Pipeline wall thickness is measured as a function of position using ultrasound propagation. A series of predictive models is used, which define predictions of the ultrasound response signals as a function of different sets of parameters. The different sets that are determine of position dependent ultrasound speed at different sound frequencies and different spatial resolution. Successive iterative fitting process are executed, each fitting a combination of values of a successive set of parameters to the detected ultrasound response signals according to a respective model, using the values fitted values from the previous fitting process to initialize the next set of parameters for iterative fitting. At least the first model defines predictions of wave vector values as a function of circumferential position in successive rings around the pipe as sums of wave vector value for a plurality of circumferential positions in a preceding one of the rings multiplied by propagation coefficients, using propagation coefficients that depend on a first set of parameters.