Abstract

Inversion of open hole logs is performed by solving the simultaneous system of logging tool response equations through statistical approach by using weighted least square minimization technique. It involves minimization of the objective function i.e. summation of square of errors between the measured and constructed logs by incorporating the total uncertainties on tools, parameters and response equations. Global minimum for objective function is ensured for a particular combination of input and output parameters. However, theoretically same value of objective function can be achieved with infinite number of combinations of input / output parameters, even with uniquely determined system of equations. Imposition of geological and geophysical constraints on the solutions brings it to a finite but still too large to fix it for a unique set of parameters. Further, imposition of constraints from core measurements viz. porosity, mineral volumes and grain density and production testing results on input/output parameters, makes the parameters selection easier and more realistic in a particular geological setting. Hence, validation of input/output parameters becomes essential part of log data processing / interpretation with greater degree of authenticity, similar to calibration of logging tools prior to recording / presentation of logs.