Stress drop is the stress that is effectively available to drive fault motion. It is a key parameter in predicting peak ground acceleration (PGA), since PGA∝, and it is very important in estimating ground motion. However, it is difficult to get an accurate estimation of stress drop. In order to get a more stable measurement of stress drop, we test two methods in this thesis: the first one is the Brune stress drop, which is more commonly applied, and the second one is the Arms stress drop, which less applied before and theoretically should have less uncertainty. By comparing these two methods we would like to test the feasibility and stability of the Arms method. We applied these two methods to data of earthquakes M3-5.5 in California and Oklahoma. We found that, taking Oklahoma results as an example, the mean value of Brune stress drop is 0.38 MPa, with a multiplicative uncertainty of 3.12, and the mean value of Arms stress drop is 1.04, with a multiplicative uncertainty of 1.79. Therefore we concluded that the Arms method is a good estimator of stress drop, with a smaller uncertainty. We determine the path attenuation so that we can increase the source-station distance of events studied to be as much as 76 km. The path seismic attenuation is a critical parameter that must be included in the analysis.