Elastic waves in finely layered sediments: The equivalent medium and generalized O’Doherty‐Anstey formulas

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1282-1300 ◽  
Author(s):  
Sergei A. Shapiro ◽  
Peter Hubral
Keyword(s):  
Phase Velocity ◽  
Multiple Scattering ◽  
Random Media ◽  
Plane Waves ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Seismic Velocities ◽  
Statistical Parameters ◽  
Practical Applications ◽  
Backus Averaging

We study the influence of elastic 1-D inhomogeneous random media (e.g., finely layered media with variable density and shear and compressional velocities) on the kinematics and dynamics of the transmitted obliquely incident P‐ and SV‐plane waves. Multiple scattering (resulting in localization and spatial dispersion of the elastic wavefield) is the main physical effect controlling the properties of the wavefield in such media. We analyze the wave propagation assuming the fluctuations of velocities and density to be small (of the order of 20% or smaller). We obtain explicit analytic solutions for the attenuation coefficient and phase velocity of the transmitted waves. These solutions are valid for all frequencies. They agree very well with results of numerical modeling. Our theory shows that fine elastic multilayering is characterized by a frequency‐dependent anisotropy. At typical acquisition frequencies this anisotropy differs significantly from the low‐frequency anisotropy described by the well‐known Backus averaging. The increase of the phase velocity with frequency is quantified. It can partly explain the difference between well‐log‐derived velocities and lower frequency seismic velocities [e.g., vertical seismic profiling (VSP) velocities] in terms of localization. The low‐ and high‐frequency asymptotical results for the phase velocity agree with those of Backus averaging and ray approximation, respectively. The theory describes the angle‐dependent attenuation caused by multiple scattering. The proposed formulas are simple enough to be used in many practical applications as, e.g., in an amplitude variation with offset (AVO) analysis. They can be implemented for taking into account the angle dependence of transmission effects, or they can be used in an inversion for statistical parameters of sediments.

Effects of Soil Parameters Uncertainties on the Behaviour of Anisotropic Porous Media to Shear Waves

2019 ◽  
Vol 10 (2) ◽  
pp. 32-49
Author(s):  
Amina Sadouki ◽  
Zamila Harichane ◽  
Ayfer Erken
Keyword(s):  
Porous Media ◽  
Phase Velocity ◽  
Random Media ◽  
Wave Equations ◽  
Shear Waves ◽  
Anisotropic Fluid ◽  
Soil Parameters ◽  
Anisotropic Porous Media ◽  
Practical Applications ◽  
Phase Velocity And Attenuation

In the present study, the wave equations for shear waves propagating in anisotropic fluid-saturated porous media are established in order to obtain the solutions in terms of displacements and dispersion equation. The wave velocities in the vertical and horizontal directions are derived. The uncertainties of the soil parameters due to their spatial variability are taken into account via Monte Carlo Simulations. The results are restricted to the effects of the porosity and permeability uncertainties on the phase velocity and attenuation for SH wave in addition to the anisotropy for Love wave. Results show that the mean velocities are more sensitive to the random variations of the permeability than to that of the porosity, but both phase velocity and attenuation decrease as the uncertainties increase. On the other hand, the anisotropy level and the randomness significantly affect the dispersion of Love waves. The present approach which converts a deterministic solution in a probabilistic one may be used as an everyday tool for practical applications of shear wave propagation in random media.

Magnetoelastic Plane Waves in Infinite Rotating Media

1983 ◽  
Vol 50 (2) ◽  
pp. 283-287 ◽  
Author(s):  
S. K. Roy Choudhuri ◽  
L. Debnath
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Velocity ◽  
Applied Magnetic Field ◽  
Plane Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Elastic Solid ◽  
Finite Conductivity ◽  
The Waves

A study is made of the propagation of magnetoelastic plane waves in an electrically conducting, infinite elastic solid permeated by a primary uniform magnetic field when the entire medium rotates with a constant angular velocity. A more general dispersion relation is obtained to investigate the effects of rotation and the external magnetic field on the phase velocity of the waves. This analysis reveals that when the applied magnetic field has both longitudinal and transverse components, the coupled magnetoelastic waves are dispersive and damped in an infinitely conducting medium in contrast to the nonrotating medium where the coupled waves are dispersive, but undamped. In the case of finite conductivity, the waves are dispersive and undamped in the absence of the applied magnetic field. At low frequency ω, the phase velocity of the waves varies as ω1/2 for finite conductivity, and is independent of the external magnetic field and rotation; while in the nonrotating case with low frequency (when the applied magnetic field has either longitudinal or transverse components) the phase speed is less than that in the rotating medium and is found to depend on the applied magnetic field. Also in both rotating and nonrotating cases, the phase velocity becomes very small for finitely conducting material with a very high magnetic permeability.

scholarly journals Polytetrafluoroethylene Films in Rigid Polyurethane Foams’ Dielectric Permittivity Measurements with a One-Side Access Capacitive Sensor

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1173
Author(s):  
Ilze Beverte ◽  
Ugis Cabulis ◽  
Sergejs Gaidukovs
Keyword(s):  
Dielectric Properties ◽  
Dielectric Permittivity ◽  
Low Frequency ◽  
Capacitive Sensor ◽  
Polyurethane Foams ◽  
Active Area ◽  
Ptfe Film ◽  
Practical Applications ◽  
Permittivity Measurements ◽  
The Impact

