Synthetic aperture radar (SAR) is one of the most versatile tools ever invented for imaging. Due to its better Rayleigh resolution, SAR imaging provides the highest quality radar imagery. These images are used for many applications including but not limited to terrestrial mapping, disaster reconnaissance, medical imaging and military applications. Imaging techniques or geometries which can improve the resolution of the reconstructed imagery is always desired in the SAR imaging. In this dissertation both the linear and nonlinear frequency modulated chirp signals are discussed. The most widely used frequency modulated chirp signal, linear frequency modulated chirp signal, and some of its properties such as spectrum, point spread function and matched filter are summarized. A new nonlinear frequency modulated chirp signal which can be used to improve the image resolution is introduced. In order to validate the offered chirp signal, spotlight SAR imaging geometry together with 2D polar and Stolt format reconstruction algorithms are considered. The synthetic examples are generated using both chirps both with polar and Stolt format processing. Additionally a new change detection method which depends on the idea of generating two different final change maps of the initial and final images in a sequence is offered. The specific algorithms utilized for testing this method are the widely used correlation coefficient change statistic and the intensity ratio change statistic algorithms. This method together with the algorithms mentioned is first applied to synthetic data generated by Stolt format processing. It is shown that the method works on synthetic data. The method together with the algorithms mentioned is also applied to two case studies dfreal disasters, one is 2010 Gulf of Mexico oil spill and the second is 2008 China Sichuan earthquake. It is shown that two final change map method can reduce the false identifications of the changes. Also it is shown that intensity ratio change statistics is a better tool for identifying the changes due to oil contamination. The data used in this study is acquired by Japanese Aerospace Agency's Advanced Land Observing Satellite (ALOS) through Alaska SAR Facility (ASF), at the University of Alaska, Fairbanks.