Estimating cement voids in between a casing and a borehole wall of a borehole penetrating the earth formation includes forming with a computing device an actual ratio of radiation induced by a neutron source and measured by a first detector and a second detector when the tool is at two or more different locations in the borehole. A relationship between the actual ratio and the porosity at each of the two or more different locations is used and compared to two different cases of estimates of the ratio. Based on the comparison, an estimate of the cement voids at the two or more locations.