Patent ID: 7392137

Claim:
A method of logging an earth formation comprising a plurality of layers each having a horizontal conductivity and a vertical conductivity, said method comprising: (a) conveying an electromagnetic logging tool through a borehole in said earth formation, said logging tool including at least one transmitter and at least one receiver, said borehole having an axis inclined at a relative dip angle θ to a normal to said layers; (b) getting measurements at a number n 1 of transmitter-receiver orientations at a number n 2 of frequencies, wherein n 1 and n 2 are greater than 1; (c) processing said measurements in (b) to give n 1 focused measurements; (d) processing said n 1 focused measurements using θ and Φ (a relative azimuth angle) to obtain at least two fundamental modes of a diagonal tensor of multi-frequency focused measurements; (e) determining from one of said at least two fundamental modes an estimate of said horizontal conductivity of said earth formation; and (f) storing said estimate of horizontal conductivity to a suitable medium; wherein said n 1 focused measurements are independent and wherein the processing in (d) further comprises solving an equation of the form: ( h ~ xx h ~ xy h ~ xz h ~ yx h ~ yy h ~ yz h ~ zx h ~ zy h ~ zz ) = ( c ϕ 2 ⁢ c θ 2 + s φ 2 c ϕ 2 ⁢ s φ 2 c φ ⁢ s φ - c φ ⁢ s φ ⁢ c θ 2 - c φ ⁢ s φ ⁢ s θ 2 c φ ⁢ c θ ⁢ s θ - c φ ⁢ c θ ⁢ s θ c φ ⁢ s φ - c φ ⁢ s φ ⁢ c θ 2 - c φ ⁢ s φ ⁢ s θ 2 s ϕ 2 ⁢ c θ 2 + c φ 2 s ϕ 2 ⁢ s φ 2 - s φ ⁢ c θ ⁢ s θ s φ ⁢ c θ ⁢ s θ c φ ⁢ c θ ⁢ s θ - c φ ⁢ c θ ⁢ s θ - s φ ⁢ c θ ⁢ s θ s φ ⁢ c θ ⁢ s θ s θ 2 c θ 2 ) ⁢ ( ℏ xx ℏ zz ) where θ is a relative inclination of the borehole axis to the normal to the bedding, φ is an azimuth in a tool coordinate system, s φ =sin φ, c φ =cos φ, s θ =sin θ, c θ =cos θ, and h- xx and h- zz are said at least two fundamental modes.