Time And Frequency-domain Back Projection For Great Earthquake Rupture Process Imaging: Methodology And Applications

Earthquakes have always been severe catastrophes that plague human since ancient times, and the great earthquakes are the most lethal ones among them, so the nucleation, development, rupture process, and disaster feature of great earthquake are essential problems in seismology. To gain a better understanding of great earthquakes,many methods have been proposed to study them in different perspectives. Among them, back projection can reconstruct the spatial and temporal distribution of coseismic high-frequency radiation by utilizing local or global dense array data.In this paper, the basic theory of back projection is illustrated in the view of signal transmission. The advantages and disadvantages of back projection are derived naturally, along with the data property required by back projection. Based on theory,the process of conventional time-domain and frequency-domain back projection is shown in details, and the common variation and frequently used developments are also explicated.To evaluate the performance of multiple-array time-domain back projection, the data from North America, Europe, and Australia were processed to study the rupture process and characteristics of high-frequency radiation of the 2015 Mw 7.8 Gorkha,Nepal earthquake. The result illustrates a rupture propagating southeastward along strike at a relatively stable velocity of 2.8km/s, which was confirmed by the observation of 3 arrays. The high-frequency radiations are on the north margin of larges slip area.Combining the result and slip and aftershocks distribution, we conclude that the coseismic high and low-frequency radiations were controlled by the depth-dependent temperature and stress environments, and the heterogeneity of stress and structure along strike determined the rupture initiation and termination.In the conventional back projection, only the traveltime predicted by 1-D velocity model and variations caused by structure heterogeneity underneath stations is considered, and the structure heterogeneity in source area is ignored. To evaluate the influence of source area structure, a systematic traveltime calibration method based on aftershocks is proposed, and it's used to investigate the rupture process and high-frequency radiation of the 2011 Tohoku earthquake. The calibrated radiation location is closer to the trench and farther away from the coast. This shift illustrates the lateral structure heterogeneity in the Tohoku area and the effectiveness of the calibration method. The calibration method can vary depending on prior information and hypothesis, which is quite flexible.Besides the time domain back projection, the frequency-domain compressive sensing back projection is also promoted from one array to multiple arrays on the basis of l2,1-norm. The new method only assumes that the high-frequency radiation observed by different arrays is from the same location, without constraining the amplitude and initial phase observed by each array. This assumption and constraint utilize multiple array observation more reasonably. To evaluate the performance of the new method, it is tested by both mathematical and synthetic data, and the tests are all passed successfully, illustrating the validity and reliability of the new method.In the future, combining multiple array frequency-domain compressive sensing back projection and source area traveltime calibration will enhance the rationality,stability, and accuracy of back projection, providing better constraint for rupture process research.