Effect of saturation on the characteristics of P-wave and S-wave propagation in nearly saturated soils using bender elements

2021 ◽  
Vol 145 ◽  
pp. 106742
Author(s):  
Xiaoqiang Gu ◽  
Kangle Zuo ◽  
Anthony Tessari ◽  
Guangyun Gao
Keyword(s):  
Wave Propagation ◽  
P Wave ◽  
Saturated Soils ◽  
S Wave ◽  
Bender Elements

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

The effects of pore‐fluid salinity on ultrasonic wave propagation in sandstones

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 928-934 ◽  
Author(s):  
Simon M. Jones ◽  
Clive McCann ◽  
Timothy R. Astin ◽  
Jeremy Sothcott
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
Wave Attenuation ◽  
Clay Content ◽  
Seismic Wave Propagation ◽  
Ultrasonic Pulse ◽  
Pore Fluid ◽  
P Wave ◽  
S Wave ◽  
Shear Moduli

Petrophysical interpretation of increasingly refined seismic data from subsurface formations requires a more fundamental understanding of seismic wave propagation in sedimentary rocks. We consider the variation of ultrasonic wave velocity and attenuation in sandstones with pore‐fluid salinity and show that wave propagation is modified in proportion to the clay content of the rock and the salinity of the pore fluid. Using an ultrasonic pulse reflection technique (590–890 kHz), we have measured the P-wave and S-wave velocities and attenuations of 15 saturated sandstones with variable effective pressure (5–60 MPa) and pore‐fluid salinity (0.0–3.4 M). In clean sandstones, there was close agreement between experimental and Biot model values of [Formula: see text], but they diverged progressively in rocks containing more than 5% clay. However, this effect is small: [Formula: see text] changed by only 0.6% per molar change in salinity for a rock with a clay content of 29%. The variation of [Formula: see text] with brine molarity exhibited Biot behavior in some samples but not in others; there was no obvious relationship with clay content. P-wave attenuation was independent of pore‐fluid salinity, while S-wave attenuation was weakly dependent. The velocity data suggest the frame bulk and shear moduli of sandstones are altered by changes in the pore‐fluid salinity. One possible mechanism is the formation damage caused by clay swelling and migration of fines in low‐molarity electrolytes. The absence of variation between the attenuation in water‐saturated and brine‐saturated samples indicates the attenuation mechanism is relatively unaffected by changes in the frame moduli.

Automatic Classification of Impact-Echo Spectra II

2011 ◽  
pp. 199-205
Author(s):  
Addisson Salazar ◽  
Arturo Serrano
Keyword(s):  
Neural Networks ◽  
Wave Propagation ◽  
Propagation Velocity ◽  
Sampling Frequency ◽  
P Wave ◽  
Material Surface ◽  
S Wave ◽  
Wave Propagation Velocity ◽  
Impact Echo

We study the application of artificial neural networks (ANNs) to the classification of spectra from impact-echo signals. In this paper we focus on analyses from experiments. Simulation results are covered in paper I. Impact-echo is a procedure from Non-Destructive Evaluation where a material is excited by a hammer impact which produces a response from the material microstructure. This response is sensed by a set of transducers located on material surface. Measured signals contain backscattering from grain microstructure and information of flaws in the material inspected (Sansalone & Street, 1997). The physical phenomenon of impact-echo corresponds to wave propagation in solids. When a disturbance (stress or displacement) is applied suddenly at a point on the surface of a solid, such as by impact, the disturbance propagates through the solid as three different types of stress waves: a P-wave, an S-wave, and an R-wave. The P-wave is associated with the propagation of normal stress and the S-wave is associated with shear stress, both of them propagate into the solid along spherical wave fronts. In addition, a surface wave, or Rayleigh wave (R-wave) travels throughout a circular wave front along the material surface (Carino, 2001). After a transient period where the first waves arrive, wave propagation becomes stationary in resonant modes of the material that vary depending on the defects inside the material. In defective materials propagated waves have to surround the defects and their energy decreases, and multiple reflections and diffraction with the defect borders become reflected waves (Sansalone, Carino, & Hsu, 1998). Depending on the observation time and the sampling frequency used in the experiments we may be interested in analyzing the transient or the stationary stage of the wave propagation in impact- echo tests. Usually with high resolution in time, analyzes of wave propagation velocity can give useful information, for instance, to build a tomography of a material inspected from different locations. Considering the sampling frequency that we used in the experiments (100 kHz), a feature extracted from the signal as the wave propagation velocity is not accurate enough to discern between homogeneous and different kind of defective materials. The data set for this research consists of sonic and ultrasonic impact-echo signal (1-27 kHz) spectra obtained from 84 parallelepiped-shape (7x5x22cm. width, height and length) lab specimens of aluminium alloy series 2000. These spectra, along with a categorization of the quality of materials among homogeneous, one-defect and multiple-defect classes were used to develop supervised neural network classifiers. We show that neural networks yield good classifications (

