Determination of Smoothing Factor for the Inversion of Co-seismic Slip Distribution

doi:10.11947/j.JGGS.2020.0103

Abstract

Abstract:

For the determination of the smoothing factor (also known as the regularization parameter) in the co-seismic slip distribution inversion, the compromise curve between the model roughness and the data fitting residual is generally used to determine (in order to distinguish the method proposed in this paper, the method is called “L curve” according to its shape). Based on the L-curve, the Eclectic Intersection curve as a new method is proposed to determine the smoothing factor in this paper. The results of the simulated experiment show that the inversion accuracy of the parameters of the seismic slip distribution with the smoothing factor determined by the Eclectic Intersection curve method is better than that of the L curve method. Moreover, the Eclectic Intersection curve method and the L curve method are used to determine the smoothing factor of L’Aquila earthquake and the Taiwan Meinong earthquake slip distribution inversion respectively, and the inversion results are compared and analyzed. The analysis results show that the L’Aquila and the Taiwan Meinong actual earthquake slip distribution results are in the range of other scholars at home and abroad, and compared with the L curve method, the Eclectic Intersection curve method has advantages of high computation efficiency, no need to depend on data fitting degree and more appropriate of smoothing factor and so on.

Key words: co-seismic slip distribution; smoothing factor; Eclectic Intersection curve method; L curve method; the L’Aquila earthquake;; the Meinong earthquake

Leyang WANG,Xiong ZHAO. Determination of Smoothing Factor for the Inversion of Co-seismic Slip Distribution[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1): 25-35.

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Method	Smoothing factor /(α)	Calculation time/(s)	Max slip /(m)	Mean slip /(m)	Mean slip angle /(°)	Moment magnitude /(Mw)	Seismic moment /(10¹⁸N·m)	RMS /(mm)
preset parameters	—	—	1.4721	0.3104	45	6.5822	8.3806	—
L curve	0.179	126.6230	1.3049	0.3168	45.9012	6.5881	8.5546	3.0
EI curve	0.095	18.8387	1.3722	0.3138	45.8826	6.5853	8.4725	2.9

D-values	Max slip /(m)	Mean slip /(m)	Mean slip angle /(°)
L curve	0.1672	0.0064	0.9012
EI curve	0.0999	0.0034	0.8826
L-EI*	5.23%	0.95%	0.04%

Method	Smoothing factor /(α)	Calculation time/(s)	Max slip /(m)	Mean slip /(m)	Mean slip angle /(°)	Moment magnitude /(Mw)	Seismic moment /(10¹⁸N·m)	RMS /(mm)
L curve	0.588	145.5253	1.005	0.1535	-101.3043	6.3478	3.7294	14.6
EI curve	0.159	19.8612	1.02	0.1468	-103.9264	6.3349	3.5676	13.8

Source	L curve	EI curve	Literature[28]	Literature[6]	Literature[27]	Literature[30]	Literature[31]	USGS
Max slip/m	1.01	1.02	0.95	1.07	0.66	0.49	1.1	—
Mean slip angle/(°)	-101.3	-103.9	-96.4	-102.8	-105	-98	-98.5	—
Moment magnitude /(Mw)	6.35	6.33	6.34	6.32	6.23	6.32	6.36	6.29

Method	Smoothing factor /(α)	Calculation time/(s)	Max slip /(m)	Mean slip /(m)	Mean slip angle /(°)	Moment magnitude /(Mw)	Seismic moment /(10¹⁸N·m)	RMS /(mm)
L curve	0.445	118.4569	0.4529	0.0517	45.3159	6.3441	3.6828	12.9
EI curve	0.328	43.7275	0.4793	0.0521	43.4510	6.3466	3.7140	12.8