The detection of transient behaviour in environmental vibration data is an important issue when considering the precision of the Watt balance, an electromechanical apparatus for the new definition of the kilogram in the International System of Units (SI). In this paper, the authors have developed a two-stage method for the analysis of large numbers of datasets containing measured vibration data. In the first stage, all the datasets are explored and statistical methods used to identify those datasets that potentially contain transient events. In the second stage, the transient events are separated from the background noise. This stage is implemented using a biorthogonal wavelet technique with Bayesian denoising.