A blanket of sedimentary and regolith material covers approximately three-quarters of the Australian continent, obscuring the crustal geology below and potential mineral resources within. Sedimentary basins also trap seismic energy increasing seismic hazard and generating noisy seismograms that make determining deeper crustal and lithospheric structure more challenging. The most fundamental question that can first be asked in addressing these challenges is how thick are the sediments? Borehole drilling and active seismic experiments using a controlled seismic source (e.g. vibroseis) provide excellent constraints, but they are limited in geographical coverage due to their expense, especially when operating in remote areas. On the other hand, passive-seismic experiments that involve the deployment of seismic receivers only (i.e. seismometers) are relatively low-cost and portable, providing a practical alternative for initial surveys. Here we utilize receiver functions obtained for both temporary and permanent seismic stations in South Australia, covering regions with a diverse sediment distribution. We present a straightforward method to determine the basement depth based on the arrival time of the P-converted-to-S phase generated at the boundary between the crustal basement and sedimentary strata above. Utilizing the available borehole data, we establish a simple predictive relationship between Ps arrival time and the basement depth, which could then be applied to other sedimentary basins with some consideration. The method is found to work best for Phanerozoic sediments and offers a way to determine the sediment-basement interface in unexplored areas requiring only temporary seismic stations deployed for < 6 months.