Sensitivity function technique for modeling nuclear tools

A method of logging a formation comprising:

• traversing a borehole in the formation with a logging tool;
• detecting nuclear radiation in the formation with nuclear detectors in the tool;
• producing a first log of data representing the detected nuclear radiation and an estimation of formation properties including formation density and formation photoelectric absorption as a function of borehole depth;
• producing a three dimensional model of the tool, borehole, and formation;
• using the three dimensional model to calculate separate Compton sensitivity values and photoelectric sensitivity values for each of a plurality of three dimensional sectors of the formation;
• using the estimation of formation properties and the sensitivity values to predict responses of the nuclear detectors in the tool such that the predicted responses are calculated as a function of borehole depth, formation density and formation photoelectric absorption;
• producing a synthetic second log of the predicted nuclear detector responses;
• comparing the synthetic second log to the first log of data;
• modifying the estimation of formation properties based on the comparison of the synthetic second log and the first log of data;
• and
• producing a record indicating formation properties when the synthetic second log and first log of data are substantially similar.

A method of logging a formation comprising:

• traversing a borehole in the formation with a logging tool;
• detecting nuclear radiation in the formation with nuclear detectors in the tool;
• producing a first log of data representing an estimation of fomation density and formation photoelectric absorption, P.sub.e in light of the detected nuclear radiation;
• producing a three dimensional model of the tool, borehole, and formation;
• using the three dimensional model to calculate separate Compton sensitivity values and photoelectric sensitivity values for each of a plurality of three dimensional sectors of the formation;
• using the estimation of formation properties and the sensitivity values to predict responses of the nuclear detectors in the tool for each three dimensional sector such that the predicted responses are calculated as a function of borehole depth, formation density and formation P.sub.e and such that the predicted responses vary as the logging tool traverses the borehole;
• producing a synthetic second log of the predicted nuclear detector responses;
• comparing the synthetic second log to the first log of data;
• modifying the estimation of formation properties based on the comparison of the synthetic second log and the first log of data;
• and
• producing a record indicating formation properties when the synthetic second log and first log of data are substantially similar.