Transmission Of Elastic Waves Research Articles

SAMPLE--Seismic Amplitude Measurement for Primary Lithology Estimation: ABSTRACT

SAMPLE is a method of seismic interpretation that extracts shear wave velocities or Poisson's ratios from the seldom used amplitude variations within a common-depth-point (CDP) gather. From a crossplot of pressure wave velocity and Poisson's ratio, lithologies and pore fluids are then estimated. The SAMPLE method works because reflection and transmission of elastic waves (seismic waves) at the boundary between two media are a function of 6 parameters. Three elastic parameters in each media are P-wave velocity, Poisson's ratio or S-wave velocity, and density. Given these 6 parameters and the angle of incidence of a plane elastic wave, the reflection and transmission amplitudes (coefficients) can be calculated using Zoeppritz's equations. SAMPLE is an inversion of this calculation. P-wave velocity is determined in a conventional manner (i.e., Dix interval velocities). Density is assumed to be a function of P-wave velocity. The unknown Poisson's ratios can be determined from the reflection amplitude variation with angle of incidence (offset versus amplitude variations within a C P gather.) Having solved for P-wave velocities and Poisson's ratios, lithologies and fluids are estimated. End_of_Article - Last_Page 479------------

Erratum: ‘‘Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water’’[J. Acoust. Soc. Am. 6 7, 1947–1953 (1980)

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Reflection and transmission of elastic waves by the spatially periodic interface between two solids (Numerical results for the sinusoidal interface)

The integral-equation method for calculating the reflection and transmission of elastic waves by the spatially periodic interface between two solids, developed in a previous paper, is applied to a sinusoidal interface, and numerical results are presented. The computations have been carried out for four different heights of the profile (the plane interface included), a single frequency of operation, two combinations of elastic solids, and the four types of excitation. We have considered the interface between granite and slate, the interface between copper and flint glass, and P- as well as SV-wave incidence in either of the media. A peaked behaviour of the reflection and transmission factor occurs at angles of incidence where an elastodynamic spectral mode changes from propagating to evanescent and vice versa. An additional anomaly occurs in cases where the horizontal wave number of one of the spectral orders coincides with the horizontal wave number of a Stoneley wave along the corresponding plane interface. The latter phenomenon is the more pronounced, the shallower the corrugation of the interface is.

Reflection and transmission of elastic waves by the spatially periodic interface between two solids (Theory of the integral-equation method)

The linear theory of two-dimensional reflection and transmission of time-harmonic, elastic waves by the spatially periodic interface between two perfectly elastic media is developed. A given phase progression of the incident wave in the direction of periodicity induces a modal structure in the elastodynamic field and leads to the introduction of the so-called spectral orders. The main tools in the analysis are the elastodynamic Green-type integral relations. They follow from the two-dimensional form of the elastodynamic field reciprocity theorem, where in the latter a Green state adjusted to the periodicity of the structure at hand is used. One of these relations is a vectorial integral equation from which the elastodynamic field quantities can be determined. The consequences of field reciprocity in the structure and of the conservation of energy are developed in view of their serving as a check on numercal results to be obtained from the relevant integral equations. The formalism thus developed applies to profiles, if periodic, of arbitrary shape and size and can without too serious difficulties be implemented on a computer. The major difficulty in this respect is the relevant Green function, the series representation of it being slowly convergent. Its evaluation becomes tractable after an appropriate technique for accelerating the convergence. The only practical limitations are then put by the speed of the computer and its storage capacity.

Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water

Reflection and transmission coefficients for plane elastic waves obliquely incident on the boundary between two isotropic materials have been known for some time. The solution for anisotropic materials, however, has not been fully treated in the literature. Here we derive these coefficients for the case of a piezoelectric ceramic in contact with water. This problem is of significant practical interest, since in a variety of applications, piezoelectric ceramics, which are inherently anisotropic, are used as transducers to radiate acoustic energy into water. Due to the anisotropy, velocities of both compressional and shear waves are functions of the angle of incidence. Piezoelectric equations are solved to find the variations of compressional and shear wave velocities with the angle of incidence. Reflection and transmission coefficients are then obtained and numerical results are presented for four piezoelectric ceramics.

