A fast forward method of gamma-gamma density logging based on perturbation theory

The fast forward modeling result of gamma-gamma density is used as the input of the neutron and density joint inversion model, which is of great significance for real-time inversion to determine the formation geometry and attribute parameters. Based on the time-independent Boltzmann transport equation, combined with the perturbation theory and Monte Carlo simulation, a fast calculation method of gamma-gamma density is proposed. The compensation density logging is adopted to establish the database of the perturbation sensitivity function under different reference formation conditions. The density responses and errors of fast calculation and MCNP simulation under different lithological densities, horizontally layered formations and inclined formations are analyzed and compared. The results show that the fast calculation results of gamma-gamma density logging under different formation conditions are consistent with the MCNP simulations. The average error of the three lithological (sandstone, carbonatite and dolomite) density calculations is less than 0. 01 g . cm (3) and compared with the MCNP simulation speed, the fast calculation efficiency is increased by 10(6) times.