Forward modelling and inverse problem in the comprehensive interpretation of well logs

Comprehensive interpretation of well logs often consists in solving a set of equations with complex boundary conditions. For each log, the equation combines geological parameters and a response by the device. Minimization is a way of obtaining the best solution that involves finding the minimum of the defined error function. In the case discussed here, an error is a measure of the difference between recorded and theoretical logs.
The simplest and quickest way to determine a solution to the presented problem is to apply the conjugate gradient descent method to minimize the error function. This approach is not efficient in some cases when logging in regions with complex geology.
We prove that a special algorithm using the Monte Carlo method combined with the conjugate gradient descent method gives considerably better results in comprehensive interpretation. A measure of the quality of the proposed method is the discrepancy between the standard solution obtained from commercial software used in the petroleum industry and the new algorithm result.
We present examples of the application of the proposed algorithm for comprehensive interpretation in typical Zechstein dolomite beds and the Carboniferous sandstone layer in the Polish Lowland.