Optimum transmission of elastic waves through joints

An elastic wave transmitting system (e.g. a nonuniform elastic rod) consisting of an input section with constant impedance, a joint with variable impedance, and an output section with constant impedance is considered. The efficiency of energy transmission (the ratio of transmitted to incident elastic wave energy) is determined and the following optimization problem is solved for two sample cases: Given the properties of the wave transmitting system and a limited duration of the incident wave, determine the shape of this wave such that the efficiency of energy transmission is maximized. In the first case (a joint with constant impedance) the optimization problem leads to a matrix eigenvalue problem. In the second case (a joint with concentrated mass) it leads to an eigenvalue problem for an integral equation. The efficiencies obtained for the optimum incident waves are compared with those obtained for rectagular incident waves an it is found that the differences are generally small. The results, which are discussed with particular reference to the transmission of elastic wave energy through drill rod joints, can also be interpreted for e.g. shallow water waves and electromagnetic waves in a transmission line.

Symmetries in the reflection and transmission of elastic waves

Summary. The symmetry relations between the reflection and transmission coefficients for plane elastic waves incident upon an arbitrary horizontally stratified medium are derived by a novel approach. Previous results, particularly for a single interface, are obtained as special cases of this treatment. In addition, for perfectly elastic media, projection operators for travelling and evanescent waves are introduced and used to derive a number of new relationships between the reflection and transmission coefficients.

An Approximate Method of Analysis of the Transmission of Elastic Waves Through a Frictional Boundary

An approximate analytical method is presented for determining the transmission and reflection of elastic waves at a frictional boundary. The method is applied to the case of plane harmonic shear waves normally incident on a Coulomb friction boundary between semi-infinite elastic media. The accuracy of the method is determined by comparison of approximate and exact solutions in a numerical example.

New calculation of the acoustical mismatch in the Kapitza conductance of bulk helium

Elastic wave transmission at the interface between a substrate and liquid helium has been calculated using a model that takes into account the inhomogeneous character of the acoustical impedance in helium and in particular the existence of a solid helium layer intermediate between the substrate and bulk liquid helium. The properties of this layer (width, velocity, and attenuation of elastic waves) have a great influence on the calculated transmission. A width of about 10 A seems to fit many quoted experimental results. The Kapitza conductanceh k derived from this model and the temperature variation ofh k agree with experimental results obtained from clean copper samples.

Reflection, Transmission and Attenuation of Elastic Waves at a Loosely-Bonded Interface of Two Half Spaces

Summary The problem of reflection and transmission of a longitudinal plane periodic wave incident on the interface between loosely-bonded half spaces is investigated by assuming that the interface behaves like a dislocation which preserves the continuity of traction while allowing a finite amount of slip. The wave equations are solved by imposing further the interface conditions that the normal displacement is continuous and that the shearing stress is proportional to velocity of slip. The results of numerical calculations are given in the form of graphs for different degrees of bonding, ranging from no bonding (zero shear stress) to full bonding (welded contact) between the half spaces. It is found that the elastic wave energy is attenuated at a loosely-bonded interface except at normal incidence, grazing incidence and at (approximately) critical incidence of the longitudinal wave at the interface.

The Passage of Elastic Waves through an Anomalous Region--III. Transmission of obliquely incident body waves

