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Rheology and wave propagation by J. M. Carcione (OGS) firstname.lastname@example.org
Page: 2 Shot gather Distance (m) Distance (m) Depth (m) Geological model Seismic exploration
Page: 5 Poro-elasticity
Page: 6 Strain energy - Stress-strain relation
Page: 7 Jacketed test
Page: 8 Unjacketed test
Page: 9 Elastic moduli
Page: 10 Gassmann modulus
Page: 11 Gassmann modulus- variation of fluid content
Page: 12 Gassmann modulus - Examples
Page: 13 Gassmann modulus - Examples
Page: 14 Gassmann modulus - Examples
Page: 15 Gassmann modulus - Fluid substitution
Page: 16 Kinematics of the porous medium
Page: 17 Dissipation and equations of motion
Page: 18 The waves
Page: 19 Visco-elasticity
Page: 20 Burgers model
Page: 21 Burgers model - stress-strain relation
Page: 22 Burgers model - Creep function
Page: 23 Mechanical models Maxwell Kelvin-Voigt Zener
Page: 24 Zener model - Creep function
Page: 25 Zener model - Relaxation function
Page: 26 Zener model - velocity and attenuation
Page: 27 Maxwell model - creep and relaxation
Page: 28 Memory variable
Page: 29 Viscoelastic equations
Page: 30 Anisotropy
Page: 31 Stress-strain relation
Page: 32 Triclinic media (21)
Page: 33 Transversely-isotropic media (5)
Page: 34 Orthorhombic media (9)
Page: 35 Monoclinic media (12)
Page: 36 Anisotropy - eigenstrains - attenuation iso
Page: 37 Anisotropy - Kelvin-Christoffel matrix
Page: 38 Anisotropy - Slowness-Wavefronts
Page: 39 Anisotropy and attenuation
Page: 40 Relevant references
Rheology and wave propagation by J. M. Carcione (OGS)
The acoustic-electromagnetic analogy José M. Carcione OGS, Trieste, Italy.
On the Physics and Simulation of Waves at Fluid-Solid Interfaces: Application to NDT, Seismic Exploration and Earthquake Seismology by José M. Carcione.
U.S. Geological Survey Menlo Park, CA Workshop Active and Passive Seismics in Laterally Inhomogeneous Media Loučeň Castle, Czech Republic.
6. Seismic Anisotropy A.Stovas, NTNU Definition (1) Seismic anisotropy is the dependence of seismic velocity upon angle This definition yields both.
Geol 4068 Class presentation to accompany reading of Chapter 2- Waves in Fluids Elements of 3D Seismology, 2nd Edition by Christopher Liner September 6,
Measureable seismic properties Seismic velocities – P & S – Relationship to elastic moduli Seismic anisotropy -- directional variation in seismic velocity.
Geology 5660/6660 Applied Geophysics Last time: Brief Intro to Seismology & began deriving the Seismic Wave Equation: Four types of seismic waves: P.
Constitutive Equations CASA Seminar Wednesday 19 April 2006 Godwin Kakuba.
Jiaguo Liu, Mingyu Xu School of Mathematics, Shandong University, Jinan, , P.R. China.
Geology 5660/6660 Applied Geophysics Last time: Seismic Thought Exercise Seismic Concepts : Velocity is distance traveled per unit time, V = x/ t.
A Biot model describing wave propagation in a porous solid saturated by a three-phase fluid Juan E. Santos 1,2 and Gabriela B. Savioli Instituto.
Computational Continuum Mechanics in M&M SMR A. V. Myasnikov D.Sc., Senior Research Scientist, SMR Stavanger, 28 th April, 2006 From Seismics to Simulations.
Equation of State Thermal Expansion Bulk Modulus Shear Modulus Elastic Properties.
Waves Disturbances which travel through space and matter Carry energy and information Sometimes need medium to propagate in (mechanical waves, sound),
Viscoelasticity – 1 Lumped Parameter Models for time-dependent behavior DEQ’s as Constitutive Equations.
Material Point Method Solution Procedure Wednesday, 10/9/2002 Map from particles to grid Interpolate from grid to particles Constitutive model Boundary.
Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.
