Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact

1988 ◽  
Vol 415 (1849) ◽  
pp. 389-419 ◽  
Keyword(s):  
Anisotropic Media ◽  
Wave Mode ◽  
Sliding Contact ◽  
Stoneley Wave ◽  
Shear Stresses ◽  
Wave Problem ◽  
Numerical Computations ◽  
Cubic Symmetry ◽  
Anisotropic Elastic ◽  
Wave Modes

A variant of the Stoneley-wave problem, namely slip waves between two homogeneous elastic half-spaces whose interface is incapable of supporting shear stresses, is studied. For two isotropic half-spaces there is either no or one slip-wave mode. In the case of anisotropic half-spaces, the possibility of a new slip-wave mode, called the second slip-wave mode, arises. The case of two identical anisotropic half-spaces of the same orientation is discussed in detail; criteria for the existence of a second slip-wave mode in terms of the nature of the transonic state are developed. It is concluded that for many anisotropic media a second slip-wave mode will exist within certain ranges of orientation of the slip-wave geometry. Numerical computations for iron (cubic symmetry) demonstrate that second slip-wave modes indeed exist in this material.

Local and global fluid effects on sonic wave modes

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. D369-D381 ◽  
Author(s):  
Elliot J. H. Dahl ◽  
Kyle T. Spikes
Keyword(s):  
Rayleigh Wave ◽  
Wave Velocity ◽  
Fluid Pressure ◽  
Wave Mode ◽  
P Wave ◽  
Stoneley Wave ◽  
S Wave ◽  
Local Pressure ◽  
Wave Velocities ◽  
Wave Modes

Most subsurface formations of value to exploration contain a heterogeneous fluid-filled pore space, where local fluid-pressure effects can significantly change the velocities of passing seismic waves. To better understand the effect of these local pressure gradients on borehole wave propagation, we combined Chapman’s squirt-flow model with Biot’s poroelastic theory. We applied the unified theory to a slow and fast formation with permeable borehole walls containing different quantities of compliant pores. These results are compared with those for a formation with no soft pores. The discrete wavenumber summation method with a monopole point source generates the wavefields consisting of the P-, S-, leaky-P, Stoneley, and pseudo-Rayleigh waves. The resulting synthetic wave modes are processed using a weighted spectral semblance (WSS) algorithm. We found that the resulting WSS dispersion curves closely matched the analytical expressions for the formation compressional velocity and solutions to the period equation for dispersion for the P-wave, Stoneley-wave, and pseudo-Rayleigh wave phase velocities in the slow and fast formations. The WSS applied to the S-wave part of the waveforms, however, did not correlate as well with its respective analytical expression for formation S-wave velocity, most likely due to interference of the pseudo-Rayleigh wave. To separate changes in formation P- and S-wave velocities versus fluid-flow effects on the Stoneley-wave mode, we computed the slow-P wave dispersion for the same formations. We found that fluid-saturated soft pores significantly affected the P- and S-wave effective formation velocities, whereas the slow-P wave velocity was rather insensitive to the compliant pores. Thus, the large phase-velocity effect on the Stoneley wave mode was mainly due to changes in effective formation P- and S-wave velocities and not to additional fluid mobility.

Considerations of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces

1985 ◽  
Vol 402 (1822) ◽  
pp. 153-166 ◽  
Keyword(s):  
Surface Impedance ◽  
Wave Mode ◽  
Impedance Tensor ◽  
Stoneley Wave ◽  
Stoneley Waves ◽  
Interface Impedance ◽  
Linear Elastic ◽  
Existence Criterion ◽  
Uniqueness And Existence ◽  
Anisotropic Elastic

The questions of uniqueness and existence of subsonic Stoneley waves in bonded anisotropic linear elastic half-spaces are settled by using the notion of the interface impedance tensor, which is a simple linear combination of the hermitian surface impedance tensors of the separate half-spaces. A definite existence criterion is presented in a form that proves most useful in numerical searches for Stoneley waves, in the sense that such searches need not be conducted when a Stoneley wave mode does not exist.

scholarly journals Elastic wave-mode separation for VTI media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB19-WB32 ◽  
Author(s):  
Jia Yan ◽  
Paul Sava
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
Anisotropic Media ◽  
Single Mode ◽  
Wave Mode ◽  
Density Variation ◽  
Helmholtz Decomposition ◽  
Elastic Wave Equations ◽  
Vti Media ◽  
Wave Modes

Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P- and S-modes are both propagated using elastic wave equations, there is a need to separate P- and S-modes to efficiently apply single-mode processing tools. In isotropic media, wave modes are usually separated using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory results and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires more sophisticated operators that depend on local material parameters. Anisotropic wavefield-separation operators are constructed using the polarization vectors evaluated at each point of the medium by solving the Christoffel equation for local medium parameters. These polarization vectors can be represented in the space domain as localized filtering operators, which resemble conventional derivative operators. The spatially variable pseudo-derivative operators perform well in heterogeneous VTI media even at places of rapid velocity/density variation. Synthetic results indicate that the operators can be used to separate wavefields for VTI media with an arbitrary degree of anisotropy.

