System, method and apparatus for petrophysical and geophysical measurements at the drilling bit

A method for determining at least one characteristic of a downhole formation, the method comprising:

• disposing at least two axially spaced sensors on a long gauge bit;
• taking a first pair of data samples of a formation with the at least two axially spaced sensors at a first time;
• taking a second pair of data samples of the formation with the at least two axially spaced sensors at a second time;
• and
• determining a distance traveled by the long gauge bit by comparing the first and second pairs of data samples;
• and
• determining the formation characteristic based, at least in part, on a radial distance traveled by the long gauge bit.

A formation characteristic measurement system, comprising:

• a logging-while-drilling tool for coupling to a drill string;
• a drive system coupled to the logging-while-drilling tool;
• a long gauge bit;
• and
• at least one sensor disposed in an insert of the long gauge portion of the long gauge bit, the sensor configured to sample data from a formation at rotation intervals of the long gauge bit;
• a computer comprising at least one processor and a memory, wherein the memory includes executable instruction that cause the at least one processor to determine at least one formation characteristic base, at least in part, on the sampled data.