I would think it is "Frequency warping"

Definition: Frequency warping is a process of resolution preserving from one frequency scale to another .

From this link:

https://earth.esa.int/documents/10174/1567860/Sentinel-1+System_Fringe_final_1.pdf

It looks like the azimuth measurements varies from the point of observation , thus changing the captured data .

I do not see a reference to warping in the linked document. The level of processing detail is not as high in this reference as it is in the following: "https://sentinels.copernicus.eu/web/sentinel/user-guides/sentinel-1-sar/document-library/-/asset_publisher/1dO7RF5fJMbd/content/sentinel-1-level-1-detailed-algorithm-definition" - which is the basis of my image formation algorithm. Section 6.2.4 deals with the Azimuth Frequency UFR (UnFolding and Resampling). I am using "wrapping" synonymously with "folding". Figure 6.6 shows the collected data to be wrapped into PRF extent and the subsequent sections discuss how to remove this. This is truly wrapped information and can only properly be processed when unwrapped. There likely is some sort of sampling/hardware interaction that is specifically causing this, but I have not seen or experienced it in any SAR system or collection modality before. I am looking for a better description than I have found in the other posted/published ESA documentation.

Generally image correction is software , like the way they have mentioned low pass filter (FIR) in the given bandwidth .

Again here they talk about "phase wrapping"

http://earth.esa.int/workshops/ers97/program-details/speeches/rocca-et-al/

Phase over time (can be frequency ) ...e.g cos and sine wave

From what I understand , it seems to be a distortion correction process .

Also an interesting reference, but does not directly address the question. Is it really as simple as the PRF generates harmonics that wrap through the digitizer during the deramp? If so, why don't other SAR systems (spotlight in particular) have the same artifact in the collected data? How is it it only shows up in the azimuth processing direction? I still don't understand the physical interpretation of this wrapping in azimuth processing. Anyone else game to concretely explain the phenomenon?

I like pictures. Here is an example using real Sentinel-1 data taken right after range processing.

The upper left image is the time-frequency representation of a single azimuth column of data. Here frequency is the y axis (not correct numbers) and down is positive, time is the x axis right to left (also not correct numbers) increasing. The equivalent time domain amplitude and frequency are plotted directly below it. Notice how, in time-frequency, there are several bands of data running from upper left to lower right - it is this wrapping that UFR looks to undo.

The rest of the UFR processing steps down through the middle. First (top) the frequency replication, followed by the deramp (middle) and the LPF (bottom). Reramping is in the upper right with the time domain magnitude and frequency below it.

I understand how to do the UFR processing, but I am still unsure how or why the system induces this artifact in the azimuth domain - particularly after the range processing (shifting and compressing). I'm still open to a detailed explanation of how this happens.

May be , azimuth image frames capturing and post processing is involved .

http://home.deib.polimi.it/monti/papers/ghost.pdf

OR : Overlap of wavefronts while capturing/compression !!

OR: Depending on Doppler effect the artifacts are more pronounced in azimuth direction ...