Enabling isotropic reflectivity modeling and inversion in anisotropic media

2021 ◽  
Vol 40 (4) ◽  
pp. 267-276
Author(s):  
Peter Mesdag ◽  
Leonardo Quevedo ◽  
Cătălin Tănase
Keyword(s):  
Synthetic Data ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Effective Parameters ◽  
Elastic Parameters ◽  
Pp Wave ◽  
Anisotropic Elastic ◽  
And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

3D passive wavefield imaging using the energy norm

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. KS13-KS27 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava ◽  
Jeffrey Shragge ◽  
Ben Witten
Keyword(s):  
Wave Mode ◽  
Source Location ◽  
Time Step ◽  
Elastic Wave Equation ◽  
Imaging Condition ◽  
Mode Decomposition ◽  
Passive Seismic ◽  
Anisotropic Elastic ◽  
Wavefield Extrapolation ◽  
Multicomponent Data

In passive seismic monitoring of microseismicity, full-wavefield imaging offers a robust approach for the estimation of source location and mechanism. With multicomponent data and the full 3D anisotropic elastic wave equation, the coexistence of P- and S-modes at the source location in time-reversal wavefield extrapolation allows the development of imaging conditions that identify the source position and radiation pattern. We have developed an imaging condition for passive wavefield imaging that is based on energy conservation and is related to the source mechanism. Similar to the correlation between the decomposed P- and S-wavefields — the most common imaging condition used in passive elastic wavefield imaging — our proposed imaging condition compares the different modes present in the displacement field producing a strong and focused correlation at the source location without costly wave-mode decomposition at each time step. Numerical experiments demonstrate the advantages of the proposed imaging condition (compared to PS correlation with decomposed wave modes), its sensitivity with respect to velocity inaccuracy, and its quality and efficacy in estimating the source location.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

Inertial wave dynamics in a rotating liquid metal

2014 ◽  
Vol 753 ◽  
pp. 472-498 ◽  
Author(s):  
Tobias Vogt ◽  
Dirk Räbiger ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Swirling Flow ◽  
Harmonic Wave ◽  
Wave Mode ◽  
Rotating Magnetic Field ◽  
Inertial Waves ◽  
Aspect Ratios ◽  
Inertial Wave ◽  
Wave Modes

AbstractThe dynamics of free and forced inertial waves inside cylinders of different aspect ratios ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A=H_0/2R_0$) were investigated experimentally in this study. The liquid metal GaInSn was chosen as the fluid in order to enable a contactless stimulation of the flow by means of alternating electromagnetic fields. A rotating magnetic field generates the rotating motion of the liquid, whereas periodic modulations of the field strength and short pulses excite specific wave modes. Ultrasound Doppler velocimetry was used to record the flow structure and to identify inertial waves in the set-up. Our experiments demonstrate selective excitation of different inertial wave modes by deliberate variation of the magnetic field parameters. Furthermore, it was found that turbulent perturbations in the boundary layers of the swirling flow are able to induce an inertial wave mode that survives over a long time. Experiments at the fundamental resonance have shown that multiple harmonic wave modes appeared simultaneously. The measured inertial wave frequencies were compared to the predictions of the linear inviscid theory.

scholarly journals Evanescent acoustic-gravity modes in the isothermal atmosphere: systematization, applications to the earth's and solar atmospheres

2019 ◽  
Author(s):  
Oleg K. Cheremnykh ◽  
Alla K. Fedorenko ◽  
Evgen I. Kryuchkov ◽  
Yuriy A. Selivanov
Keyword(s):  
Dispersion Relation ◽  
Evanescent Wave ◽  
Wave Mode ◽  
The Sun ◽  
New Wave ◽  
Horizontal Scale ◽  
Different Types ◽  
Isothermal Atmosphere ◽  
Amplitude Versus ◽  
Wave Modes

Abstract. The objects of research in this work are evanescent wave modes in a gravitationally stratified atmosphere and their associated pseudo-modes. Whereas the former, according to the dispersion relation, rapidly decrease with distance from a certain surface, the latter, having the same dispersion law, differ from the first by the form of polarization and the character of its decreasing away from the surface. Within a linear hydrodynamic model, the propagation features of evanescent wave modes in an isothermal atmosphere are studied. Research carried out for different assumptions about the properties of the medium. On this way, a new wave mode – anelastic evanescent wave mode – was discovered. Also, the possibility of the existence of a pseudo-mode related to it is indicated. The case of two isothermal media differing in temperature at the interface is studied in detail. It is shown that a non-divergent pseudo-mode with the dispersion of solar f-mode type can be realized on the interface for the specified horizontal scale. The newly discovered dispersion relation, at the interface of two media, is satisfied by the wave mode, which has different types of amplitude versus height dependencies at different horizontal scales. The applicability of the obtained results to clarify the properties of f-mode observed on the Sun is analyzed.

Derivation of Wave Mode Orthogonality From Reciprocity in Direct Notation

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Annamaria Pau
Keyword(s):  
Continuum Mechanics ◽  
Classical Result ◽  
Wave Mode ◽  
Tensor Algebra ◽  
Orthogonality Relations ◽  
Wave Modes

The purpose of this brief note is to present an alternative way of deriving the orthogonality relations for wave modes, by approaching the reciprocity relationship in direct notation, with the tools provided by tensor algebra and analysis. In this way, the classical result of elastodynamics is obtained through the instruments of continuum mechanics.

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