Abstract: Methods and apparatus for evaluating an earth formation for generating a numerical model comprising an expression equating a representation for the effective conductivity under Archie's law with respect to direct current with a function for the effective conductivity representative of the mixing model with respect to direct current; and solving a system of equations to obtain values for the Archie parameters including at least i) the expression; ii) a second expression equating a first order variation of the representation with a first order variation of the function with respect to water saturation of the formation (Sw); and iii) a third expression equating a first order variation of the representation with a first order variation of the function with respect to porosity of the formation (?). The second and third expressions may equate derivatives of the representation with derivatives of the function.

Abstract: A method for performing a formation physical action includes: transmitting a first time-domain transient electromagnetic (EM) signal into a borehole and the formation using a downhole EM wave propagation tool, the first EM signal having frequency domain components in a range of at least 1 MHz to 1 GHz; receiving a second time-domain transient EM signal due to the transmitting of the first EM signal, the second EM signal having frequency domain components in the range of at least 1 MHz to 1 GHz; calculating attenuation and phase shift S-parameters as a function of frequency using the first and second EM signals; assigning to the formation at least one of a resistivity value and a permittivity value of a reference that matches or is within a selected range of the attenuation and phase shift S-parameters; and performing the physical action using the at least one of the resistivity value and the permittivity value.

Abstract: A method for performing a formation physical action includes: transmitting a first time-domain transient electromagnetic (EM) signal into a borehole and the formation using a downhole EM wave propagation tool, the first EM signal having frequency domain components in a range of at least 1 MHz to 1 GHz; receiving a second time-domain transient EM signal due to the transmitting of the first EM signal, the second EM signal having frequency domain components in the range of at least 1 MHz to 1 GHz; calculating attenuation and phase shift S-parameters as a function of frequency using the first and second EM signals; assigning to the formation at least one of a resistivity value and a permittivity value of a reference that matches or is within a selected range of the attenuation and phase shift S-parameters; and performing the physical action using the at least one of the resistivity value and the permittivity value.

Abstract: A cutting element for an earth-boring drilling tool comprises a cutting body having a cutting surface thereon, and a sensor coupled with the cutting surface, the sensor configured to determine resistivity of a contacting formation. An earth-boring drilling tool comprises a bit body and an instrumented cutting element coupled with the bit body. The cutting element includes a cutting body having a cutting surface thereon, and at least one sensor located proximate the cutting surface. The at least one sensor is oriented and configured to determine resistivity of a contacting formation. A method of determining resistivity of a subterranean formation during a drilling operation comprises energizing a sensor of an instrumented cutting element of a drill bit, sensing a return signal flowing on or through the subterranean formation through the instrumented cutting element, and determining a resistivity of the subterranean formation based, at least in part, on the return signal.

Abstract: A method for inverting dielectric logging tool measurement data to estimate an electrical characteristic of an earth formation includes: receiving measurement data from the logging tool having a transmitter antenna and receiver antennas spaced known distances from the transmitter antenna; establishing an equation relating magnetic field measurements made by the receiver antennas to the distances and a wave vector; establishing an error equation that quantifies a difference between the magnetic field measurements made by the receiver antennas to magnetic field measurements made by the receiver antennas that would be obtained with an estimated formation electrical characteristic; calculating an error using the error equation for an initial estimated value of the wave vector that comprises a term having a first number multiplied times a second number of radians to provide a plurality of calculated errors; and determining a minimum error from the plurality of calculated errors to estimate the electrical character

Abstract: Methods and apparatus for evaluating an earth formation for generating a numerical model comprising an expression equating a representation for the effective conductivity under Archie's law with respect to direct current with a function for the effective conductivity representative of the mixing model with respect to direct current; and solving a system of equations to obtain values for the Archie parameters including at least i) the expression; ii) a second expression equating a first order variation of the representation with a first order variation of the function with respect to water saturation of the formation (Sw); and iii) a third expression equating a first order variation of the representation with a first order variation of the function with respect to porosity of the formation (?). The second and third expressions may equate derivatives of the representation with derivatives of the function.

