scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 251-253
Author(s):  
H. T. Prodaivoda ◽  
◽  
S. A. Vyzhva ◽  
Yu. A. Onanko ◽  
A. P. Onanko ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Elastic Constants ◽  
Elastic Symmetry ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Non Destructive

The elastic constants are appraised sandstones of Volino – Podolskiy region, which testify that elastic symmetry is orthorhombic. The anisotropy parameters of rock-collectors are explored from the ultrasonic results measurements of elastic wave velocities. The method of measurings of anisotropy parameters of elastic wave velocities is offered for non-destructive control of structure of sandstones.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Da Shuai ◽  
Alexey Stovas ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Yang Zhao
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Significant Influence ◽  
Transversely Isotropic ◽  
Azimuth Angle ◽  
Effective Medium ◽  
P Wave ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

scholarly journals On three-stage temperature dependence of elastic wave velocities for rocks

2021 ◽  
Vol 18 (3) ◽  
pp. 328-338
Author(s):  
Nianqi Li ◽  
Li-Yun Fu ◽  
Jian Yang ◽  
Tongcheng Han
Keyword(s):  
Elastic Wave ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Nonlinear Behavior ◽  
P Wave ◽  
Shape Model ◽  
Wave Velocities ◽  
Nonlinear Thermoelasticity ◽  
Velocity Variations ◽  
Shape Curve

Abstract For most rocks, the typical temperature behavior of elastic wave velocities generally features a three-stage nonlinear characteristic that could be expressed by a reverse S-shape curve with two inflexion points. The mechanism regulating the slow-to-fast transition of elastic constants remains elusive. The physics of critical points seems related to the multimineral composition of rocks with differentiated thermodynamic properties. Based on laboratory experiments for several rocks with different levels of heterogeneity in compositions, we conduct theoretical and empirical simulations by nonlinear thermoelasticity methods and a S-shape model, respectively. The classical theory of linear thermoelasticity based on the Taylor expansion of strain energy functions has been widely used for crystals, but suffers from a deficiency in describing thermal-associated velocity variations for rocks as a polycrystal mixture. Current nonlinear thermoelasticity theory describes the third-order temperature dependence of velocity variations by incorporating the fourth-order elastic constants. It improves the description of temperature-induced three-stage velocity variations in rocks, but involves with some divergences around two inflexion points, especially at high temperatures. The S-shape model for empirical simulations demonstrates a more accurate depiction of thermal-associated three-stage variations of P-wave velocities. We investigate the physics of the parameters ${a_1}$ and ${b_1}$ in the S-shape model. These fitting parameters are closely related to thermophysical properties by being proportional to the specific heat and thermal conductivity of rocks. We discuss the mechanism that regulates the slow-to-fast transition in the three-stage nonlinear behavior for various rocks.

Thermoelastic Properties of (Mg,Fe)SiO3 Perovskite

2002 ◽  
Vol 718 ◽  
Author(s):  
Boris Kiefer ◽  
Lars Stixrude
Keyword(s):  
Elastic Wave ◽  
Elastic Properties ◽  
Solid Solutions ◽  
Elastic Constants ◽  
Lower Mantle ◽  
High Pressures ◽  
Thermoelastic Properties ◽  
Wave Velocities ◽  
Lateral Variations ◽  
Iron Bearing

AbstractMagnesium rich (Mg1-x,Fex perovskite is thought to be the most abundant mineral in the earth's lower mantle between 660 km and 2900 km depth. We discuss (mg,Fe) solid solutions and their elastic properties at lower mantle pressures. The diffrences of the elastic constants between the Mg-endmember and the iron bearing perovskite with x=0.25 are used to predict the compositional contribution to lateral variations of elastic wave-velocities at high pressures. These predictions are compared and discussed in the context of seismic observations.

A vertical fracture cluster embedded into thinly layered medium

2021 ◽  
Author(s):  
Alexey Stovas ◽  
Da Shuai
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Gaussian Function ◽  
Azimuth Angle ◽  
Effective Medium ◽  
Compliance Matrix ◽  
Stiffness Coefficients ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

<p>The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium, according to Schoenberg and Helbig, 1997), the effective medium becomes orthorhombic.  The vertical fractures may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures’ azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the (x<sub>2</sub>; x<sub>3</sub>) plane than that in the (x<sub>1</sub>; x<sub>3</sub>) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium. Assuming that the fracture cluster has a preferred azimuth angle and other fractures are statistically distributed around it, we define the effective compliance matrix by a Gaussian function,  the Bond transformation matrix and  the excess compliance matrix of the vertical fractures in the eigen-coordinate system. The resulting effective medium possess the monoclinic symmetry. The monoclinic anisotropy parameters (Stovas, 2021) can easily be defined from the effective stiffness coefficients.</p><p> </p><p>Schoenberg, M. and Helbig K., 1997, Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth, Geophysics, <strong>62</strong>(6), 1954-1974.</p><p>Stovas, A., 2021, On parameterization in monoclinic media with a horizontal symmetry plane, Geophysics (early online).</p>

Assessing rock brittleness and fracability from radial variation of elastic wave velocities from borehole acoustic logging

2016 ◽  
Vol 64 (4) ◽  
pp. 958-966 ◽  
Author(s):  
Xiao-Ming Tang ◽  
Song Xu ◽  
Chun-Xi Zhuang ◽  
Yuan-Da Su ◽  
Xue-Lian Chen
Keyword(s):  
Elastic Wave ◽  
Radial Variation ◽  
Acoustic Logging ◽  
Wave Velocities ◽  
Rock Brittleness

Elastic Wave Velocities in Laminated Media

1954 ◽  
Vol 26 (5) ◽  
pp. 949-949
Author(s):  
J. E. White ◽  
F. A. Angona
Keyword(s):  
Elastic Wave ◽  
Wave Velocities
Sign in / Sign up

Export Citation Format

Share Document