NDLI: Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium

Please wait, while we are loading the content...

A mathematical model for 2D heat transfer dynamics in fluid systems with localized sink of magmatic fluid into local fractured zones above the top of crystallizing intrusions

Three-dimensional inversion of the single-profile magnetotelluric data

Three-dimensional geoelectrical model of metallogenic zones in the Kuznetsk-Alatau folded area

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 9-10, September 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 7-8, July 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 6, June 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 5, May 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 4, April 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 3, March 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 2, February 2012

Izvestiya, Physics of the Solid Earth : Volume 48, Issue 1, January 2012

Izvestiya, Physics of the Solid Earth : Volume 47

Izvestiya, Physics of the Solid Earth : Volume 46

Izvestiya, Physics of the Solid Earth : Volume 45

Izvestiya, Physics of the Solid Earth : Volume 44

Izvestiya, Physics of the Solid Earth : Volume 43

Izvestiya, Physics of the Solid Earth : Volume 42

Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium

Content Provider	Springer Nature Link
Author	Kevorkyants, S. S.
Copyright Year	2012
Abstract	The system of Biot vector equations in the frequency space includes two elliptic-type vector partial differential equations with unknown displacement vectors in the solid and liquid phases. Considering the Biot equations, alongside with Pride’s equations, the key approaches to the theoretical study of the elastic waves in the two-phase fluid-saturated media, the author suggests an analytical solution for the inhomogeneous Biot equations in the frequency space, which is reduced to finding its fundamental solution (Green’s function). The solution of this problem consists of solutions for two systems of Biot equations. In the first system, only the first equation is inhomogeneous, while in the second system, only the second equation is inhomogeneous and, as it is shown, its right-hand side is exclusively a potential function. The fundamental solution of the full system of inhomogeneous Biot equations (in which both equations are inhomogeneous) is represented in the form of Green’s matrix-tensor, for the scalar elements of which the analytical relations are presented. The obtained formulas describing the elastic displacements of both the solid and liquid phases reflect three wave types, namely, compressional waves of the first and the second kind (the fast and the slow waves, respectively) and shear waves. Similar terms (those describing the same type of the elastic waves in the solid and liquid phases) in the expressions for Green’s functions are linked with each other through the coefficient that links the components of the displacement vectors of the solid and liquid phases corresponding to the given wave type.
Starting Page	798
Ending Page	805
Page Count	8
File Format	PDF
ISSN	10693513
Journal	Izvestiya, Physics of the Solid Earth
Volume Number	48
Issue Number	11-12
e-ISSN	15556506
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2012-12-14
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	two-phase medium inhomogeneous Biot equations fundamental solution Green’s matrix tensor fast and slow compressional waves shear waves Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Environmental Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On the applicability of the Biot solution to the problems of elastic propagation in saturated porous media

Shock tube experiments and the observation of the biot slow wave in natural rocks.

Simulation of Wave Propagation Through Inhomogeneous Medium Waveguides Based on Green’s Functions

The phase relations between the first arrivals of compressional and shear waves, and their signification to full wave logging

About the Integral Equations for Calculation of Green’s Tensor in Elastic Inhomogeneous Medium

Transport solutions of the Lamé equations and shock elastic waves

Determining Green’s Functions for Coupled Elastic Waves and Electromagnetic Fields in a Homogeneous Porous Medium

Green’s Functions for Axially Symmetric Elastic Waves in Unbounded Inhomogeneous Media Having Constant Velocity Gradients

Two-dimensional models of elastic tides in a horizontally heterogeneous medium

Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium

Similar Documents

On the applicability of the Biot solution to the problems of elastic propagation in saturated porous media

Shock tube experiments and the observation of the biot slow wave in natural rocks.

Simulation of Wave Propagation Through Inhomogeneous Medium Waveguides Based on Green’s Functions

The phase relations between the first arrivals of compressional and shear waves, and their signification to full wave logging

About the Integral Equations for Calculation of Green’s Tensor in Elastic Inhomogeneous Medium

Transport solutions of the Lamé equations and shock elastic waves

Determining Green’s Functions for Coupled Elastic Waves and Electromagnetic Fields in a Homogeneous Porous Medium

Green’s Functions for Axially Symmetric Elastic Waves in Unbounded Inhomogeneous Media Having Constant Velocity Gradients

Two-dimensional models of elastic tides in a horizontally heterogeneous medium

Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium