Ultrasonic logging methods and apparatus for automatically calibrating measures of acoustic impedance of cement and other materials behind casing

Methods and apparatus for in situ, continuous, automatic, and real-time acoustic impedance calibration of a transducer in an acoustic logging system. By taking the frequency characteristics of the ultrasonic transducer which are present in the internal casing reflection and convolving them with the frequency characteristics of the casing being logged, a theoretical model is created with a theoretical acoustic impedance fluid producing a theoretical free pipe signal at each measure point. The measured signal is then compared to the theoretical free pipe signal thereby yielding a calibrated acoustic impedance value for at each measure point. The only model employed is in the theoretical calculation of spectrum characteristics of free pipe.