Expected-value techniques for Monte Carlo modeling of well logging problems

This article describes research performed to develop an expected-value (EV) estimation capability for improving the efficiency of Monte Carlo simulations of oil well logging problems. The basic idea underlying EV estimation is that event-level interaction and transport probabilities are known and can be averaged exactly to produce unbiased estimators that properly account for potential future events in the simulation. Conventional surface-crossing and track-length based estimators do not provide any information unless a particle history actually reaches a detector region. Expected-value estimators, however, can extract information from particles that merely travel along a direction intercepting the detector region. This paper describes two expected-value estimators that have been developed for oil well logging simulations. The first estimates the volume-averaged scalar flux or reaction rate in a detector. The second estimates a weighted surface-averaged incident current that can be enfolded with a detector response function to estimate pulse-height spectra. Though EV estimation reduces variance at the event level, it does not guarantee reduced variance at the history level. However, our oil well logging tests indicate that the EV approach generally improves information content, enhances the efficiency of the transport simulation, and provides an efficient technique to obtain the fluxes, reaction rates, and pulse-height spectra in detectors, especially when applied in conjunction with weight-window variance reduction techniques.