剪切强度,将泥石流视为固体颗粒散体重力流,在理论分析基础上建立的阻力和运动方程。用粘性泥石流动力学实验数据对三类阻力运动方程进行了验证,结果表明第三类阻力和运动方程与实际接近。  相似文献   

11.
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12.
泥石流颗粒组成的分形特征   总被引：5，自引：0，他引：5  
泥石流是主动的流域物质输移形式,土体的颗粒组成决定了泥石流的活动。不同地区、不同流域、不同密度的泥石流样本分析表明,高密度(如籽s>2g/cm3)泥石流的颗粒分布曲线总体上具有指数形式,指数呈现出显著的区域性差异。泥石流多发生在一定的指数区间;颗粒组成具有良好的分形特征,不同密度泥石流颗粒的分形区间不同,这个区间可以认为是形成泥石流结构的颗粒区间,从而也确定了泥石流基质的颗粒界限;颗粒的分维随密度变化,密度越大(大颗粒含量越多),分维越大。颗粒的分形结构也是颗粒孔隙的分形结构,它决定了土体的液化,因而也决定了泥石流所表现的特征。  相似文献   

13.
Summary. The statistical analysis necessary for isolating the between-site dispersion in palaeomagnetic studies is presented, both for the case of a common within-site precision and for variable within-site precision.
Approximate distributions are derived for all the relavant statistics. It is shown that if it is necessary to perform a two-tier analysis the overall true mean direction should be estimated as the mean of individual site mean directions and an equation for the semi-angle of the cone of confidence about this mean direction is derived.
The last section of the paper lays out the process by which a two-tier analysis should be performed together with relevant equations.  相似文献   

14.
We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.  相似文献   

15.
An algorithm for the numerical modelling of magnetotelluric fields in 2-D generally anisotropic block structures is presented. Electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor. The problem leads to a coupled system of partial differential equations for the strike-parallel components of the electromagnetic field. E x, and H x These equations are numerically approximated by the finite-difference (FD) method, making use of the integro-interpolation approach. As the magnetic component H x, is constant in the non-conductive air, only equations for the electric mode are approximated within the air layer. The system of linear difference equations, resulting from the FD approximation, can be arranged in such a way that its matrix is symmetric and band-limited, and can be solved, for not too large models, by Gaussian elimination. The algorithm is applied to model situations which demonstrate some non-trivial phenomena caused by electrical anisotropy. In particular, the effect of 2-D anisotropy on the relation between magnetotelluric impedances and induction arrows is studied in detail.  相似文献   

16.
Summary. A numerically efficient global matrix approach to the solution of the wave equation in horizontally stratified environments is presented. The field in each layer is expressed as a superposition of the field produced by the sources within the layer and an unknown field satisfying the homogeneous wave equations, both expressed as integral representations in the horizontal wavenumber. The boundary conditions to be satisfied at each interface then yield a linear system of equations in the unknown wavefield amplitudes, to be satisfied at each horizontal wavenumber. As an alternative to the traditional propagator matrix approaches, the solution technique presented here yields both improved efficiency and versatility. Its global nature makes it well suited to problems involving many receivers in range as well as depth and to calculations of both stresses and particle velocities. The global solution technique is developed in close analogy to the finite element method, thereby reducing the number of arithmetic operations to a minimum and making the resulting computer code very efficient in terms of computation time. These features are illustrated by a number of numerical examples from both crustal and exploration seismology.  相似文献   

17.
Summary. Wave-induced stress in a porous elastic medium is studied on the basis of Biot's linearized theory which is a special case of the mixture theory. For sufficiently high frequencies which are pertinent to ocean waves and seismic waves, a boundary layer of Stokes' type is shown to exist near the free surface of the solid. Outside the boundary layer, fluid and the solid skeleton move together according to the laws of classical elasticity for a single phase. This division simplifies the analysis of the equations governing the two phases; and several examples of potential interest to geophysics and foundation mechanics are treated analytically.  相似文献   

18.
谢学纲 《地理研究》1990,9(1):55-58
本文提出了一个包括流体的角动量平衡方程的新的流体力学方程组。  相似文献   

19.
Using a combination of geophysical and geotechnical data from Storfjorden Trough Mouth Fan off southern Svalbard, we investigate the hydrogeology of the continental margin and how this is affected by Quaternary glacial advances and retreats over the continental shelf. The geotechnical results show that plumites, deposited during the deglaciation, have high porosities, permeabilities and compressibilities with respect to glacigenic debris flows and tills. These results together with margin stratigraphic models obtained from seismic reflection data were used as input for numerical finite element models to understand focusing of interstitial fluids on glaciated continental margins. The modelled evolution of the Storfjorden TMF shows that tills formed on the shelf following the onset of glacial sedimentation (ca. 1.5 Ma) acted as aquitards and therefore played a significant role in decreasing the vertical fluid flow towards the sea floor and diverting it towards the slope. The model shows that high overpressure ratios (up to λ ca. 0.6) developed below the shelf edge and on the middle slope. A more detailed model for the last 220 kyrs accounting for ice loading during glacial maxima shows that the formation of these aquitards on the shelf focused fluid flow towards the most permeable plumite sediments on the slope. The less permeable glacigenic debris flows that were deposited during glacial maxima on the slope hinder fluid evacuation from plumites allowing high overpressure ratios (up to λ ca. 0.7) to develop in the shallowest plumite layers. These high overpressures likely persist to the Present and are a critical precondition for submarine slope failure.  相似文献   

20.
The effect of cracks on the elastic properties of an isotropic elastic solid is studied when the cracks are saturated with a soft fluid. A polynomial equation in effective Poisson's ratio is obtained, whose coefficients are functions of Poisson's ratio of the uncracked solid, crack density and saturating fluid parameter. Elastic and dynamical constants used in Blot's theory of wave propagation in poroelastic solids are modified for the introduction of cracks. The effects of cracks on the velocities of three types of waves are observed numerically. The frequency equation is derived for the propagation of Rayleigh-type surface waves in a saturated poroelastic half-space lying under a uniform layer of liquid. Dispersion curves for a particular model of oceanic crust containing cracks are plotted. The effects of variations in crack density and saturation on the phase and group velocity are also analysed.  相似文献   

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