On disturbances in a visco-elastic medium of Maxwell type in contact with a liquid medium and subjected to a magnetic field

Summary The problem of disturbances in a visco-elastic medium due to Maxwell in contact with a liquid medium — both being perfectly conductive — has been investigated when an impulsive force acts along the plane of the contact. The electro-magnetic equations of Maxwell, equation of elasticity and the stress-strain relations of the material have been used in the investigation.     

On disturbances in an elastic medium in contact with a liquid medium and subjected to a magnetic field

Summary The present note makes use of electromagnetic equations of Maxwell and those of mechanical motions to work out the problem of disturbances in two perfectly conductive media—an ideal liquid and a perfectly elastic solid-acted upon by a magnetic field perpendicular to their plane of contact. The displacement suffered by solid medium has been determined when a tangential force, exponentially decaying with time, acts in the plane of contact of the two media. The solution of the problem is achieved by using the method of Laplace transform.     

Reference transversely isotropic medium approximating a given generally anisotropic medium

For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we can estimate the extent to which the medium is transversely isotropic, and determine the direction of its reference symmetry axis. In this paper, we rotate the given stiffness tensor about this reference symmetry axis, and determine the reference transversely isotropic (uniaxial) stiffness tensor as the average of the rotated stiffness tensor over all angles of rotation. The obtained reference transversely isotropic (uniaxial) stiffness tensor represents an analytically differentiable approximation of the given generally anisotropic stiffness tensor. The proposed analytic method is compared with a previous numerical method in two numerical examples.     

Transient electromagnetic response of a sphere in a layered medium

The integral equation for the electromagnetic response of a sphere in a layered medium may be solved as follows. First, the unknown time harmonic electric field in the sphere is expanded in spherical vector waves. Secondly, the coefficients for these wave functions are found by a set of equations. The equations are found by multiplying the integral equation throughout by each wave function and integrating over the spherical conductor.Once the unknown coefficients have been determined, then the transient response may be found by taking the inverse Fourier transform. In carrying out the Fourier transform one learns that for most of the time range used in prospecting, only the lowest order vector wave function is significant. A study of the singularities of the spectrum of the transient shows that, for the time range considered, only a single branch cut is significant. There are no pole type responses. That is, the field does not decay exponentially. Previous studies of a sphere in free space reported only pole type responses. That is, at the later stages, the field decays exponentially. This study shows that, in order to model satisfactorily the effect of the host rock on transient electromagnetic fields, the sphere must be placed in layered ground.     

Propagation of a fracture in an infinite medium

Summary The displacement produced in an infinite homogeneous, isotropic elastic medium due to a steadily progressing crack has been obtained in a closed form by using Laplace transforms andCagniard's method. Numerical values of the displacement have been obtained and presented graphically.     

Ray amplitudes in a three-dimensional inhomogeneous medium

Summary A system of five ordinary differential equations of the first order to compute the geometrical spreading of the wave front of seismic body waves in a three-dimensional medium is suggested.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

Intensity of waves in a randomly non-homogeneous layered medium

The intensity of shear waves in the model of a multilayered stratum, the material properties of which are random functions, is considered. The solutions for displacements and stresses are obtained for one layer and then the formulation is extended to a multilayered stratum through transfer matrices. The solution for a random medium has been compared with the solution for the homogeneous medium. The analysis indicates that the stochastic inhomogeneities are likely to increase the damping in a significant way.     

Torsional response of pile embedded in a poroelastic medium

The response of a cylindrical elastic pile embedded in a homogeneous poroelastic medium and subjected to torsional loading is studied for the first time. Based on the Muki's model, the pile-porous medium system is decomposed into a fictitious pile system and an extended porous medium system. The one-dimensional, vertical, elastic pile and the three-dimensional poroelastic medium are solved, respectively. Considering the mixed boundary-value conditions at the interface of pile and soil, a Fredholm's integral equation of the second kind for the bar-force is established. The force and the displacement of the pile are calculated by applying numerical quadrature.     

