Adaptive approximation of zero variance biasing in Monte Carlo gamma ray transport models of oil well logging tools

This research developed Monte Carlo codes that adaptively adjust the applied biasing parameters in the calculation of the response from gamma-ray oil well logging devices. Very low counting yields are common making analog Monte Carlo methods impractical. Collimation in the tool makes biasing the Monte Carlo calculation complex. The adjoint flux for the tool changes very rapidly, because of the collimation, making general biasing techniques prone to weight fluctuations. Weight fluctuations can be reduced by approaching an ideal, zero-variance, biasing scheme. Zero-variance biasing depends on knowing the adjoint flux values. An estimate of the adjoint flux by using the early histories. Successive recalculation of the adjoint flux values and biasing parameters allows the biasing scheme to approach zero-variance biasing. User input and detailed knowledge requirements can also be reduced.; A zero-variance biasing scheme is calculated from the adjoint flux values and true event probabilities. The true event probabilities are the analog probabilities of physical gamma-ray interactions. Phase space is discretized into states that contribute an approximately uniform score to the detector response. The average score of a state, or the importance, is learned from earlier histories. The states reached and the weights are recorded for each history, allowing the importance values to be updated at the end of a batch of histories. Weight limits based on the shape of the adjoint flux and the results of simple analog calculations are used to improve stability.; A series of programs that modeled gamma-rays were developed. Finite state systems were modeled first. One, two and three-dimensional homogeneous programs were developed. The final program developed, MCLDLA (Monte Carlo Litho Density Log-Adaptive) includes the essential details required in an oil well logging model. Initial programs performed very well. MCLDLA does not perform as well as the current conventionally biased program, MCLDL. The large number of necessary states is the primary cause of this low performance. The size of each state is larger than the uniform state approximation can successfully model. Using more states of smaller size is not practical because of the large computational cost of recomputing the probabilities in very large systems. A weight window approach would minimize the size and computational limits.