skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Seismic modeling in viscoelastic media

Abstract

Anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories. A general way to take all these mechanisms into account is to use a phenomenologic model. Such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash-pots. A suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology. Two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed. This model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation. This work presents two-dimensional (2-D) and three-dimensional (3-D) forward modeling in linear viscoelastic media. The theory implements Boltzmann's superposition principle based on a spectrum of relaxation mechanisms in the time-domain equation of motion by the introduction of the memory variables. The algorithm uses a polynomial interpolation of the evolution operator for time integration and the Fourier pseudospectral method for computation of the spatial derivatives. This scheme has spectral accuracy for band-limited functions with no temporal or spatialmore » dispersion, a very important fact in anelastic wave propagation. Examples are given of how to pose typical problems of viscoelastic forward modeling for geophysical problems in two and three dimensions.« less

Authors:
 [1]
  1. Osservatorio Geofisico Sperimentale, Trieste (Italy) Hamburg Univ. (Germany). Geophysical Inst.
Publication Date:
OSTI Identifier:
5931111
Resource Type:
Journal Article
Journal Name:
Geophysics; (United States)
Additional Journal Information:
Journal Volume: 58:1; Journal ID: ISSN 0016-8033
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; SEISMIC SURVEYS; DATA PROCESSING; MATHEMATICAL MODELS; DATA ANALYSIS; REFLECTION; SEISMIC WAVES; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; WAVE PROPAGATION; GEOPHYSICAL SURVEYS; PROCESSING; SURVEYS; 580000* - Geosciences

Citation Formats

Carcione, J M. Seismic modeling in viscoelastic media. United States: N. p., 1993. Web. doi:10.1190/1.1443340.
Carcione, J M. Seismic modeling in viscoelastic media. United States. https://doi.org/10.1190/1.1443340
Carcione, J M. Fri . "Seismic modeling in viscoelastic media". United States. https://doi.org/10.1190/1.1443340.
@article{osti_5931111,
title = {Seismic modeling in viscoelastic media},
author = {Carcione, J M},
abstractNote = {Anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories. A general way to take all these mechanisms into account is to use a phenomenologic model. Such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash-pots. A suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology. Two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed. This model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation. This work presents two-dimensional (2-D) and three-dimensional (3-D) forward modeling in linear viscoelastic media. The theory implements Boltzmann's superposition principle based on a spectrum of relaxation mechanisms in the time-domain equation of motion by the introduction of the memory variables. The algorithm uses a polynomial interpolation of the evolution operator for time integration and the Fourier pseudospectral method for computation of the spatial derivatives. This scheme has spectral accuracy for band-limited functions with no temporal or spatial dispersion, a very important fact in anelastic wave propagation. Examples are given of how to pose typical problems of viscoelastic forward modeling for geophysical problems in two and three dimensions.},
doi = {10.1190/1.1443340},
url = {https://www.osti.gov/biblio/5931111}, journal = {Geophysics; (United States)},
issn = {0016-8033},
number = ,
volume = 58:1,
place = {United States},
year = {1993},
month = {1}
}