A method for monitoring cement quality of a cased well, the method comprising: obtaining, by well controller system, a cement-bond log, CBL, for a well, the CBL obtained via a cement-bond logging of the well conducted after casing the well and when mud effects for the well are present, the well comprising: a wellbore penetrating a subsurface formation; casing disposed in the wellbore; and cement disposed in a casing-borehole annulus, CBA, located between the casing and the formation; obtaining, by the well control system, a first pulsed neutron log, PNL, for the well, the first PNL obtained via a first pulsed neutron, PN, logging of the well conducted after casing the well and at a time when mud effects for the well are present; determining, by the well control system, a first baseline cement quality index, CQI, for the well based on the CBL and the first PNL, the first baseline CQI comprising a first mapping of cement qualities to normalized carbon-oxygen ratios; obtaining, by the well control system, a second PNL for the well, the second PNL obtained via a second PN logging of the well conducted after casing the well, after the first PN logging of the well, and at a time when the mud effects for the well are not present; determining, by the well control system, a second baseline CQI for the well based on the CBL and the second PNL, the second baseline CQI comprising a second mapping of cement qualities to normalized carbon-oxygen ratios; determining, by the well control system, a tuned CQI for the well based on the first baseline CQI and the second baseline CQI, the tuned CQI comprising a third mapping of cement qualities to normalized carbon-oxygen ratios; obtaining, by the well control system, a follow-up PNL for the well, the follow-up PNL obtained via a follow-up PN logging of the well conducted after the second PN logging of the well, the follow-up PNL indicating carbon-oxygen ratios for the well at the time of the follow-up PN logging of the well; and determining, by the well control system, an updated cement quality log for the well based on the tuned CQI and the follow-up PNL for the well, the updated CQL comprising a mapping of cement quality values versus depth in the wellbore. obtaining, by well controller system, a cement-bond log, CBL, for a well, the CBL obtained via a cement-bond logging of the well conducted after casing the well and when mud effects for the well are present, the well comprising: a wellbore penetrating a subsurface formation; casing disposed in the wellbore; and cement disposed in a casing-borehole annulus, CBA, located between the casing and the formation; a wellbore penetrating a subsurface formation; casing disposed in the wellbore; and cement disposed in a casing-borehole annulus, CBA, located between the casing and the formation; obtaining, by the well control system, a first pulsed neutron log, PNL, for the well, the first PNL obtained via a first pulsed neutron, PN, logging of the well conducted after casing the well and at a time when mud effects for the well are present; determining, by the well control system, a first baseline cement quality index, CQI, for the well based on the CBL and the first PNL, the first baseline CQI comprising a first mapping of cement qualities to normalized carbon-oxygen ratios; obtaining, by the well control system, a second PNL for the well, the second PNL obtained via a second PN logging of the well conducted after casing the well, after the first PN logging of the well, and at a time when the mud effects for the well are not present; determining, by the well control system, a second baseline CQI for the well based on the CBL and the second PNL, the second baseline CQI comprising a second mapping of cement qualities to normalized carbon-oxygen ratios; determining, by the well control system, a tuned CQI for the well based on the first baseline CQI and the second baseline CQI, the tuned CQI comprising a third mapping of cement qualities to normalized carbon-oxygen ratios; obtaining, by the well control system, a follow-up PNL for the well, the follow-up PNL obtained via a follow-up PN logging of the well conducted after the second PN logging of the well, the follow-up PNL indicating carbon-oxygen ratios for the well at the time of the follow-up PN logging of the well; and determining, by the well control system, an updated cement quality log for the well based on the tuned CQI and the follow-up PNL for the well, the updated CQL comprising a mapping of cement quality values versus depth in the wellbore.