The distributed acoustic sensing (DAS) has great potential for monitoring natural-resource reservoirs as well as borehole conditions. However, the large volume of data, complicated wavefield, and higher noise level often make processing and interpretation difficult. To this end, seismic interferometry based on deconvolution becomes a convenient tool for analyzing complex wavefield and extracting coherent waves from noise. It separates the structure response and allows us to examine the wavefields that satisfy different boundary conditions. Thus, we can utilize the dense spatial coverage of DAS receivers deployed in the borehole for monitoring structural changes, diagnosing well-casing integrity, and constrain the seismic energy sources in space and time. We apply this technique on the DAS data in the vertical borehole at the Brady geothermal field in Nevada to extract coherent and interpretable waves. Using results from analytical and numerical modeling, we discover that a simple string model can explain the extracted coherent waves well. By analyzing the strong reverberating signals due to resonance of the upper borehole casing with this numerical model, we constrain the dominant energy sources in the system and the configuration of the structure that causes the resonance. We investigate the propagating velocity of the extracted waves as well as the velocity variation with depth, observation time, temperature, and pressure. The velocity variations due to these parameters suggest that the waves are sensitive to thermal condition, casing condition, and borehole processes induced by pressure changes. The amplitude spectra of the deconvolved wavefields show clear normal modes of such reverberations, which are useful for dispersion analysis of the waves. At the bottom half of the borehole, which does not show clear resonance, we only obtain signals during the active seismic operation time due to poor coupling. To extract the time-lapse changes of formation, we need better coupling between DAS cables and the borehole.