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Long-wavelength P-wave and S-wave propagation in jointed rock masses

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. E205-E214 ◽  
Author(s):  
Minsu Cha ◽  
Gye-Chun Cho ◽  
J. Carlos Santamarina
Keyword(s):  
Wave Propagation ◽  
Rock Mass ◽  
Normal Stress ◽  
Jointed Rock ◽  
P Wave ◽  
Rock Masses ◽  
S Wave ◽  
Jointed Rock Masses ◽  
Long Wavelength ◽  
Joint Properties

Field data suggest that stress level and joint condition affect shear-wave propagation in jointed rock masses. However, the study of long-wavelength propagation in a jointed rock mass is challenging in the laboratory, and limited data are available under controlled test conditions. Long-wavelength P-wave and S-wave propagation normal to joints, using an axially loaded jointed column device, reproduces a range of joint conditions. The effects of the normal stress, loading history, joint spacing, matched surface topography (i.e., joint roughness), joint cementation (e.g., after grouting), joint opening, and plasticity of the joint filling on the P-wave and S-wave velocities and on S-wave attenuation are notable. The ratio [Formula: see text] in jointed rock masses differs from that found in homogeneous continua. The concept of Poisson’s ratio as a function of [Formula: see text] is unwarranted, and [Formula: see text] can be interpreted in terms of jointed characteristics. Analytic models that consider stress-dependent stiffness and frictional loss in joints as well as stress-independent properties of intact rocks can model experimental observations properly and extract joint properties from rock-mass test data. Thus, joint properties and normal stress have a prevalent role in propagation velocity and attenuation in jointed rock masses.

The effects of near-source heterogeneity on shear-wave evolution

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. T233-T241 ◽  
Author(s):  
Christopher S. Sherman ◽  
James Rector ◽  
Steven Glaser
Keyword(s):  
Wave Propagation ◽  
Wave Energy ◽  
Mode Conversion ◽  
Near Field ◽  
Seismic Source ◽  
Elastic Half Space ◽  
P Wave ◽  
S Wave ◽  
Rytov Approximation ◽  
Model Features

The Born and Rytov approximation, radiative transfer theory, and other related techniques are commonly used to model features of wave propagation through heterogeneous geologic media such as scattering, attenuation, and pulse-broadening. However, due to the underlying assumptions about the scattering direction and the reference Green’s function, these methods overlook important features of the wavefield such as mode conversion and near-field term coupling. These effects are particularly important within the predicted S-wave nodes of a seismic source, so we analyzed the problem of wave propagation beneath a vertical-point force on the surface of a heterogeneous, elastic half space. To do this, we generated a suite of 3D synthetic heterogeneous geologic models using fractal statistics and simulated the wave propagation using the finite-difference method. We derived an estimate for the effective source radiation patterns, and we used these to compare the results of the models. Our numerical results showed that, due to a combination of mode conversion and near-source coupling effects, S-wave energy on the order of 10% of the P-wave energy is generated within the shear-radiation node. In some cases, this S-wave energy may occur as a coherent pulse and may be used to enhance seismic imaging.

Experimental study on the effects of fractures on elastic wave propagation in synthetic layered rocks

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D441-D451 ◽  
Author(s):  
Tianyang Li ◽  
Ruihe Wang ◽  
Zizhen Wang ◽  
Yuzhong Wang
Keyword(s):  
Wave Propagation ◽  
Fractal Dimension ◽  
Power Spectrum ◽  
Elastic Wave ◽  
Power Law ◽  
Layered Media ◽  
Physical Models ◽  
P Wave ◽  
Fracture Density ◽  
S Wave

