The 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 extract coherent wave from the observation of a borehole DAS system at the Brady geothermal field in Nevada. Then, we analyze the coherent reverberating waves, which are used for monitoring temporal changes of the system. These reverberations are tirelessly observed in the vertical borehole DAS data due to cable or casing ringing. The deconvolution method allows us to examine the wavefield at different boundary conditions. We interpret the deconvolved wavefields using a simple 1D string model. 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, which potentially suggests that the DAS cable or the casing are subjected to high temperature. This reverberation can be decomposed into distinct vibration modes in the spectrum. We find that the wave is dispersive, and the the fundamental mode propagate with a large velocity. The method can be useful for monitoring borehole conditions or reservoir property changes. For the later, we need better coupling than through only friction in the vertical borehole to obtain coherent energy from the formation.