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Interaction of seismic waves with a viscous liquid layer

DEPARTMENT OF EARTH AND PLANETARY SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139

Abstract

The interaction of seismic waves with a layer filled with a viscous fluid is studied. This study is intended to provide the basis for designing active seismic experiments to detect the existence of hydraulically induced fractures in a Hot Dry Rock Geothermal energy system. We compute transmission and reflection coefficients for P, SV, and SH waves incident at arbitrary angles onto a fluid layer embedded between two homogeneous half-spaces. We find that coefficients for SH waves at normal incidence can be written in terms of two dimensionless parameters. One of these parameters, I, is the ratio of acoustic impedance of the fluid to the acoustic impedance of the solid. The other dimensionless parameter, d, is a measure of the amount of energy the SH wave loses during one pass through the fluid layer. We find that the amplitude of the SH wave transmitted through the fluid layer is equal to the amplitude of the incident SH wave if I is nearly 1 and d is small. As d increases, energy is lost due to viscous dissipation in the fluid and transmitted wave amplitude diminishes. If I is not nearly 1, some energy is reflected by the fluid layer. Three dimensionless parameters are required for solution for the case of P waves normally incident on the fluid layer. One parameter, R, is the ratio of the bulk modulus to effective shear modulus of the fluid. The second parameter is the ratio of elastic impedance of the solid to the shear impedance of the fluid and the third is d. We find that the value of R is a good measure of the importance of fluid viscosity on the propagation of P waves through the fluid. Detailed studies of the effects of fluid and solid physical properties on the amplitudes of transmitted and reflected waves when waves are normally incident provide valuable insight into the importance of physical properties in the calculations for non-normal incidence. Finally, reflection and transmission coefficients are computed for P and SV waves incident at arbitrary angle on a viscous fluid layer. Physical properties of fluid and rock are chosen to be those thought appropriate for the Los Alamos National Laboratory Hot Dry Rock Geothermal test site located at Fenton Hill, New Mexico.

Footnotes

^* Present address: School of Oceanography, Oregon State University, Corvallis, Oregon 97331.

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