In:
Journal of Geophysical Research: Solid Earth, American Geophysical Union (AGU), Vol. 92, No. B8 ( 1987-07-10), p. 7931-7944
Abstract:
According to Biot's (1956 a , b ) model, the presence of water plays an important role in the propagation of seismic waves in at least three different ways: (1) in an infinite medium, water saturation induces an attenuation that can be accounted for by a complex formulation of wave velocities, as in viscoelastic media; (2) at the boundaries of the saturated medium, pore pressure and water flux determine specific continuity conditions; and (3) there is a second compressional wave, called the P 2 wave. In this paper, we discuss the latter two effects. Biot's model is presented first, with homogenization theory used to provide the numerical values of the different coefficients used in the model. In an infinite medium, the model is of practical interest when the frequency ƒ is about the same order of magnitude as a characteristic frequency noted ƒ c , which depends on the properties of the constituents. This limits the application of Biot's model to a few particular fields in geophysics. In a layered medium, Biot's model has a wider scope in that it provides a tool for modeling fluid‐solid interaction at the boundaries of the saturated medium. This is illustrated in our paper for the case of a very permeable water‐saturated surface layer over an elastic half‐space. Two examples are given; in the first example (rigid sands) we discuss the physics of the strongly attenuated P 2 wave predicted by Biot, the amplitude of which becomes significant when the ƒ/ƒ c ratio is about equal to or greater than 0.1. In the second example (soft unconsolidated sediments) the P 2 wave is negligible, but the calculation of the complete wave field is required when the ƒ/ƒ c ratio is about 0.01. There is no adequate equivalent single phase model that gives a correct estimation of the amplitude of the ground motion. In this case, we argue that the P 2 wave is not important in itself, but Biot's model allows the description of the fluid‐solid interaction at the water table; continuity of effective stress and pore pressure can be explicitly formulated.
Type of Medium:
Online Resource
ISSN:
0148-0227
DOI:
10.1029/JB092iB08p07931
Language:
English
Publisher:
American Geophysical Union (AGU)
Publication Date:
1987
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