Non-planar antennae for directional resistivity logging

A downhole tool comprising:

• a downhole tool body having a longitudinal axis;
• a non-planar antenna deployed on the tool body, the antenna including at least one non-planar loop of antenna wire deployed about the tool body;
• the loop of antenna wire including first and second sections defining corresponding first and second geometric planes;
• and
• at least one antenna circuit electrically connected to the antenna wire.

A downhole tool comprising:

• a downhole tool body having a longitudinal axis;
• a non-planar antenna deployed on the tool body, the antenna including first and second antenna wires deployed about the tool body in a single non-planar, circumferential recess formed in the tool body;
• and
• the first and second antenna wires being electrically connected to corresponding first and second antenna circuits such that the first antenna wire is configured to transceive z-mode electromagnetic radiation and the second antenna wire is configured to transceive x-mode electromagnetic radiation.