Geology 5640/6640 Introduction to Seismology 30 Jan 2015 © A.R. Lowry 2015 Read for Mon 2 Feb: S&W (§2.4); Last time: The Equations of Motion.
Rheology Relations between stress and strain. Not easy to define Rheology: describes the ability of stressed materials to deform. strain rate creep regimes.
Session: Computational Wave Propagation: Basic Theory Igel H., Fichtner A., Käser M., Virieux J., Seriani G., Capdeville Y., Moczo P. The finite-difference.
Rheology two basic relationships between stress and strain (geologic rheology) Elastic (Hookes law) Viscous Combinations of elastic and viscous Strain.
Geology 5660/6660 Applied Geophysics 20 Jan 2016 © A.R. Lowry 2016 Last time: Brief Intro to Seismology & derivation of the Seismic Wave Equation: Four.
VostokVostok José M. Carcione (OGS, Italy). Location in Antarctica.
Fluid substitution effects on seismic anisotropy Long Huang, Robert Stewart, Samik Sil, and Nikolay Dyaur Houston April 2 nd,
Assumptions introduced to explain a thing must not be multiplied beyond necessity.
11-5 Damped Harmonic Motion Typically, harmonic motion decreases in amplitude with time….this realistic model describes damped harmonic motion. The damping.
O Elasticity. o Viscosity. o Plasticity. Ideal materials fall into one of the following categories : Rheology Different materials deform differently under.
By Paul Delgado Advisor – Dr. Vinod Kumar Co-Advisor – Dr. Son Young Yi.
1D Kinematics Equations and Problems. Velocity The rate at an object changes position relative to something stationary. X VT ÷ x ÷
Earthquake Seismology: The stress tensor Equation of motion Hooke’s law The elastodynamic equation of motion P-waves and S-waves Follows mainly on Lay.
Wave-Equation Migration in Anisotropic Media Jianhua Yu University of Utah.
Topic 3: Constitutive Properties of Tissues. The Continuum Mechanics Problem 1.Geometry and Structure 2.Boundary Conditions 3.Governing Equations: –Conservation.
8-1 Interpretation of The stress-strain relationship at a point in an elastic material each stress component is related to each of the nine strain components.
Linear Viscoelasticity. Elastic Response Viscous Response.
Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics II tom.h.wilson Department of Geology.
Geology 5660/6660 Applied Geophysics 17 Jan 2014 © A.R. Lowry 2014 Read for Wed 22 Jan: Burger (Ch 2.2–2.6) Last time: The Wave Equation; The Seismometer.
Petrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief Models Digital Formation,
The Asymptotic Ray Theory In order to compute the seismic waves radiated by an earthquake, it is necessary to appropriately compute the Green Functions.
Istituto Nazionale di Oceanografia e di Geofisica Sperimentale - OGS ( Italy) Modeling techniques to study CO 2 -injection induced micro-seismicity by.
WAVES Wave - a periodic disturbance that propagates energy through a medium or space, without a corresponding transfer of matter. e.g.1 sound wave (regular.
Viscoelasticity Soft tissues and cells exhibit several anelastic properties: –hysteresis during loading and unloading –stress relaxation at constant strain.
Constitutive Relations in Solids Elasticity H. Garmestani, Professor School of Materials Science and Engineering Georgia Institute of Technology Outline:
NSF-JHU Workshop on Probability & Materials Multi-Scale Micro-Mechanical Poroelastic Modeling of Fluid Flow in Cortical Bone Colby C. Swan, HyungJoo Kim.
Ground Vibrations and Air Blasts: Causes, Effects and Abatement.
1 Vibration: A repeated back-and-forth or up-and-down motion. Energy: The ability to do work.
The kinematic representation of seismic source. The double-couple solution double-couple solution in an infinite, homogeneous isotropic medium. Radiation.
Introduction to Waves Auto slide change for this page, WAIT…..
1 Lecture # 20: Engineering Properties of Wood. 2 Grain Orientation Density Moisture Temperature Duration, Rate of loading Defects Other Variability MECHANICAL.
MEEN Stress Analysis in Viscoelastic Materials MEEN 5330, Fall 2006 Presented by: SURESH KUMAR ANBALAGAN SAI PRASEN SOMSETTY VEERABHADRA REDDY KAJULURI.
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