Apparatus and Methods for Estimating Tool Inclination Using Bit-Based Gamma Ray Sensors

An apparatus for use in drilling a wellbore in a formation, comprising:

• a drill bit having a cone and a longitudinal axis;
• at least two gamma ray sensors placed spaced-apart in the cone of the drill bit in a plane at an angle to the longitudinal axis, wherein each gamma ray sensor is configured to detect gamma rays from the formation in front of such sensor during drilling of the wellbore and to provide signals corresponding to the detected gamma rays;
• and
• a circuit configured to process the signals from the at least two gamma ray sensors to estimate an inclination of the drill relative to the longitudinal axis.

A method of drilling a wellbore, comprising:

• drilling a wellbore in a formation using a drill bit having a plurality of gamma ray sensors in the drill bit;
• obtaining measurements from each of the plurality of gamma ray sensors relating to detection of gamma rays from the formation;
• and.
• estimating an inclination of the drill bit using the measurements from the plurality of gamma ray sensors.