Study On The Inversion Methods Of Source Rupture Process

Study on the earthquake rupture process based on the theory of seismic source, seismic waveform data and inversion technology is the most efficient way to quantitatively understanding the kinematical characteristics of earthquake sources. Thus, inversion or imaging of the earthquake rupture process using digital waveforms has been frontier and highlight issue of seismological study in recent years. Development of the study on kinematics of earthquake source is very important theoretically and realistically to the study on dynamics of earthquake source, earthquake prediction and earthquake hazard reduction. Therefore, to obtain more and more information about the details of earthquake kinematics from observed seismic data for describing source rupture complexity becomes a direction of this kind study. However, uncertainty of solution will be getting higher with the number of unknown parameters increasing. Therefore, it becomes a difficult problem how to obtain the information as much as possible about kinematical information of earthquake source from digital seismic waveform data analyzing the complexity of rupture process under a precondition that certainty or stability of solutions is guaranteed. For example, in most of the current research works, value of rupture velocity, shape of the sub-fault source time function and focal mechanism are kept fixed artificially as preconditions in performing inversion process in order to stabilize solution. As we know, improper precondition usually results in distorted solutions. So the task of this study is to develop, improve and optimize the methods for investigating the source kinematical issues using seismic waveform data on a basis of seismic source theory. The goal is to reduce artificial preconditions and obtain more information about earthquake source under condition of insuring inversion stable. In this paper, at first, we derived the basic equations for rupture process inversion from the law of displacement representation, got the general forms for the methods of the apparent-source-time-function (ASTF) inversion and the direct-waveform inversion, and theoretically discussed the resolution ability (especially the space resolution ability) of different dataset for the first time; and then we developed, improved and optimized several efficient methods for rupture process analysis based on the existing methods; finally, we tested the methods for advantages by application to synthetic and observed data.In order to obtain stable and reliable ASTFs, we introduced and improved the PLD (Projected Landweber Deconvolution) method, and newly constructed a genetic algorithm especially for ASTF deconvolution. Numerical tests and practical applications showed that both the methods have more advantages compared with traditional ones such as the water-level method. By the two methods, we retrieved the ASTFs of the 2005 Kashmir M_W7.6 earthquake from all phases and the ASTFs of the 2001 Kunlun M_W7.8 earthquake from Rayleigh waves only. The comparison with other results suggested that our results are highly reliable.In order to get stable, reliable and more realistic inversion results using the ASTF method and direct-waveform method in case that focal mechanism is kept unchanged, we freed the precondition on the shape of sub-fault STF, imposed the smoothing constraints in time and space by adding Laplatian equations and the scalar-moment -minimum constraint, and constructed new equations of linear inversion. The practical applications to the 2005 M_W7.6 Kashmir earthquake, the 2001 Kunlun M_W7.8 earthquake and the 2007 Ning'er M_S6.4 earthquake indicated that this approach was very good.In order to obtain the information about rakes' variation on the fault plane and insure the stability of inversion results, we improved the existing method by proposing a new way of constraining the slips in strike direction and dip direction to have the same time function. By the improved linear inversion method, we analysised the rupture process of the 2004 Sumatra—Andaman M_W9.3 earthquake. The comparison with the others results from different methods and data showed that the improvement of the method was very successful.In order to get the information about focal-mechanism variation in earthquake rupture process and redisplay the mechanisms of different sub-events at different locations, for the first time, we developed a linear inversion technique for investigating the mechanism variation and rupture process. By this method, we can also obtain the estimation of the variable rupture velocity by grid-searching process beside the information about variable mechanisms in the earthquake process. The advantages of this method and technical way were illustrated adequately in the application to the 2001 Kunlun M_W7.8 earthquake.At last, for the Wenchuan huge earthquake, we carried rupture process inversions with all methods in this paper after the fast estimations, and finally obtained many rupture details for the earthquake.