The three-dimensional (3D) distributed acoustic sensing (DAS) vertical seismic profile (VSP) technique is an effective tool to characterize subsurface reservoirs, enabling the use of large and densely sampled borehole receiver arrays with many surface vibrator source points for onshore time-lapse monitoring. However, the processing of the DAS VSP signals for imaging purposes is based on a reliable wavefield separation, which may depend on the recognition and quality of the direct arrivals. To overcome this limitation for common-source gathers with poor signal-to- noise ratio or with interferences, we apply the dual-signal processing method, which allows us to estimate and separate the DAS wavefields by signals' combination without arrival picking. We present a case study of a 3D VSP DAS dataset recorded at a geothermal reservoir in Turkey, showing that the method, similar to a geophone and hydrophone combination, is robust and effective and can be advantageously integrated with the conventional processing. Supported by signal benchmarking, modelling and signal-to-noise ratio analysis, we treat common-source and common-receiver data. Our analysis shows the advantages and limitations of the proposed approach, valuable in the time-lapse perspective.