Bearing noise may be a possibility, deep rumble may be the noise of the turntable bearing, all turntables have bearings and some are quieter than others. If yours is a vintage unit the bearing may be dry and adding some lubrication could transform things. Similarly with vintage units dismantling, cleaning and re-lubricating the bearing can sometimes clear up bearing noise problems. Discs vary in the quality of equipment used to make them originally, an inferior disc cutting lathe, perhaps used by a smaller independent record company can leave behind on the final pressed disc the signature sound of bearing noise.
If it is the bearing noise of your turntable it may change when you change speed, and it will be the same all the time with all discs.