A method of performing ultrasonic pipeline wall property measurements, the method comprising - providing a set of ultrasound transmitters (12a-d, 22) and a set of ultrasound receivers (12a-d, 24) coupled to a pipeline at mutually different positions on the pipeline; - transmitting ultrasound signals from the ultrasound transmitters (12a-d, 22) into a wall of the pipeline; - detecting the ultrasound response signals at the ultrasound receivers (12a-d, 24) due to propagation of the ultrasound signals through the wall; - providing a first and second predictive model, defining predictions of the ultrasound response signals as a function of a first and second set of parameters that are determinative of position dependent ultrasound speed in the wall at a first and second spatial resolution at a first and second sound frequency, or sound frequencies up to the first and second frequency respectively, the second sound frequency being higher than the first sound frequency, the second spatial resolution being higher than the first spatial resolution, at least the first model defining predictions of wave vector values representing amplitude and phase as a function of circumferential position in successive rings around the pipe as sums of wave vector values for a plurality of circumferential positions in a preceding one of the rings multiplied by propagation coefficients, using propagation coefficients that depend on the first set of parameters; - executing a first and second iterative fitting process, fitting a combination of values of the first and second set of the parameters to the detected ultrasound response signals according to the first and second predictive model respectively, the fitted combination of values of the first set being used to initialize the second set for the second iterative fitting process. - providing a set of ultrasound transmitters (12a-d, 22) and a set of ultrasound receivers (12a-d, 24) coupled to a pipeline at mutually different positions on the pipeline; - transmitting ultrasound signals from the ultrasound transmitters (12a-d, 22) into a wall of the pipeline; - detecting the ultrasound response signals at the ultrasound receivers (12a-d, 24) due to propagation of the ultrasound signals through the wall; - providing a first and second predictive model, defining predictions of the ultrasound response signals as a function of a first and second set of parameters that are determinative of position dependent ultrasound speed in the wall at a first and second spatial resolution at a first and second sound frequency, or sound frequencies up to the first and second frequency respectively, the second sound frequency being higher than the first sound frequency, the second spatial resolution being higher than the first spatial resolution, at least the first model defining predictions of wave vector values representing amplitude and phase as a function of circumferential position in successive rings around the pipe as sums of wave vector values for a plurality of circumferential positions in a preceding one of the rings multiplied by propagation coefficients, using propagation coefficients that depend on the first set of parameters; - executing a first and second iterative fitting process, fitting a combination of values of the first and second set of the parameters to the detected ultrasound response signals according to the first and second predictive model respectively, the fitted combination of values of the first set being used to initialize the second set for the second iterative fitting process.