[en] A neutron source and a gamma ray source are positioned in the instrument housing of a well logging instrument to irradiate the formations surrounding a well bore. A short-spaced gamma ray detector and a long-spaced gamma ray detector positioned in the instrument housing detect radiation from the formations and transmit electrical signals representing the radiation to the surface. The electrical signals are compared to provide a signal representing mud cake in the well bore. A third detector positioned in the instrument housing detects radiation from the formations surrounding the well bore and transmits a neutron logging signal to the surface. The signal representing mud cake in the well bore is applied to the neutron logging signal to provide a mud cake compensated neutron log. (Patent Office Record)