Bounds on the complex conductivity of geophysical mixtures
Alan C. Tripp, Elena Cherkaeva and Jeff Hulen
Journal name: Geophysical Prospecting
Issue: Vol 46, No 6, October 1998 pp. 589 - 601
Info: Article, PDF ( 1.49Mb )
Following previous work on bounds for complex dielectrics, bounds on the complex conductivity of a mixture of two isotropic components can be developed which are independent of any special assumption concerning the geometry of the mixture. If certain broad restrictions are assumed, such as isotropy of the mixture, then the bounds can be made more restrictive. These bounds reveal the range of the induced polarization response which can be caused by a mixture of two materials of known complex conductivity. The bounds can also be generalized for spectral responses. The bounds are conservative lithologically in the sense that many of the special models corresponding to boundary responses have lithological counterparts.
The chief use for the given bounds is to gain insight into the nature of the induced polarization response. It is also possible to use the bounds to estimate the volume fractions of the components. We illustrate how this is done for the case of a general anisotropic medium.