On: “A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars” by X. M. Tang (June 1992 GEOPHYSICS, p. 854–859)

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 904-904 ◽  
Author(s):  
Dane P. Blair
Keyword(s):  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Inversion Technique ◽  
Attenuation Characteristics

The author has recently presented a waveform inversion technique for measuring elastic wave attenuation in cylindrical bars. However, it is worthwhile pointing out some previous, relevant studies which may have been overlooked. The Pochhammer technique employed to derive the pulse attenuation characteristics is not new. In fact it was first used by Hsieh and Kolsky (1958); Blair (1985, 1990) also implemented the method using a Fast Fourier Transform.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

scholarly journals Research on the Attenuation Characteristics of AE Signals of Marble and Granite Stone

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Haiyan Wang ◽  
Ji Ma ◽  
Feng Du ◽  
Gongda Wang ◽  
Quan Zhang ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Large Scale ◽  
Wave Attenuation ◽  
Propagation Distance ◽  
Internal Force ◽  
Residual Energy ◽  
P Wave ◽  
S Wave ◽  
Attenuation Characteristics ◽  
Ae Signals

When an underground rock is deformed or fractured by an external or internal force, the energy will be released in the form of an elastic wave, which is known as the acoustic emission (AE) phenomenon. Extracting useful information from complex AE signals for the early warning of fracture characteristics and the damage monitoring of rock materials is of great significance for the prevention and control of dynamic disasters in coal mines. In this work, by taking rod-shaped rocks and plate-shaped rocks with different lithologies as the research objects, the elastic wave propagation characteristics of the rod-shaped rocks and plate-shaped rocks were studied by a self-constructed experimental platform. The results demonstrate that the elastic wave attenuation of the rod-shaped marble was the fastest, and the elastic wave attenuation characteristics of the three groups of rod-shaped granite were similar. The attenuation of the P-wave preceded that of the S-wave. With the increase in the propagation distance, the amplitude of the large-scale plate-shaped rock showed an approximate exponential attenuation characteristic. The elastic wave attenuation of the plate-shaped granite in the 0° direction was stronger than that of the plate-shaped marble, and it was weaker than that of the plate-shaped marble in the 45° and 90° directions. The energy changes in marble were more severe than those in granite. The main dominant energy of the AE signals of experimental rock was concentrated in the range of 0–176.78 kHz, and part of the residual energy was located in the high-frequency band of 282.25–352.56 kHz.

Elastic Wave Attenuation Characteristics and Relevance for Rock Microstructures

2020 ◽  
Vol 56 (2) ◽  
pp. 216-225
Author(s):  
X. L. Liu ◽  
M. S. Han ◽  
X. B. Li ◽  
J. H. Cui ◽  
Z. Liu
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Attenuation Characteristics

Seismic wave modeling in vertically varying viscoelastic media with general anisotropy

Geophysics ◽  
2021 ◽  
pp. 1-88
Author(s):  
Fang Ouyang ◽  
Jian-guo Zhao ◽  
Shikun Dai ◽  
Shangxu Wang
Keyword(s):  
Fourier Transform ◽  
Seismic Anisotropy ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Elastic Stiffness ◽  
Dynamic Features ◽  
General Anisotropy ◽  
Wavenumber Domain ◽  
Full Waveform ◽  
Stiffness Reduction

Seismic anisotropy, wave attenuation and dispersion are critical phenomena of wave propagation in real media. Full wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion (FWI) of anisotropic parameters and velocity dispersion. We present a numerical scheme to model full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be simply described by a complex elastic stiffness matrix, and frequency-dependent moduli can also be readily incorporated. In the proposed scheme, we solve the elastodynamic equations for general anisotropy through finite element method in the frequency-wavenumber domain and use the stiffness reduction method (SRM) to suppress reflections from artificial boundaries along the depth direction. A non-uniform 2-D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing numerical results with exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with both velocity and attenuation anisotropy. The proposed scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic response in practical application.

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