Abstract: An apparatus for estimating a property of an earth formation includes: a carrier configured to be conveyed through a borehole penetrating an earth formation; a first fractal-shaped antenna element disposed on the carrier and configured to at least one of transmit electromagnetic energy into the formation and receive electromagnetic energy from the formation; and a second fractal-shaped antenna element electrically connected to the first fractal-shaped antenna element at a connection and configured to at least one of transmit electromagnetic energy into the formation and receive electromagnetic energy from the formation; wherein the second fractal-shaped antenna element is substantially a mirror image of the first fractal antenna element with respect to a reflection about the connection.

Abstract: A cutting element for an earth-boring drilling tool comprises a cutting body having a cutting surface thereon, and a sensor coupled with the cutting surface, the sensor configured to determine resistivity of a contacting formation. An earth-boring drilling tool comprises a bit body and an instrumented cutting element coupled with the bit body. The cutting element includes a cutting body having a cutting surface thereon, and at least one sensor located proximate the cutting surface. The at least one sensor is oriented and configured to determine resistivity of a contacting formation. A method of determining resistivity of a subterranean formation during a drilling operation comprises energizing a sensor of an instrumented cutting element of a drill bit, sensing a return signal flowing on or through the subterranean formation through the instrumented cutting element, and determining a resistivity of the subterranean formation based, at least in part, on the return signal.

Abstract: A cutting element for an earth-boring drilling tool comprises a cutting body having a cutting surface thereon, and a sensor coupled with the cutting surface, the sensor configured to determine resistivity of a contacting formation. An earth-boring drilling tool comprises a bit body and an instrumented cutting element coupled with the bit body. The cutting element includes a cutting body having a cutting surface thereon, and at least one sensor located proximate the cutting surface. The at least one sensor is oriented and configured to determine resistivity of a contacting formation. A method of determining resistivity of a subterranean formation during a drilling operation comprises energizing a sensor of an instrumented cutting element of a drill bit, sensing a return signal flowing on or through the subterranean formation through the instrumented cutting element, and determining a resistivity of the subterranean formation based, at least in part, on the return signal.

Abstract: A method for inverting dielectric logging tool measurement data to estimate an electrical characteristic of an earth formation includes: receiving measurement data from the logging tool having a transmitter antenna and receiver antennas spaced known distances from the transmitter antenna; establishing an equation relating magnetic field measurements made by the receiver antennas to the distances and a wave vector; establishing an error equation that quantifies a difference between the magnetic field measurements made by the receiver antennas to magnetic field measurements made by the receiver antennas that would be obtained with an estimated formation electrical characteristic; calculating an error using the error equation for an initial estimated value of the wave vector that comprises a term having a first number multiplied times a second number of radians to provide a plurality of calculated errors; and determining a minimum error from the plurality of calculated errors to estimate the electrical character

Abstract: An apparatus for estimating a property of an earth formation includes: a carrier configured to be conveyed through a borehole penetrating an earth formation; a first fractal-shaped antenna element disposed on the carrier and configured to at least one of transmit electromagnetic energy into the formation and receive electromagnetic energy from the formation; and a second fractal-shaped antenna element electrically connected to the first fractal-shaped antenna element at a connection and configured to at least one of transmit electromagnetic energy into the formation and receive electromagnetic energy from the formation; wherein the second fractal-shaped antenna element is substantially a mirror image of the first fractal antenna element with respect to a reflection about the connection.

Abstract: A cutting element for an earth-boring drilling tool comprises a cutting body having a cutting surface thereon, and a sensor coupled with the cutting surface, the sensor configured to determine resistivity of a contacting formation. An earth-boring drilling tool comprises a bit body and an instrumented cutting element coupled with the bit body. The cutting element includes a cutting body having a cutting surface thereon, and at least one sensor located proximate the cutting surface. The at least one sensor is oriented and configured to determine resistivity of a contacting formation. A method of determining resistivity of a subterranean formation during a drilling operation comprises energizing a sensor of an instrumented cutting element of a drill bit, sensing a return signal flowing on or through the subterranean formation through the instrumented cutting element, and determining a resistivity of the subterranean formation based, at least in part, on the return signal.

