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Spectrograms provide an efficient way to analyse surface elevation signals ofship waves taken from a sensor fixed at a single point in space. Recent workbased on a simplified model for the ship's disturbance suggests that matchingthe spectrogram heat-map patterns to a so-called dispersion curve has thepotential for estimating of properties of a steadily moving ship, such as theship's speed and closest distance to the sensor. Here we extend the theorybehind the dispersion curve so that it can be applied to ships acceleratingalong arbitrary paths and demonstrate how acceleration affects the structure ofthe associated spectrograms. Examples are provided for of a simple model of aship accelerating/decelerating in a straight line or travelling in a circlewith constant angular speed. We highlight a problem with non-uniqueness of thedispersion curve when comparing ships moving along different paths. Finally, wevalidate the new dispersion curve against experimental results of ship modelsaccelerating in a finite depth basin. Our work will provide a basis for morecomprehensive studies that extend the simplified model to take into account theshape of the hull in question.

Spectrogram analysis of surface elevation signals due to accelerating ships