Method and system of determining elemental content of an earth formation

A system comprising:

• a tool configured to be placed within a borehole in an earth formation, the tool comprising:
• a source of neutrons;
• and
• a gamma detector to detect gammas of different energy levels;
• and
• a processor coupled to the gamma detector to:
• find a solution to a system of equations based on the spectrum of counted gammas obtained by counting gammas of different energy levels detected at the gamma detector, the system of equations having a plurality of solutions, and the solution being indicative of a plurality of weight percentages for a respective plurality of elements within the formation;
• determine whether the solution meets a predetermined constraint on the relative weight percentages indicated for at least two of the elements;
• and
• if the solution does not meet the predetermined constraint, discard the solution and repeat the processes to find a different solution to the system of equations until a solution is found which is determined to meet the predetermined constraint.

A non-transitory computer-readable medium storing a program that, when executed by a processor, causes the processor to:

• find a solution to a system of equations based on a spectrum of counted gammas received from a gamma detector of a tool positioned in a borehole of a formulation, which system of equations has a plurality of solutions, the solution being indicative of a plurality of weight percentages for a respective plurality of elements within formation;
• determine whether the solution meets a predetermined constraint on the relative weight percentages indicated for at least two of the elements with the formulation;
• and
• if the solution does not meet the predetermined constraint, discard the solution and repeat the processes to find a different solution to the system of equations until a solution is found which is determined to meet the predetermined constraint.