A method for estimating cement voids in a layer of cement between a casing and a borehole wall of a borehole, the method comprising: conveying a tool through a borehole penetrating the earth formation, the borehole including a borehole wall, a casing, and a layer of cement between the casing and the borehole wall; irradiating an earth formation external to the borehole wall with neutrons from a neutron source disposed at the tool ; forming measurements of radiation emitted from the earth formation resulting from the irradiating using a first detector and a second detector in the tool, when the tool is in two or more different locations in the borehole; forming an actual ratio of radiation measured the by first detector and the second detector at two or more of the different locations; determining a porosity of the earth formation at the two or more locations; forming a relationship between the actual ratio and the porosity at each of the two or more different locations in the borehole; forming an estimate, via numerical techniques, of the actual ratio versus porosity, the estimate including at least a first case and second case; comparing the relationship at the two more locations to both the first and second cases at corresponding locations; and determining an estimate of cement voids in the layer of cement between the casing and the borehole wall at the two or more locations based on the comparing; characterized in that the first detector is a gamma ray detector and is spaced a distance apart from the second detector; the second detector is a gamma ray detector, and the ratio of radiation is a ratio of gamma rays due to inelastic scattering detected by the first detector to gamma rays due to inelastic scattering detected by the second detector . conveying a tool through a borehole penetrating the earth formation, the borehole including a borehole wall, a casing, and a layer of cement between the casing and the borehole wall; irradiating an earth formation external to the borehole wall with neutrons from a neutron source disposed at the tool ; forming measurements of radiation emitted from the earth formation resulting from the irradiating using a first detector and a second detector in the tool, when the tool is in two or more different locations in the borehole; forming an actual ratio of radiation measured the by first detector and the second detector at two or more of the different locations; determining a porosity of the earth formation at the two or more locations; forming a relationship between the actual ratio and the porosity at each of the two or more different locations in the borehole; forming an estimate, via numerical techniques, of the actual ratio versus porosity, the estimate including at least a first case and second case; comparing the relationship at the two more locations to both the first and second cases at corresponding locations; and determining an estimate of cement voids in the layer of cement between the casing and the borehole wall at the two or more locations based on the comparing; characterized in that the first detector is a gamma ray detector and is spaced a distance apart from the second detector; the second detector is a gamma ray detector, and the ratio of radiation is a ratio of gamma rays due to inelastic scattering detected by the first detector to gamma rays due to inelastic scattering detected by the second detector . <EOS>