# US 7,609,066 B2 · Apparatus and method for measuring micro-resistivity anisotropy > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 7,609,066 B2 - Document ID: US7609066B2 - Status: Granted - Kind: B2 - Application number: 11/683,754 - Filed: 2007-03-08 - Published: 2007-11-08 - Granted: 2009-10-27 - Earliest claimed: 2006-05-03 - Assignees: Baker Hughes Incorporated - Inventors: Tsili Wang - Web page: https://patentgrep.com/patent/US7609066B2 ## CPC - G01V 3/20: operating with propagation of electric current - G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02) ## Abstract A method for measuring anisotropy in thin-bed formations calls for placing a logging tool into a borehole in the formation and applying current to at least one set of injection electrodes and at least one set of return electrodes to measure resistivity in the formation. Resistivity measurements are used to determine aspects of thin-bed formations exposed in the borehole to the tool. The aspects include the formation azimuth angle (Θ) and the formation dip angle (θ). Typically, the measurements and determinations are completed using apparatus including a computer program product. ## Claims ### Claim 1 A method for determining anisotropic properties in a formation, comprising: measuring, with respect to a coordinate system comprising an x-axis and a z-axis, a potential difference Vxx along the x-axis using a first set of electrodes disposed along the x-axis and a potential difference Vxz along the z-axis using a second set of electrodes disposed along the z-axis for excitation directed along the x-axis, and a potential difference Vzx along the x-axis using the first set of electrodes and a potential difference Vzz along the z-axis using the second set of electrodes for excitation directed along the z-axis; producing a tensor V comprising potential difference components Vxx, Vxz, Vzx and Vzz; and converting the tensor V to apparent resistivity R for the formation, by solving the relationship comprising R = ( Vxx Vzx Vxz Vzz ) ⁢ ( Kx / Ix Kz / Iz ) ; where Kx represents a first geometric factor for the excitation directed along the x-axis; Kz represents a second geometric factor for the excitation directed along the z-axis; Ix represents a first injection current for the excitation directed along the x-axis; and Iz represents a second injection current for the excitation directed along the z-axis. ### Claim 2 (depends on 1) The method as in claim 1, wherein the method further comprises providing on a pad at least one of the first set of electrodes disposed along the x-axis and the second set of electrodes disposed along the z-axis wherein each set of electrodes comprises an injection electrode, a return electrode spaced therefrom and a plurality of measuring electrodes disposed therebetween. ### Claim 3 (depends on 2) The method as in claim 2, wherein at least one potential difference is measured between two measurement electrodes. ### Claim 4 (depends on 2) The method as in claim 2, wherein at least one potential difference is measured between a measurement electrode and at least one of one injection electrode and one return electrode. ### Claim 5 (depends on 1) The method as in claim 1, further comprising rotating the apparent resistivity (R) to determine a dip angle (θ) between a bedding plane for the formation and an azimuth direction (φ) by solving the relationship comprising: Θ T ⁢ R ⁢ ⁢ Θ = ( Rh Rv ) where Θ = ( cos ⁢ ⁢ θ sin ⁢ ⁢ θ - sin ⁢ ⁢ θ cos ⁢ ⁢ θ ) ⁢ ⁢ and Rh represents resistivity of the formation in a direction parallel to the bedding plane; Rv represents resistivity of the formation in a direction perpendicular to the bedding plane; θ represents an angle between the bedding plane and a tool axis Zt; and ΘT represents the transpose of Θ. ### Claim 6 (depends on 1) The method as in claim 1, wherein each set of electrodes comprises an injection electrode, a return electrode spaced therefrom and a plurality of measuring electrodes disposed therebetween, the first set of electrodes and the second set of electrodes comprising an orthogonal relationship with each other. ### Claim 7 A method for determining anisotropic properties in a formation, comprising: measuring, with respect to a coordinate system comprising an x-axis, a y-axis and a z-axis, a potential difference Vxx along the x-axis using a first set of electrodes disposed along the x-axis, a potential difference Vxy along the y-axis using a second set of electrodes disposed along the y-axis and a potential difference Vxz along the z-axis using a third set of electrodes disposed along the z-axis for excitation directed along the x-axis; and a potential difference Vyx along the x-axis using the first set of electrodes, a potential difference Vyy along the y-axis using the second set of electrodes and a potential difference Vyz along the z-axis