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《Chinese Journal of Geophysics》 2015-02
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Error analysis for focal mechanisms from CAP method inversion:An example of 2 moderate earthquakes in Jiaodong Peninsula

ZHENG Jian-Chang;LIN Mei;WANG Peng;XU Chang-Peng;Earthquake Administration of Shandong Province;  
As an effective focal mechanism inversion method for regional earthquakes,CAP(Cut and Paste)is widely used in China in recent years.Its quality and error level need to be evaluated for such solutions are increasingly retrieved.On the other hand,when using the CAP method,those phases which fitted well are usually chosen for inversion,and the other phases which are thought‘bad'or fitted not so good are ignored.It has been found that different station combinations will lead to varied results with unneglectable discrepancies.Objectively speaking,in a scientific perspective,this artificially selected process will increase uncertainties in final inversion results,especially under the present instrument status in China.Furthermore,because the grid search scheme used in the CAP method which is not evenly distributed on focal sphere,we can not give a convincing proof to illustrate that whether the cause of badly-fitted waveforms comes from data error or from un-sufficient searched solutions.Two earthquakes of M4.6and M4.3occurred in Shandong Peninsula on 23 November 2013and 7January 2014,respectively.The former is the largest event in the Shandong area since1995.For convenience,we label the former event as the Laizhou earthquake,and the latter as the Rushan earthquake,according to their epicenters.Taking these two events for example,this paper discusses error estimation for focal mechanism inversion using the CAP method.The paper also presents an uncertainty analysis process for the inversion results.Briefly,a bootstrap technique is adopted,waveforms are randomly sampled with equal probability from origin dataset,and then used as data for a repeating inversion procedure.After a large number of inversions,e.g.,1000 times,we finally get bootstrap results consisting of 1000 focal mechanisms.Based on these focal mechanisms,we conduct the following work.(1)We employ a PSO(particle swarm optimization)algorithm to search a solution,of which the Kagan angle is minimal to all the double couple models,and use its standard deviation as the inversion results uncertainty range.The uncertainty of solutions for the Laizhou event is±23.7°;for Rushan event,is ±6.4°.These two solutions can be evaluated as ‘A'level according to the Hardebeck′s indicator of mechanisms quality.(2)A clustering analysis is used for bootstrap results.For the Rushan event,the clustering center is coincident to the PSO optimized solution;for the Laizhou event,several centers are found in clustering,despite isolate solutions.There are two clustering centers,of which the corresponding data proportion is about 98.7percent.(3)Projecting P and T axes of bootstrap results onto a focal sphere,calculating its probability density,we get the probability density distribution of focal mechanisms on the focal sphere.Then we can give the confidence interval on different levels for mechanism solutions.The method demonstrated in this paper is not confined to achieving more accurate focal mechanism and obtaining rational inversion error,while it can also be used to exclude isolate and incorrect solutions effectively,and avoid the effect of data from stations with larger disturbances.Therefore,this method can be used to invert focal mechanisms automatically immediately after moderate earthquakes occur.Sustaining by powerful computational capabilities,we can get more accurate and reliable focal mechanism results without manual work.
【Fund】: 国家科技支撑计划项目(2012BAK19B04-01-05);; 山东省自然科学基金(ZR2012DQ006);; 中国地震局监测预报司震情跟踪工作专项(2014020103)资助
【CateGory Index】: P315.33
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