CSEM modeling of a VTI layered medium with the effective anisotropic medium

CSEM modeling of a VTI layered medium with the effective anisotropic medium

Ogunbo, J.N.

Slob, E.C. (mentor)
Mulder, W. (mentor)

Civil Engineering and Geosciences

Section of Applied Geophysics and Petrophysics

2011-08-25

The numerical modeling with the diffusive controlled source electromagnetic (CSEM) method has been used to validate the published results of Ellis et al. (2010a) by first investigating the validity of effective medium theory for both horizontally layered isotropic and vertically transverse isotropic (VTI) layered earth. Ellis et al. (2010a) used ’moving window average method’ to calculate bulk vertical and horizontal resistivities of resistivity logs, from which they calculated effective anisotropic ratio. The question is if the application of their local averaging scheme is valid also for a layered earth. The investigation of effective medium theory is done in horizontal wavenumber-frequency domain (k??) which allows us to evaluate the influence of propagation and attenuation parts of the complex vertical wavenumber on the existence and stability of the effective solution for the whole range of wavenumber, k. For the layered models considered, the total thickness is held constant while the number of layers is varied with consequent changes in thickness of the individual layer. Also, reflection and transmission interactions are both ignored and included. For the horizontally layered isotropic earth, with only propagation-diffusion term, a stable effective transverse electric (TE-mode) isotropic conductivity exists from 0.5% of maximum wavenumber irrespective of the unit thickness of a layer. But with the inclusion of reflection and transmission interactions, the effective skin depth or wavelength has to be sufficiently large compared with unit thickness of the layered earth for a stable solution to exist at all values of wavenumber, k. It is noted that effective transverse magnetic (TM-mode) isotropic conductivity is not the same as that of TE-mode for large wavenumber, k, because of the different limits of their reflection coefficients at large k. However, there are no effective vertically transverse isotropic (VTI) parameters which satisfy the horizontally layered isotropic or VTI layered earth because the effective VTI parameters are wavenumber, k-dependent, though with approximately constant effective anisotropic ratio. We conclude that the effective medium theory adopted by Ellis et al. (2010a) is not a valid approach for modeling a layered earth, though it may be valid for a local measurement.

CSEM
VTI
Effective

http://resolver.tudelft.nl/uuid:2874d588-e0ed-4dae-90c4-e1d7ba61ea6c

Student theses

master thesis

(c) 2011 Ogunbo, J.N.