A method for well integrity assessment using machine-trained prediction of physical characteristics related to well integrity across a depth interval of a cased wellbore having one or more casing strings. The method includes collecting scattered X-ray signals from a plurality of X-ray detectors arranged within a well logging tool, learning trained weights to predict wellbore characteristics from the scattered X-ray signals, collecting further scattered X-ray signals from the X-ray detectors, using the trained weights to quantitatively predict the wellbore characteristics from the further X-ray signals, and using the predicted wellbore characteristics to assess well integrity.