A combined weight window and biasing approach based on a subspace importance map in the Monte Carlo simulation of a gamma-gamma lithodensity logging tool response with the revised McLDL code

A combined weight window and biasing approach has been developed to optimize the specific purpose McLDL code for simulating the spectral response of gamma-gamma lithodensity logging tools. The method is based on the use of photon importance maps which are strongly dependent upon the geometric configuration of the logging tool. A subspace in the formation is taken as an importance region and a one-group importance generator is used in conjunction with the current McLDL code. The splitting of a photon only occurs within the important subspace, and direction biasing and the exponential transform are applied to drive photons into that region or the detector. The approach has been tested on a theoretical benchmark problem and the Atlas Wireline Services´ commercial gamma-gamma lithodensity logging tool. Compared to the results from the previous McLDL code, this new approach has eliminated the unacceptably large weight fluctuations and substantially improved the code´s performance in computational accuracy and efficiency