Optimization of the Monte Carlo simulation for gamma-gamma litho-density logs

A new method for modelling photon transport in the presence of deep-penetration and streaming effects by combining a subspace weight window and biasing schemes has been developed. This method is based on the usage of the importance map from which an important subspace is identified for a given particle transport system. The biasing schemes, including direction biasing and the exponential transform, are applied to drive particles into the important subspace. The subspace weight window is a splitting and Russian roulette technique that acts as a particle weight stabilizer in the subspace to control weight fluctuations caused by the biasing schemes. This approach has been implemented in the optimization of the McLDL code, a specific purpose Monte Carlo code for modelling the spectral response of dual-spaced gamma-gamma litho-density logging tools, which are highly collimated, deep-penetration, three-dimensional, and low-yield photon transport systems.; The purpose of this work is to provide an efficient and accurate Monte Carlo simulation tool for the design and calibration of gamma-gamma litho-density logging tools. The McLDL code has been tested on the computational benchmark tool and benchmarked against the laboratory test pit data for a commercial gamma-gamma litho-density logging tool Z-Densilog. Compared to the first generation McLDL code, the second generation McLDL code has substantially improved the simulation performance in accuracy and efficiency by decreasing the relative standard deviation by about an order of magnitude and increasing the figure of merit by 20-200 times, depending on the formation property and the source-detector spacing. The McLDL code is also more efficient than the general purpose Monte Carlo code MCNP in modelling the gamma-gamma logging tool response.; The Monte Carlo Multiply Scattered Components (MCMSC) approach has also been developed for gamma-gamma litho-density logging. The MCMSC approach constructs the gamma-ray scattered spectrum for a given set of formation parameters through the library least-squares analysis. The MCMSC approach may provide an efficient method for tool calibrations with a small set of experiments or Monte Carlo calculations.