Abstract: This disclosure describes a dielectric logging tool for evaluating the earth formation using at least one transmitter antenna disposed in a cavity on a pad engaged with a borehole wall. The logging tool may comprise at least one power driver in electrical communication with the at least one transmitter antenna and configured to modulate a phase of output current of the at least one power driver. The logging tool may enforce symmetric current on both feeds of the at least one transmitter antenna causing a point of symmetry of the current to align with an axis of geometric symmetry of the at least one transmitter antenna. A parameter of interest of the formation may be estimated by using the attenuation and phase difference between the received and transmitted signals or between received signals from spaced receivers.

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.