双相介质中地震波衰减的物理机制

High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results from the interference of elastic microscopic multiple scattering waves. First, I propose a new theory on wave propagation in a two-phase medium which is based on the concept that the basic unit for wave propagation is a nano- mass point. As a result of the elasticity variations of pore fluid and rock framework, micro multiple scattering waves would emerge at the wavelength of the seismic waves passing through the two-phase medium and their interference and overlap would generate high- frequency seismic attenuation. Second, I present a study of the frequency response of seismic transmitted waves by modeling thin-layers with thicknesses no larger than pore diameters. Results indicate that high-frequency seismic waves attenuate slightly in a near-surface water zone but decay significantly in a near-surface gas zone. Third, I analyze the seismic attenuation characteristics in near-surface water and gas zones using dual-well shots in the Songliao Basin, and demonstrate that the high-frequency seismic waves attenuate slightly in water zones but in gas zones the 160-1600 Hz propagating waves decay significantly. The seismic attenuation characteristics from field observations coincide with the modeling results. Conclusions drawn from these studies theoretically support seismic attenuation recovery.     

A moving magnetic dipole in a conductive medium

A thorough investigation of the role that the source velocity has in the spatial and temporal variation of the secondary electromagnetic energy scattered by the Earth is necessary because marine controlled-source electromagnetic geophysical surveys employ moving sources. A first step towards this goal is the analysis, for this type of survey, of the difference of the measured value of the secondary electromagnetic energy between two systems: one with a moving source and the other with a fixed source. The model that suffices to stress this kinematic aspect is a vertical magnetic dipole moving at a constant speed along a horizontal line in a homogeneous medium separated from two homogeneous half-spaces by horizontal boundaries both above and below the dipole. The results show that both the velocity and the relative displacement between the source and the medium may cause a measurable variation relative to the static condition. Therefore, it may be necessary to take them into account in geophysical interpretation and to adapt the concepts of time and frequency domain for electromagnetic systems with moving sources.     

Stochastic study of solute transport in a nonstationary medium

A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects.     

Upscaling relative permeabilities in a structured porous medium

Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.     

Dispersion of waves in a continuously stratified elastic medium

Summary It is shown that the waves travelling at normal incidence in a continuously stratified elastic medium in which the longitudinal and the transverse wave velocities increase linearly are appreciably dispersed. Dispersion curves are given showing the variation of phase and group velocities, with frequency and different laws of increase in density. The results are relevant to seismology and underwater acoustics.A part of this paper was presented at the meetings of the Canadian Association of Physicists held in Toronto in June 1967     

Dynamic response of a multi-layered poroelastic medium

An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.     

Amplitude of a reflected wave in a horizontally stratified medium

Zusammenfassung Den Gegenstand der Arbeit bildet die Berechnung der Amplitudenkurve einer Reflexionswelle für ein bestimmtes gegebenes Medium anhand der Ersetzung dieses Mediums durch ein horizontal geschichtetes Medium mit einem einfachen Geschwindigkeitsgang in den Schichten. Die Amplitude wird nach der Nulln?herung der Strahlen-Theorie berechnet.

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Address: Ke Karlovu 3, Praha 2.     

Dynamic response of a piecewise circular tunnel embedded in a poroelastic medium

Recently, considerable efforts have been devoted to evaluation of seismic dynamic response of a circular tunnel. Conventional approaches have considered integral liners embedded in an elastic medium. In this study, we re-examine the problem with piecewise liners embedded in a porous medium. Surrounding saturated porous medium of tunnels is described by Biot's poroelastic theory, while the liner pieces and the connecting joints are treated as curved beams and characterized by curved beam theories. The scattered wave field in the porous medium is obtained by the wave function expansion method. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise tunnel. The surrounding soil and the tunnel are coupled together via the stress and the displacement continuation conditions which are implemented by the boundary collocation method. Numerical results demonstrate that the stiffness difference between the liner piece and the connecting joints has a considerable influence on the internal forces of the liner piece.     

Dynamic impedances of a weakly anelastic medium

Approximate formulas are derived to evaluate in the frequency domain the dynamic impedances of a weakly anelastic medium based on its pure elastic behaviour. The correspondence principle is applied to the elastic solution of a boundary-value problem followed by the expansion of the anelastic solution in a Taylor series about the elastic state. Taking the magnitude of material damping into account (small damping) only the first two terms of the Taylor series have been used. The derivatives of first order in the expansion can be determined by the central difference approximation; this requires only the evaluation of differences between neighbouring elastic solutions.