Abstract: An apparatus for detecting a position of a component in an earth formation is disclosed. The apparatus includes: a transmitter configured to emit a first magnetic field into the earth formation and induce an electric current in the component, the transmitter having a first magnetic dipole extending in a first direction; and a receiver for detecting a second magnetic field generated by the component in response to the first magnetic field, the receiver having a second magnetic dipole extending in a second direction orthogonal to the first direction. A method and computer program product for detecting a position of a component in an earth formation is also disclosed. Apparatus and methods are also disclosed for estimating a position of a second borehole being drilled relative to an existing first borehole.

Abstract: An apparatus for estimating a property of a formation penetrated by a borehole, the apparatus having: a first electrode and a second electrode configured to couple to a characteristic impedance of a material disposed in the borehole; a third electrode configured with the first electrode to electrically couple to a characteristic impedance of the formation; a circuit element coupled to the first electrode and to the second electrode and having a characteristic impedance; a first sensing circuit coupled to the circuit element and configured to provide a first signal related to the impedance of the borehole material; and a second sensing circuit coupled to the first electrode and the third electrode and configured to provide a second signal related to the characteristic impedance of the formation; wherein the first signal and the second signal are used to estimate the property. A method is also provided.

Abstract: An apparatus, method and computer-readable medium for evaluating an earth formation are disclosed. The apparatus includes at least one coil on a logging tool conveyed in a borehole in the earth formation. Passage of a current through the coil induces an electrical current in the earth formation. At least two electrodes associated with the logging tool and in proximity to a wall of the borehole have a potential difference in response to the induced electrical current that is indicative of a property of the earth formation. The at least one coil may be mounted on a mandrel of a downhole assembly. The electrodes may be positioned on a first pad extendable from a mandrel of the downhole assembly.

Abstract: A mixed mode tool uses an inductive source and detects galvanic currents and/or potentials at electrodes in proximity to a borehole wall to produce a resistivity image of the earth formation. Alternative, the magnetic field produced by a galvanic current is detected by an antenna coil and used to produce a resistivity image.

Abstract: An apparatus for estimating a property of a formation penetrated by a borehole, the apparatus having: a first electrode and a second electrode configured to couple to a characteristic impedance of a material disposed in the borehole; a third electrode configured with the first electrode to electrically couple to a characteristic impedance of the formation; a circuit element coupled to the first electrode and to the second electrode and having a characteristic impedance; a first sensing circuit coupled to the circuit element and configured to provide a first signal related to the impedance of the borehole material; and a second sensing circuit coupled to the first electrode and the third electrode and configured to provide a second signal related to the characteristic impedance of the formation; wherein the first signal and the second signal are used to estimate the property. A method is also provided.

Abstract: An apparatus for detecting a position of a component in an earth formation is disclosed. The apparatus includes: a transmitter configured to emit a first magnetic field into the earth formation and induce an electric current in the component, the transmitter having a first magnetic dipole extending in a first direction; and a receiver for detecting a second magnetic field generated by the component in response to the first magnetic field, the receiver having a second magnetic dipole extending in a second direction orthogonal to the first direction. A method and computer program product for detecting a position of a component in an earth formation is also disclosed. Apparatus and methods are also disclosed for estimating a position of a second borehole being drilled relative to an existing first borehole.

Abstract: A mixed mode tool uses an inductive source and detects galvanic currents and/or potentials at electrodes in proximity to a borehole wall to produce a resistivity image of the earth formation.

Abstract: A mixed mode tool uses an inductive source and detects galvanic currents and/or potentials at electrodes in proximity to a borehole wall to produce a resistivity image of the earth formation. Alternative, the magnetic field produced by a galvanic current is detected by an antenna coil and used to produce a resistivity image. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understand that it will not be used to interpret or limit the scope or meaning of the claims.