Distributed acoustic sensing (DAS) has great potential for monitoring natural-resource reservoirs and borehole conditions. However, the large volume of data and complicated wavefield add challenges to processing and interpretation. In this study, we demonstrate that seismic interferometry based on deconvolution is a convenient tool for analyzing this complicated wavefield. We also show the limitation of this technique, in that it still requires good coupling to extract the signal of interest. We extract coherent waves from the observation of a borehole DAS system at the Brady geothermal field in Nevada. The extracted waves are cable or casing ringing that reverberate within a depth interval. These ringing phenomena are frequently observed in the vertical borehole DAS data. The deconvolution method allows us to examine the wavefield at different boundary conditions and separate the direct waves and the multiples. With these benefits, we can interpret the wavefields using a simple 1D string model and monitor its temporal changes. The velocity of this wave varies with depth, observation time, temperature, and pressure. We find the velocity is sensitive to disturbances in the borehole related to increasing operation intensity. The velocity decreases with rising temperature. The reverberation can be decomposed into distinct vibration modes in the spectrum. We find that the wave is dispersive and the fundamental mode propagates with a large velocity. This interferometry method can be useful for monitoring borehole conditions or reservoir property changes using densely-sampled DAS data.