This article presents the results of automatic detection of subsidence troughs in synthetic aperture radar (SAR) interferograms. The detection of subsidence troughs is based on the circlet transform, which is able to detect features with circular shapes. Compared to other methods of detecting circles, the circular transform takes into account the finite data frequency. Moreover, the search shape is not limited to a circle but identified on the basis of a certain width. This is especially important in the case of detection of subsidence troughs whose shapes may not be similar to circles or ellipses but to their fragments. The transformation works directly on the image gradient; it does not require further binary segmentation or edge detection as in the case of other methods, e.g., the Hough transform. The entire processing process can be automated to save time and increase reliability compared to traditional methods. The proposed automatic detection method was tested on a differential interferogram that was generated based on Sentinel-1A SAR images of the Upper Silesian Coal Basin area. The test carried out showed that the proposed method is 20% more effective in detecting troughs that than the method using Hough transform.