Fractures greatly increase the difficulty of oil and gas exploration and development in reservoirs consisting of interlayered carbonates and shales and increase the uncertainty of highly efficient development. The presence of fractures or layered media is also widely known to affect the elastic properties of rocks. The combined effects of fractures and layered media are still unknown. We have investigated the effects of fracture structure on wave propagation in interlayered carbonate and shale rocks using physical models based on wave theory and the similarity principle. We have designed and built two sets of layered physical models with randomly embedded predesigned vertically aligned fractures according to the control variate principle. We have measured the P- and S-wave velocities and attenuation and analyzed the effects of fracture porosity and aspect ratio (AR) on velocity, attenuation, and power spectral dimension of the P- and S-waves. The experimental results indicated that under conditions of low porosity ([Formula: see text]), Han’s empirical velocity-porosity relations and Wang’s attenuation-porosity relation combined with Wyllie’s time-average model are a good prediction for layered physical models with randomly embedded fractures. When the porosity is constant, the effect of different ARs on elastic wave properties can be described by a power law function. We have calculated the power spectrum fractal dimension [Formula: see text] of the transmitted signal in the frequency domain, which can supplement the S-wave splitting method for estimating the degree of anisotropy. The simple power law relation between the power spectrum fractal dimension of the P-waveform and fracture density suggests the possible use of P-waves for discriminating fracture density. The high precision and low error of this processing method give new ideas for rock anisotropy evaluation and fracture density prediction when only P-wave data are available.

scholarly journals A novel method for determining the small-strain shear modulus of soil using the bender elements technique

2017 ◽  
Vol 54 (2) ◽  
pp. 280-289 ◽  
Author(s):  
Yejiao Wang ◽  
Nadia Benahmed ◽  
Yu-Jun Cui ◽  
Anh Minh Tang
Keyword(s):  
Shear Modulus ◽  
Shear Wave ◽  
Shear Wave Velocity ◽  
High Frequency ◽  
Small Strain ◽  
P Wave ◽  
S Wave ◽  
Bender Elements ◽  
Small Strain Shear Modulus ◽  
First Arrival

Bender elements technique has become a popular tool for determining shear wave velocity, Vs, hence the small-strain shear modulus of soils, Gmax, thanks to its simplicity and nondestructive character among other advantages. Several methods were proposed to determine the first arrival of Vs. However, none of them can be widely adopted as a standard and there is still an uncertainty on the detection of the first arrival. In this study, bender elements tests were performed on lime-treated soil and both shear wave and compression wave velocities at various frequencies were measured. In-depth analysis showed that the S-wave received signal presents an identical travel time and opposite polarity compared with that of the S-wave components in P-wave received signal, especially at high frequency. From this observation, a novel interpretation method based on the comparison between the S-wave and P-wave received signals at high frequency is proposed. This method enables the determination of the arrival time of the S-wave objectively, avoiding a less reliable first arrival pick-up point. Furthermore, the “π-point” method and cross-correlation method were also employed and the obtained results agree well with those from the proposed method, indicating the accuracy and reliability of the latter. The effects of frequency on the shear wave velocity are also discussed.

Simulation of wave propagation in linear thermoelastic media

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. T1-T11 ◽  
Author(s):  
José M. Carcione ◽  
Zhi-Wei Wang ◽  
Wenchang Ling ◽  
Ettore Salusti ◽  
Jing Ba ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Wave Propagation ◽  
Grid Method ◽  
P Wave ◽  
Thermal Mode ◽  
S Wave ◽  
Splitting Algorithm ◽  
Low Frequencies ◽  
First Order ◽  
Time Stepping

We have developed a numerical algorithm for simulation of wave propagation in linear thermoelastic media, based on a generalized Fourier law of heat transport in analogy with a Maxwell model of viscoelasticity. The wavefield is computed by using a grid method based on the Fourier differential operator and two time-integration algorithms to cross-check solutions. Because the presence of a slow quasistatic mode (the thermal mode) makes the differential equations stiff and unstable for explicit time-stepping methods, first, a second-order time-splitting algorithm solves the unstable part analytically and a Runge-Kutta method the regular equations. Alternatively, a first-order explicit Crank-Nicolson algorithm yields more stable solutions for low values of the thermal conductivity. These time-stepping methods are second- and first-order accurate, respectively. The Fourier differential provides spectral accuracy in the calculation of the spatial derivatives. The model predicts three propagation modes, namely, a fast compressional or (elastic) P-wave, a slow thermal P diffusion/wave (the T-wave), having similar characteristics to the fast and slow P-waves of poroelasticity, respectively, and an S-wave. The thermal mode is diffusive for low values of the thermal conductivity and wave-like for high values of this property. Three velocities define the wavefront of the fast P-wave, i.e., the isothermal velocity in the uncoupled case, the adiabatic velocity at low frequencies, and a higher velocity at high frequencies.

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