Elastic and poroelastic analysis of Thomsen parameters for seismic waves in finely layered VTI media

James G. Berryman

berryman@sep.stanford.edu

ABSTRACT

Layered earth models are well justified by experience, and provide a simple means of studying fairly general behavior of the elastic and poroelastic characteristics of seismic waves in the earth. Thomsen's anisotropy parameters for weak elastic and poroelastic anisotropy are now commonly used in exploration, and can be conveniently expressed in terms of the layer averages of Backus. Since our main interest is usually in the fluids underground, it would be helpful to have a set of general equations relating the Thomsen parameters as directly as possible to the fluid properties. This end can be achieved in a rather straightforward fashion for these layered earth models, and the present paper develops and then discusses these relations. It is found that, although there are five effective shear moduli for any layered VTI medium, one and only one effective shear modulus for the layered system contains all the dependence of pore fluids on the elastic or poroelastic constants that can be observed in vertically polarized shear waves in VTI media. The effects of the pore fluids on this effective shear modulus can be substantial (as much as a factor of 5 in the examples presented here) when the medium behaves in an undrained fashion, as might be expected at higher frequencies such as sonic and ultrasonic waves for well-logging or laboratory experiments, or at seismic wave frequencies for low permeability regions of reservoirs, prior to hydrofracing. The results presented are strictly for velocity analysis, not for amplitude or attenuation.