Sumnary The discussion of the transmission of plane harmonic elastic waves through a layer of material in which the elastic properties vary in a complex way is continued. In Parts I and I1 of this series, the method of Schwinger and Levine was examined and the accuracy of the solutions was tested. So that this preliminary discussion would not be obscured by detail, only normal incidence of the wave onto the layer was dealt with. In this paper we apply the method of Schwinger and Levine to the general problem of oblique incidence of plane dilatational or shear waves. Furthermore, we derive expressions leading to approximations to the amplitudes of the reflected as well as the transmitted waves. The rcstriction that, in the layer, the elastic properties of the material vary in the normal direction only is retained. The problems treated in Parts I and I1 of this series (Lapwood, Hudson & Kembhavi 1973, 1975) were essentially one-dimensional: the results which were obtained applied only to waves normally incident on a heterogeneous layer. In Part I the halfspaces on either side of the layer were of the same material, in Part I1 of different materials. In this part we consider the same structure of elastic media as in Part 11, but allow oblique incidence. This causes little extra complexity for SH waves, but for incident P or SV waves we have to account for transmitted P and SV and reflected P and SK The mathematical expression of this physical fact demands the solution of two coupled differential equations. We combine these as a single matrix equation (a differential equation of the second order) and construct a Schwinger-Levine variational problem which is analogous to that of Part 11. From the functions which represent displacements we constiuct functionals which are stationary for small variations of the functions from the exact solution of the differential equations. The exact values of these functionals give the appropriate transmission and reflection ratios. Hence if we use trial functions for the displacements, which are in error by a first order quantity, we will obtain approximate values for the transmission and reflection ratios with errors of second order. The properties of the solid medium are assumedto be as follows: the elastic parameters 1 and ,u, and the density p, vary with the co-ordinate z of a rectangular Cartesian system; outside the layer IzI < d, A, ,u and p are uniform (though not the

Reflection and transmission of elastic waves by a moving slab

Scattering of elastic waves by a moving slab is considered. Two cases corresponding to strong contact and good lubrication are treated. It is shown that the motion introduces new effective compressional and shear wave velocities in the moving slab. The amplitude of the reflection and transmission coefficients are given for various angles of incidence, frequencies and velocities of motion.

Transmission of elastic waves through a second-order fluid layer sandwiched between elastic media

The present paper is concerned with the transmission of elastic waves through a second-order fluid layer sandwiched between homogeneous elastic media having identical properties. It is concluded that the transmission ratio increases with the increasing absolute values of visco-elastic co-efficient and also with the wavelength of the wave transmitted.

Reflection and transmission of elastic waves in a system of corrugated layers

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

Elastic and magnetoelastic waves in yttrium iron garnet

A discussion of plane elastic and magnetoelastic waves follows a statement of the linearized equations of motion of coupled spin and elastic waves. The dispersion equations of θ = 0 and θ = π/2 waves are examined in detail. A description of the generation and propagation of magnetoelastic waves in a nonuniform magnetic field prepares the way for a review of selected experiments which illustrate the transmission and attenuation characteristics of elastic and magnetoelastic waves in yttrium iron garnet. Experimental resuits are presented on (1) time-field behavior of θ = π/2 magnetoelastic waves, (2) time-field-frequency characteristics of θ = 0 magnetoelastic waves, (3) polarization reversal of θ = 0 magnetoelastic waves, (4) acoustic Faraday rotation, (5) Mc frequency standing magnetoelastic waves, and (6) loss measurements for elastic and magnetoelastic waves. Finally, some delay line applications of these waves are considered.

Transmission of Elastic Waves through a Homogeneous Layer Sandwiched in Homogeneous Media

The problem of transmission of an elastic wave through a homogeneous layer sandwiched between two homogeneous half spaces has been considered. The exact solution has been obtained and the results are shown graphically.

正誤表

正誤表

中間漸移層がある場合の弾性波の反射及び透過

中間漸移層がある場合の弾性波の反射及び透過

The Equivalent Circuit for the Transmission of Plane Elastic Waves through a Plate at Oblique Incidence

Equations are developed for the transmission of a plane elastic wave through a plate at oblique incidence with unequal fluid medium on each side of the plate. The plate transmitting both the dilatation and shear wave is reduced to a simple equivalent circuit with impedances which are functions of the incidence angle.

Transmission of Elastic Waves through a Stratified Solid Medium

The transmission of a plane elastic wave at oblique incidence through a stratified solid medium consisting of any number of parallel plates of different material and thickness is studied theoretically. The matrix method is used to systematize the analysis and to present the equations in a form suitable for computation.