scholarly journals Wave Propagation Through a Micropolar Slab Sandwiched by Two Elastic Half-Spaces

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Peng Zhang ◽  
Peijun Wei ◽  
Yueqiu Li
Keyword(s):  
Wave Propagation ◽  
Numerical Results ◽  
P Wave ◽  
Interface Conditions ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Amplitude Ratios ◽  
Elastic Solids ◽  
Reflection And Transmission ◽  
Elastic Slab

The problem of wave propagation through a micropolar elastic slab sandwiched by two classical elastic half-spaces is studied in this paper. Different from the classical elastic solids, the particle in micropolar solids can bear not only the displacements but also the rotations. The additional kinetic freedom results in four kinds of wave modes, namely, the longitudinal displacement (LD) wave, the longitudinal microrotational (LR) wave, and two coupled transverse (CT) waves. Apart from the LD wave, the other three waves are dispersive. The existence of couple stresses and the microrotations also makes the interface conditions between the micropolar slab and the classic elastic half-spaces different from that between two classic solids. The nontraditional interface conditions lead to a set of algebraic equations from which the amplitude ratios of reflection and transmission waves can be determined. Further, the energy fluxes carried by various waves are evaluated and the energy conservation is checked to validate the numerical results obtained. The influences of the micropolar elastic constants and the thickness of slab are discussed based on the numerical results. Two situations of incident P wave and incident SH wave are both considered.

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.

SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks

1995 ◽  
Vol 62 (2) ◽  
pp. 312-319 ◽  
Author(s):  
Y. Mikata
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Numerical Results ◽  
Crack Spacing ◽  
Periodic Array ◽  
Wave Number ◽  
Sh Wave ◽  
Reflection And Transmission ◽  
Dispersion And Attenuation

Reflection and transmission of an SH-wave by a disordered periodic array of coplanar cracks is investigated, and subsequently its application to the dispersion and attenuation of an SH-wave in a disorderedly cracked medium is also treated. This is a stochastic boundary value problem. The formulation largely follows Mikata and Achenbach (1988b). The problem is formulated for an averaged scattered field, and the governing singular integral equation is derived for a conditionally averaged crack-opening displacement using a quasi-crystalline-like approximation. Unlike our previous study (Mikata and Achenbach, 1988b) where a point scatterer approximation was used for the regular part of the integral kernel, however, no further approximation is introduced. The singular integral equation is solved by an eigenfunction expansion involving Chebyschev polynomials. Numerical results are presented for the averaged reflection and transmission coefficients of zeroth order as a function of the wave number for normal incidence, a completely disordered crack spacing, and various values of the ratio of crack length and average crack spacing. Numerical results are also presented for the dispersion and attenuation of an SH-wave in a disorderedly cracked medium.

scholarly journals Transient SH Wave Propagation of Elastic Plate

2021 ◽  
Vol 250 ◽  
pp. 02010
Author(s):  
Kotaro Miura ◽  
Makoto Sakamoto ◽  
Yuji Tanabe
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Elastic Plate ◽  
P Wave ◽  
Propagation Problem ◽  
Image Method ◽  
Sh Wave ◽  
Transient Wave ◽  
Wave Propagation Problem ◽  
Transient Wave Propagation

We consider the transient wave propagation problem of linear, isotropic and elastic plate applied SH impact loading on the surface. Analytical solution of half-space obtained by the inverse Fourier-Laplace double transform using Cagniard-De Hoop method. The wave propagation problem of plate was considered by using a half-space exact solution and reflect wave from the boundary of plate are expressed using the image method. Some numerical results of stress and displacement components are presented. The mathematical technique appear in the basic problem can apply to the transient P wave propagation and more advanced problems.

Seismogram Synthesis for Multilayered Heterogeneous Media with Irregular Interfaces by the Global Generalized Reflection–Transmission Matrices Method

2020 ◽  
Vol 110 (1) ◽  
pp. 357-368
Author(s):  
Bin Liu ◽  
Li-Yun Fu ◽  
Geng-Xin Yu ◽  
Qingqing Li ◽  
Jianping Huang
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Source Term ◽  
Volume Integral ◽  
Sh Wave ◽  
Numerical Techniques ◽  
Reflection And Transmission ◽  
Volume Integral Equation ◽  
Full Wave ◽  
Piecewise Heterogeneous Media

ABSTRACT We present a semianalytical numerical method to simulate SH-wave propagation in heterogeneous multiple layers with smooth property variations. Wave propagation in such piecewise heterogeneous media will dominate the reflection and transmission at interfaces, whereas the scattered waves by volume heterogeneities inside each geological layer are superimposed on the boundary waves to cause fluctuations in amplitude and phase. The incident, boundary-scattering, and volume-scattering waves are accurately superposed through the generalized Lippmann–Schwinger integral (GLSI) equation. The multilayered heterogeneous media with irregular interfaces are sliced into horizontal and heterogeneous slabs, with each discretized into a series of volume elements. The traditional generalized reflection–transmission matrices (GRTMs) method is extended to solve the GLSI equation for each heterogeneous slab in the frequency–wavenumber domain by incorporating the boundary–volume integral equation numerical techniques. The global GRTM is obtained by integrating all the slab’s GRTMs in terms of the boundary condition across adjacent slabs. The wavefield at an arbitrary depth can be computed in a recursive relation from a source term. The accuracy of the method is tested by comparing it with other full-wave solutions to the SH problem. To show the applicability of the method, we calculate synthetic seismograms to demonstrate the significant impact of volume heterogeneities on seismic responses in layered heterogeneous media.

