Modelling of surface waves in poroelastic saturated materials by means of a two component continuum -- Lecture notes
- Albers, Bettina
2010 Mathematics Subject Classification
- 74J15 76S05 74L05 74S99
- Surface waves, porous media, geophysics, numerical analysis of dispersion relation
These lecture notes are devoted to an overview of the modelling and the numerical analysis of surface waves in two-component saturated poroelastic media. This is an extension to the part of the lecture notes by K. Wilmanski (WIAS-Preprint No. 945) which is primarily concerned with the classical surface waves in single component media. We use the ''simple mixture model'' which is a simplification of the classical Biot's model for poroelastic media. Two interfaces are considered here: firstly the interface between a porous half space and a vacuum and secondly the interface between a porous halfspace and a fluid halfspace. For both problems we show how a solution can be constructed and a numerical solution of the dispersion relation can be found. We discuss the results for phase and group velocities and attenuations, and compare some of them to the high and low frequency approximations. For the interface porous medium/vacuum there exist in the whole range of frequencies two surface waves - a leaky Rayleigh wave and a true Stoneley wave. For the interface porous medium/fluid one more surface wave appears - a leaky Stoneley wave. For this boundary velocities and attenuations of the waves are shown in dependence on the surface permeability. The true Stoneley wave exists only in a limited range of this parameter. At the end we have a look on some results of other authors and a glance on a logical continuation of this work, namely the description of the structure and the acoustic behavior of partially saturated porous media.
- Surface waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks, C. Lai, K. Wilmanski, eds., CISM Courses and Lectures, Springer, Wien [u.a.], 2005, pp. 277-323.