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Mine tailings in Sweden are increasingly seen as potential secondary sources of critical minerals. A key step in evaluating their economic potential is estimating the tailings volume. To this end, three-component ambient noise recordings were recently collected over the Bäckegruvan mine tailings in the Bergslagen province, central Sweden, to which we apply the Horizontal-to-Vertical Spectral Ratio (HVSR) method. This method allows for the identification of the fundamental site frequency in locations where a strong seismic-impedance contrast is present, such as granular tailings material over solid bedrock. Using the fundamental site frequency and an S-wave velocity estimate, we calculate the tailings thickness at individual stations. We interpolate them to determine a 3D tailings-bedrock interface, and subsequently calculate a total tailings volume. We compare our results to those of a recent geophysical study in the same area, which employed Electrical Resistivity Tomography (ERT), Radio-Magnetotellurics (RMT), and towed Transient Electromagnetics (tTEM), and find them to be in good agreement.