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Seismic Q of inhomogeneous plane waves in porous media

Xu Liu, Stewart Greenhalgh and Jose M. Carcione
Seismic Q of inhomogeneous plane waves in porous media
Geophysics (April 2020) 85 (3): T209-T224

Abstract

Seismic waves in an attenuative porous medium are generally inhomogeneous waves, which have different directions of propagation and attenuation. The dissipation factors (1/Q) of inhomogeneous waves are strongly dependent on the degree of wave inhomogeneity and cannot be expressed correctly with the usual 1/Q expressions valid only for homogeneous waves. We have used the differing definitions of 1/Q for inhomogeneous waves (i.e., the ratio of the time-averaged dissipated energy density to the time-averaged strain energy density or time-averaged total energy density) and the complex form of the energy balance equations of poroviscoelastic media to derive concise and explicit expressions for the dissipation factors. They are given as simple functions of the material parameters and the wave inhomogeneity parameter for inhomogeneous SV-waves and fast and slow P-waves. The isotropic, poroviscoelastic medium under consideration is upscaled from effective Biot theory for a double-porosity solid, which is the most general theory to describe wave propagation in a reservoir. We find that, if the inhomogeneity parameter is infinite (i.e., the inhomogeneity angle is 90 degrees ) for all three Biot waves, then the dissipation factors only depend on the ratio of the imaginary to the real part of the complex shear modulus. Our explicit expressions for the dissipation factors of poroviscoelastic materials also are reduced to obtain their counterparts for viscoelastic media as a special case. The inhomogeneous waves in an example poroviscoelastic material are used to demonstrate that the 1/Q values of the three Biot waves strongly depend on the inhomogeneity parameters and furthermore the different definitions may cause significant differences of 1/Q values. We find that the dissipation factor of fast P-waves may decrease with the increasing degree of inhomogeneity, which contradicts previously published results.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 85
Serial Issue: 3
Title: Seismic Q of inhomogeneous plane waves in porous media
Affiliation: King Fahd University of Petroleum and Minerals, College of Petroleum Engineering & Geosciences, Dhahran, Saudi Arabia
Pages: T209-T224
Published: 20200429
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 26
Accession Number: 2020-049491
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Annotation: Includes appendices
Illustration Description: illus. incl. 1 table
Secondary Affiliation: Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, ITA, Italy
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2020, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 202014
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