<div>This paper investigates the presence of a new interferometric signal in multilooked Synthetic Aperture Radar (SAR) interferograms which cannot be attributed to atmospheric or earth surface topography changes. The observed signal is short-lived and decays with temporal baseline; however, it is distinct from the stochastic noise usually attributed to temporal decorrelation. The presence of such fading signal introduces a systematic phase component, particularly in short temporal baseline interferograms. If unattended, it biases the estimation of Earth surface deformation from SAR time series. <br></div><div>The contribution of the mentioned phase component is quantitatively assessed. For short temporal baseline interferograms, we quantify the phase contribution to be in the regime of 5 rad at C-band. The biasing impact on deformation signal retrieval is further evaluated. As an example, exploiting a subset of short temporal baseline interferograms which connects each acquisition with the successive 5 in the time series, a significant bias of -6.5 mm/yr is observed in the estimation of deformation velocity from a four-year Sentinel-1 data stack. A practical solution for mitigation of this physical fading signal is further discussed; special attention is paid to the efficient processing of Big Data from modern SAR missions such as Sentinel-1 and NISAR. Adopting the proposed solution, the deformation bias is shown to decrease to -0.24 mm/yr for the Sentinel-1 time series.</div>Based on these analyses, we put forward our recommendations for efficient and accurate deformation signal retrieval from large stacks of multilooked interferograms.