scholarly journals Reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids

2021 ◽  
Author(s):  
Pham Chi Vinh ◽  
Do Xuan Tung ◽  
Nguyen Thi Kieu
Keyword(s):  
Incident Wave ◽  
Elastic Layer ◽  
Incident Angle ◽  
P Wave ◽  
Rough Interface ◽  
Elastic Solids ◽  
P Waves ◽  
Reflection And Transmission ◽  
Reflected Waves ◽  
Transmission Coefficients

This paper deals with the reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids. The interface is assumed to oscillate between two straight lines. By mean of homogenization, this problem is reduced to the reflection and transmission of P-waves through an inhomogeneous orthotropic elastic layer. It is shown that a P incident wave always creates two reflected waves (one P wave and one SV wave), however, there may exist two, one or no transmitted waves. Expressions in closed-form of the reflection and transmission coefficient have been derived using the transfer matrix of an orthotropic elastic layer. Some numerical examples are carried out to examine the reflection and transmission of P-waves at a very rough interface of tooth-comb type, tooth-saw type and sin type. It is found numerically that the reflection and transmission coefficients depend strongly on the incident angle, the incident wave frequency, the roughness and the type of interfaces.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

A technique to eliminate the azimuth ambiguity in single-well imaging

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. D409-D416 ◽  
Author(s):  
Yi-de Zhang ◽  
Hengshan Hu
Keyword(s):  
Wave Reflection ◽  
Incident Angle ◽  
Imaging Techniques ◽  
Fluid Pressure ◽  
Displacement Component ◽  
P Wave ◽  
Reflected Waves ◽  
Single Well ◽  
The Media ◽  
Two Sides

Single-well imaging has been a technique increasingly used in the detection of near-borehole geologic structures. The azimuth of a geologic structure, however, cannot be uniquely determined with acoustic signals recorded in the borehole alone, due to the azimuth ambiguity existing in current imaging techniques. We eliminated such ambiguity by revealing the relevant acoustic principle underlying the P-wave reflection behavior. When a P-wave excited by a transducer in the logging tool impinges upon a planar interface, the P-wave reflection coefficient (RC) of the displacement is opposite in sign to that of the normal stress or fluid pressure, regardless of the incident angle and the parameters of the media on the two sides. The derived relation about signs of RCs was validated by finite-difference solutions for reflected waves from a near-borehole plane fault. With this newly discovered reflection principle, one can eliminate the azimuth ambiguity of any interface outside a borehole by checking if the waveforms of pressure and the displacement component are both changed in polarity after reflection. Furthermore, because the pressure and displacement are observable quantities and the waveform of the acoustic source is known in acoustic logging, it is convenient to implement the data acquisition for this technique, which is a major advantage over other techniques. We expounded and exemplified our new technique by numerical simulation.

Reflection and transmission of waves at a fluid/porous‐medium interface

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 282-291 ◽  
Author(s):  
Arthur I. M. Denneman ◽  
Guy G. Drijkoningen ◽  
David M. J. Smeulders ◽  
Kees Wapenaar
Keyword(s):  
Porous Medium ◽  
P Wave ◽  
Reflection And Transmission Coefficients ◽  
Sand Layer ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Wave Velocities ◽  
Medium Interface ◽  
Water Saturated ◽  
Silt Layer

We study the wave properties at a fluid/porous‐medium interface by using newly derived closed‐form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porous‐medium interface (with open‐pore or sealed‐pore boundary conditions), where the porous medium consists of (1) a water‐saturated clay/silt layer, (2) a water‐saturated sand layer, (3) an air‐filled clay/silt layer, or (4) an air‐filled sand layer. We observe in the frequency range 5 Hz–20 kHz that the fast P‐wave and S‐wave velocities in the four porous materials are indistinguishable from the corresponding frequency‐independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous‐medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air‐filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.

The viscoelastic reflection/transmission problem: Two special cases

1983 ◽  
Vol 73 (6A) ◽  
pp. 1673-1683
Author(s):  
E. S. Krebes
Keyword(s):  
Incident Wave ◽  
Incidence Angle ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Special Cases ◽  
Mathematical Formulas ◽  
Linear Viscoelastic ◽  
Ray Bending

Abstract In the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

TRANSFORMATION OF SOUND AND ELECTROMAGNETIC WAVES IN NON-STATIONARY MEDIA

2010 ◽  
Vol 24 (18) ◽  
pp. 1951-1961 ◽  
Author(s):  
A. R. MKRTCHYAN ◽  
A. G. HAYRAPETYAN ◽  
B. V. KHACHATRYAN ◽  
R. G. PETROSYAN
Keyword(s):  
Energy Flux ◽  
Sound Wave ◽  
Electromagnetic Waves ◽  
Reflection And Transmission Coefficients ◽  
Sound Waves ◽  
Reflection And Transmission ◽  
Reflected Waves ◽  
Transmission Coefficients

Transformation (reflection and transmission) of sound and electromagnetic waves are considered in non-stationary media, properties of which abruptly change in time. Reflection and transmission coefficients for both amplitudes and intensities of sound and electromagnetic waves are obtained. Quantitative relations between the reflection and transmission coefficients for both sound and electromagnetic waves are given. The sum of the energy flux reflection and transmission coefficients for both types of waves is not equal to one (for sound waves it is greater than one). The energy of both waves is not conserved, that is, exchange of the energy occurs between the corresponding waves and medium. As a result, the sound wave obtains a notable property: the transmitting wave carries energy equal to the sum of the energies of the incident and reflected waves. A possibility of the amplification of sound waves and transformation of their frequencies is illustrated.

The scattering by a dielectric spheroid of an electromagnetic surface wave travelling along a duct

1984 ◽  
Vol 391 (1800) ◽  
pp. 181-199 ◽  
Keyword(s):  
Surface Wave ◽  
Incident Wave ◽  
Wave Mode ◽  
Reflection And Transmission Coefficients ◽  
Leading Order ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Electromagnetic Surface Wave

An electromagnetic surface wave travelling between conducting walls is incident on a small dielectric axisymmetric spheroid. Reflection and transmission coefficients are found, to leading order, by a considerable generalization of the method used in an earlier paper. The possibility of zero reflection of the incident wave mode is investigated.

An Application of Elastodynamic Reciprocity to Reflection by an Obstacle in a Waveguide

2000 ◽  
Vol 16 (2) ◽  
pp. 97-101
Author(s):  
J.D. Achenbach
Keyword(s):  
Transverse Wave ◽  
Elastic Layer ◽  
Wave Motion ◽  
Elastic Solid ◽  
Orthogonality Condition ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Planar Array ◽  
Wave Modes

ABSTRACTThe reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

scholarly journals Reection and refraction of plane waves at the interface between magnetoelectroelastic and liquid media

2013 ◽  
Vol 40 (3) ◽  
pp. 427-439 ◽  
Author(s):  
Rong Zhang
Keyword(s):  
Liquid Medium ◽  
Incident Angle ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Liquid Media ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Reflection And Refraction ◽  
Acoustic Device ◽  
Wave Incidence

This paper analyzes the reflection and refraction of plane wave incidences at the interface between magnetoelectroelastic (MEE) and liquid media. The MEE medium is assumed to be transversely isotropic and the liquid medium to be nonviscous. Three cases, i.e., the coupled quasipressure wave incidence from the MEE medium, the coupled quasi-shear vertical wave incidence from the MEE medium, and the pressure wave incidence from the liquid medium, are discussed. The expressions of reflection and transmission coefficients varying with the incident angle are obtained. This investigation would be useful to the MEE acoustic device field.

Sign in / Sign up

Export Citation Format

Share Document