As a non-metallic composite material, widely applied in industry, rigid polyurethane (PUR) foams require knowledge of their dielectric properties. In experimental determination of PUR foams’ dielectric properties protection of one-side capacitive sensor’s active area from adverse effects caused by the PUR foams’ test objects has to be ensured. In the given study, the impact of polytetrafluoroethylene (PTFE) films, thickness 0.20 mm and 0.04 mm, in covering or simulated coating the active area of one-side access capacitive sensor’ electrodes on the experimentally determined true dielectric permittivity spectra of rigid PUR foams is estimated. Penetration depth of the low frequency excitation field into PTFE and PUR foams is determined experimentally. Experiments are made in order to evaluate the difference between measurements on single PUR foams’ samples and on complex samples “PUR foams + PTFE film” with two calibration modes. A modification factor and a small modification criterion are defined and values of modifications are estimated in numerical calculations. Conclusions about possible practical applications of PTFE films in dielectric permittivity measurements of rigid PUR foams with one-side access capacitive sensor are made.

Backscattered pulse shape due to small-angle multiple scattering in random media

Radio Science ◽  
1980 ◽  
Vol 15 (1) ◽  
pp. 87-93 ◽  
Author(s):  
Akira Ishimaru ◽  
Kirk J. Painter
Keyword(s):  
Multiple Scattering ◽  
Small Angle ◽  
Pulse Shape ◽  
Random Media

Multifrequency full-waveform sonic logging in the screened interval of a large-diameter production well

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. B243-B257 ◽  
Author(s):  
Majed Almalki ◽  
Brett Harris ◽  
J. Christian Dupuis
Keyword(s):  
Phase Velocity ◽  
Velocity Dispersion ◽  
Large Diameter ◽  
Low Frequency ◽  
Production Well ◽  
Frequency Wave ◽  
Full Waveform ◽  
Phase Velocity Dispersion ◽  
Production Wells ◽  
Sonic Logging

A set of field experiments using multiple transmitter center frequencies was completed to test the application potential of low-frequency full-waveform sonic logging in large-diameter production wells. Wireline logs were acquired in a simple open drillhole and a high-yield large diameter production well completed with wire-wound sand screens at an aquifer storage and recovery site in Perth, Western Australia. Phase-shift transform methods were applied to obtain phase-velocity dispersion images for frequencies of up to 4 kHz. A 3D representation of phase-velocity dispersion was developed to assist in the analysis of possible connections between low-frequency wave propagation modes and the distribution of hydraulic properties. For sandstone intervals in the test well, the highest hydraulic conductivity intervals were typically correlated with the lowest phase velocities. The main characteristics of dispersion images obtained from the sand-screened well were highly comparable with those obtained at the same depth level in a nearby simple drillhole open to the formation. The sand-screened well and the open-hole displayed an expected and substantial difference between dispersion in sand- and clay-dominated intervals. It appears that for clay-dominated formations, the rate of change of phase velocity can be associated to clay content. We demonstrated that with appropriate acquisition and processing, multifrequency full-waveform sonic logging applied in existing large-diameter sand-screened wells can produce valuable results. There are few wireline logging technologies that can be applied in this setting. The techniques that we used would be highly suitable for time-lapse applications in high-volume production wells or for reassessing formation properties behind existing historical production wells.

A theory for Langmuir solitons

1982 ◽  
Vol 27 (1) ◽  
pp. 95-120 ◽  
Author(s):  
N. Nagesha Rao ◽  
Ram K. Varma
Keyword(s):  
Mach Number ◽  
A Priori ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Smooth Transition ◽  
Langmuir Waves ◽  
Method Of Solution ◽  
Mach Numbers ◽  
Ion Waves ◽  
Langmuir Solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

scholarly journals Design and experimental analysis of dual-band polarization converting metasurface for microwave applications

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Bilawal Khan ◽  
Babar Kamal ◽  
Sadiq Ullah ◽  
Imran Khan ◽  
Jawad Ali Shah ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Polarization State ◽  
Plane Waves ◽  
Microwave Frequency ◽  
Dual Band ◽  
Orthogonal Polarization ◽  
Frequency Bands ◽  
Practical Applications ◽  
Sensor Applications ◽  
Polarized Waves

Abstract The manipulation of polarization state of electromagnetic waves is of great importance in many practical applications. In this paper, the reflection characteristics of a thin and dual-band metasurface are examined in the microwave frequency regime. The metasurface consists of a 22 × 22 element array of periodic unit cells. The geometry of the unit cell consists of three layers, including a 45° inclined dipole shape metal patch on top, which is backed by a 1.6 mm thick FR-4 substrate in the middle, and a fully reflective metallic mirror at the bottom. The proposed surface is exposed to horizontally (x) or vertically (y) polarized plane waves and the co and cross polarization reflection coefficients of the reflected waves are investigated experimentally in the 6–26 GHz frequency range. The metasurface is designed to convert incident waves of known polarization state (horizontal or vertical) to orthogonal polarization state (vertical and horizontal) in two distinct frequency bands, i.e. 7.1–8 GHz and 13.3–25.8 GHz. In these two frequency bands the simulated and experimental results are in good agreement. The polarization conversion ratio (PCR) of the surface is greater than 95% in the targeted frequency bands. A detailed parametric analysis of the metasurface is also discussed in this work and it has been estimated that the surface has the additional ability to convert linearly polarized waves to circularly polarized waves at several distinct frequencies. The proposed metasurface can be utilized in sensor applications, stealth technology, electromagnetic measurements, and antennas design.

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