using the third set of electrodes for excitation directed along the y-axis; and a potential difference Vzx along the x-axis using the first set of electrodes, a potential difference Vzy , along the y-axis using the second set of electrodes and a potential difference Vzz along the z-axis using the third set of electrodes for excitation directed along the z-axis; producing a tensor V from the potential difference components Vxx, Vxy, Vxz, Vyx, Vyy, Vyz, Vzx, Vzy, and Vzz; and converting the tensor V to apparent resistivity R for the formation, by solving the relationship comprising: R = ( Vxx Vyx Vzx Vxy Vyy Vzy Vxz Vyz Vzz ) ⁢ ( Kx / Ix Ky / Iy Kz / Iz ) ; where Kx represents a geometric factor of the tool for the excitation directed along the x-axis; Ky represents a geometric factor of the tool for the excitation directed along the y-axis; Kz represents a geometric factor of the tool for the excitation directed along the z-axis; Ix represents a first injection current for the excitation directed along the x-axis; Iy represents a second injection current for the excitation directed along the y-axis; and Iz represents a third injection current for the excitation directed along the z-axis. ### Claim 8 (depends on 7) The method as in claim 7, wherein the method further comprises providing on a pad at least one of the first set of electrodes disposed along the x-axis, the second set of electrodes disposed along the y-axis, and the third set of electrodes disposed along the z-axis, wherein each set of electrodes comprises an injection electrode, a return electrode spaced therefrom and a plurality of measuring electrodes disposed therebetween. ### Claim 9 (depends on 8) The method as in claim 8, wherein at least one potential difference is measured between two measurement electrodes. ### Claim 10 (depends on 8) The method as in claim 8, wherein at least one potential difference is measured between a measurement electrode and at least one of one injection electrode and one return electrode. ### Claim 11 (depends on 7) The method as in claim 7, further comprising rotating the apparent resistivity (R) to determine a dip angle (θ) between a bedding plane for the formation and an azimuth direction (φ) by solving the relationship comprising: Θ T ⁢ R ⁢ ⁢ Θ = ( Rx Ry Rz ) ; ⁢ where Θ = ( cos ⁢ ⁢ θ sin ⁢ ⁢ θ - sin ⁢ ⁢ θ cos ⁢ ⁢ θ ) ⁢ ⁢ and Rx represents resistivity of the formation in the excitation directed along the x-axis; Ry represents resistivity of the formation in the excitation directed along the y-axis; Rz represents resistivity of the formation in the excitation directed along the z-axis; and ΘT represents the transpose of Θ. ### Claim 12 A computer program product stored on machine readable media, the product comprising instructions for measuring anisotropy of a formation by making resistivity measurements, the instructions comprising instructions for: operating a first set of electrodes disposed along an x-axis, a second set of electrodes disposed along a-y-axis, and a third set of electrodes disposed along a z-axis wherein each set of electrodes comprises an injection electrode, a return electrode spaced therefrom and a plurality of measuring electrodes disposed therebetween; measuring a potential difference Vxx along the x-axis, a potential difference Vxy along the y-axis, and a potential difference Vxz along the z-axis for excitation directed along the x-axis; a potential difference Vyz along the x-axis, a potential difference Vyy along the y-axis, and a potential difference Vyz along the z-axis for excitation directed along the y-axis; and a potential difference Vzx along the x-axis, a potential difference Vzy along the y-axis, and a potential difference Vzz along the z-axis for excitation directed along the z-axis; producing a tensor comprising the potential differences for the first axis and the second axis to determine the potential difference V; and converting the tensor V to apparent resistivity R for the formation, by solving the relationship comprising: R = ( Vxx Vyx Vzx Vxy Vyy Vzy Vxz Vyz Vzz ) ⁢ ( Kx / Ix Ky / Iy Kz / Iz ) ; where Kx represents a geometric factor of the tool for the excitation directed along the x-axis; Ky represents a geometric factor of the tool for the excitation directed along the y-axis; Kz represents a geometric factor of the tool for the excitation directed along a third axis z-axis; Ix represents a first injection current for the excitation directed along the x-axis; Iy represents a second injection current for the excitation directed along the y-axis; and Iz represents a third injection current for the excitation directed along the z-axis. ### Claim 13 (depends on 12) The product of claim 12, further comprising rotating the apparent resistivity R to determine a formation dip angle θ between a bedding plane for the formation and an azimuth direction φ.