Comparison of Different Approach of Back Projection Method in Retrieving the Rupture Process of Large Earthquakes

Back-projection of teleseismic P waves [Ishii et al., 2005] has been widely used to image the rupture of earthquakes. Besides the conventional narrowband beamforming in time domain, approaches in frequency domain such as MUSIC back projection (Meng 2011) and compressive sensing (Yao et al, 2011), are proposed to improve the resolution. Each method has its advantages and disadvantages and should be properly used in different cases. Therefore, a thorough research to compare and test these methods is needed. We write a GUI program, which puts the three methods together so that people can conveniently use different methods to process the same data and compare the results. Then we use all the methods to process several earthquake data, including 2008 Wenchuan Mw7.9 earthquake and 2011 Tohoku-Oki Mw9.0 earthquake, and theoretical seismograms of both simple sources and complex ruptures. Our results show differences in efficiency, accuracy and stability among the methods. Quantitative and qualitative analysis are applied to measure their dependence on data and parameters, such as station number, station distribution, grid size, calculate window length and so on. In general, back projection makes it possible to get a good result in a very short time using less than 20 lines of high-quality data with proper station distribution, but the swimming artifact can be significant. Some ways, for instance, combining global seismic data, could help ameliorate this method. Music back projection needs relatively more data to obtain a better and more stable result, which means it needs a lot more time since its runtime accumulates obviously faster than back projection with the increase of station number. Compressive sensing deals more effectively with multiple sources in a same time window, however, costs the longest time due to repeatedly solving matrix. Resolution of all the methods is complicated and depends on many factors. An important one is the grid size, which in turn influences runtime significantly. More detailed results in this research may help people to choose proper data, method and parameters.