SH wave propagation in a periodic cement-based piezoelectric layered barrier

2021 ◽  
pp. 1-9
Author(s):  
Haozhe Jiang ◽  
Zhanhua Cai ◽  
Lili Yuan ◽  
Tingfeng Ma ◽  
Jianke Du ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Sh Wave

scholarly journals Recording seismic reflections using rigidly interconnected geophones

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1838-1842 ◽  
Author(s):  
C. M. Schmeissner ◽  
K. T. Spikes ◽  
D. W. Steeples
Keyword(s):  
Wave Propagation ◽  
Data Acquisition ◽  
Seismic Reflection ◽  
Spatial Sampling ◽  
P Wave ◽  
Signal Distortion ◽  
Reflection And Refraction ◽  
First Arrival ◽  
The Cost ◽  
Seismic Reflections

Ultrashallow seismic reflection surveys require dense spatial sampling during data acquisition, which increases their cost. In previous efforts to find ways to reduce these costs, we connected geophones rigidly to pieces of channel iron attached to a farm implement. This method allowed us to plant the geophones in the ground quickly and automatically. The rigidly interconnected geophones used in these earlier studies detected first‐arrival energy along with minor interfering seismic modes, but they did not detect seismic reflections. To examine further the feasibility of developing rigid geophone emplacement systems to detect seismic reflections, we experimented with four pieces of channel iron, each 2.7 m long and 10 cm wide. Each segment was equipped with 18 geophones rigidly attached to the channel iron at 15‐cm intervals, and the spikes attached to all 18 geophones were pushed into the ground simultaneously. The geophones detected both refracted and reflected energy; however, no significant signal distortion or interference attributable to the rigid coupling of the geophones to the channel iron was observed in the data. The interfering seismic modes mentioned from the previous experiments were not detected, nor was any P‐wave propagation noted within the channel iron. These results show promise for automating and reducing the cost of ultrashallow seismic reflection and refraction surveys.

Effect of Fluids on the Elastic Properties of 3D-Printed Anisotropic Rock Models

2021 ◽  
Vol 62 (5) ◽  
pp. 537-552
Author(s):  
Suresh Dande ◽  
◽  
Robert R. Stewart ◽  
Nikolay Dyaur ◽  
◽  
...  
Keyword(s):  
Wave Propagation ◽  
Elastic Properties ◽  
P Wave ◽  
Engine Oil ◽  
Rock Properties ◽  
Anisotropic Rock ◽  
Wave Velocities ◽  
Inclusion Model ◽  
3D Printed ◽  
Primary Porosity

Laboratory physical models play an important role in understanding rock properties and wave propagation, both theoretically and at the field scale. In some cases, 3D-printing technology can be adopted to construct complex rock models faster, more inexpensively, and with more specific features than previous model-building techniques. In this study, we use 3D-printed rock models to assist in understanding the effects of various fluids (air, water, engine oil, crude oil, and glycerol) on the models’ elastic properties. We first used a 3D-printed, 1-in. cube-shaped layered model. This model was created with a 6% primary porosity and a bulk density of 0.98 g/cc with VTI anisotropy. We next employed a similar cube but with horizontal inclusions embedded in the layered background, which contributed to its total 24% porosity (including primary porosity). For air to liquid saturation, P-velocities increased for all liquids in both models, with the highest increase being with glycerol (57%) and an approximately 45% increase for other fluids in the inclusion model. For the inclusion model (dry and saturated), we observed a greater difference between two orthogonally polarized S-wave velocities (Vs1 and Vs2) than between two P-wave velocities (VP0 and VP90). We attribute this to the S2-wave (polarized normal to both the layering and the plane of horizontal inclusions), which appears more sensitive to horizontal inclusions than the P-wave. For the inclusion model, Thomsen’s P-wave anisotropic parameter (ɛ) decreased from 26% for the air case to 4% for the water-saturated cube and to 1% for glycerol saturation. The small difference between the bulk modulus of the frame and the pore fluid significantly reduces the velocity anisotropy of the medium, making it almost isotropic. We compared our experimental results with theory and found that predictions using Schoenberg’s linear slip theory combined with Gassmann’s anisotropic equation were closer to actual measurements than Hudson’s isotropic calculations. This work provides insights into the usefulness of 3D-printed models to understand elastic rock properties and wave propagation under various fluid saturations.

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