Dispersive Properties of Liquid overlying an Aeolotropic Half-space

Abstract

The dispersion equation for the velocity of waves of Rayleigh type travelling in a homogeneous and transversely isotropic half-space, above which is a uniform layer of liquid of finite depth, is obtained in Part I.Phase and group velocities of the waves were calculated numerically as functions of wave number and for several different values of the elastic parameters and the dispersion curves are presented in Part 11. These are compared with the curves obtained when the solid medium is completely isotropic.PART I

Dispersion of Rayleigh, Scholte, Stoneley and Love waves in a model consisting of a liquid layer overlying a two-layer transversely isotropic solid medium

“…Fig. 3 shows the agreement of the results with those presented by Abubakar & Hudson (1961), for another special case when h = 0, where the elastic properties of the liquid and the lower VTI half-space are such that ρ S /ρ l = 2, c SV /c l = √ 2, c P /c SV = 2.032.…”

“…When h tends to zero, or the elastic constants and density of the middle layer are put equal to those of the lowermost material, we obtain from the general result the dispersion of surface waves for a liquid layer overlying a half-space consisting of the bottom material. The frequency equation in this case leads to the following which is identical to the equation obtained by Abubakar & Hudson (1961): Case 4. If h vanishes (i.e.…”

“…The root of the frequency equation is pertinent to the wavenumber of the interface wave associated with the Scholte wave for a liquid layer overlying a half-space, which consists of the middle layer material, regardless of the lowermost layer. For the Scholte wave the frequency equation reduces to the following which is the same equation obtained by Abubakar & Hudson (1961) for a model of a liquid layer overlying a transversely isotropic half-space:…”

“…Case 6. If the thickness of the liquid layer is set to zero and the material properties of the two layers are made isotropic then one can obtain the results developed by Ewing et al (1957) and Abubakar & Hudson (1961) for an isotropic solid layer overlying an isotropic solid half-space.…”

“…Khojasteh et al (2008a) extended the previous work to represent explicit expressions for the dynamic Green's functions in a transversely isotropic half-space and continued the work for full spaces comprised of two and three dissimilar materials, as well as two-layered and multilayered half-spaces (Khojasteh et al 2008b(Khojasteh et al ,c, 2011(Khojasteh et al , 2013. A transversely isotropic bed in contact with a liquid layer was first studied by Abubakar & Hudson (1961). Many years later, Sharma et al (1990Sharma et al ( , 1991 deduced the frequency (dispersion) equation for Rayleigh type surface waves on a model consisting of a liquid layer lying over a solid layer which itself is underlain by a solid halfspace.…”