This study evaluates the performance of a Support Vector Machine (SVM) classifier to learn and detect changes in single-and multi-temporal X-and L-band Synthetic Aperture Radar (SAR) images under varying conditions. The purpose is to provide guidance on how to train a powerful learning machine for change detection in SAR images and to contribute to a better understanding of potentials and limitations of supervised change detection approaches. This becomes particularly important on the background of a rapidly growing demand for SAR change detection to support rapid situation awareness in case of natural disasters. The application environment of this study thus focuses on detecting changes caused by the 2011 Tohoku earthquake and tsunami disaster, where single polarized TerraSAR-X and ALOS PALSAR intensity images are used as input. An unprecedented reference dataset of more than 18,000 buildings that have been visually inspected by local authorities for damages after the disaster forms a solid statistical population for the performance experiments. Several critical choices commonly made during the training stage of a learning machine are being assessed for their influence on the change detection performance, including sampling approach, location and number of training samples, classification scheme, change feature space and the acquisition dates of the satellite images. Furthermore, the proposed machine learning approach is compared with the widely used change image thresholding. The study concludes that a well-trained and tuned SVM can provide highly accurate change detections that outperform change image thresholding. While good performance is achieved in the binary change detection case, a distinction between multiple change classes in terms of damage grades leads to poor performance in the tested experimental setting. The major drawback of a machine learning approach is related to the high costs of training. The outcomes of this study, however, indicate that given dynamic parameter tuning, feature selection and an appropriate sampling approach, already small training samples (100 samples per class) are sufficient to produce high change detection rates. Moreover, the experiments show a good generalization ability of SVM which allows transfer and reuse of trained learning machines.