# An approach to jointly invert hypocenters and 1D velocity structure and its application to the Lushan earthquake series

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## Abstract

Earthquake location is essential when defining fault systems and other geological structures. Many methods have been developed to locate hypocenters within a 1D velocity model. In this study, a new approach, named MatLoc, has been developed which can simultaneously invert for the locations and origin times of the hypocenters and the velocity structure, from the arrival times of local earthquakes. Moreover, it can invert for layer boundary depths, such as Moho depths, which can be well constrained by the *Pm* and *Pn* phases. For this purpose, the package was developed to take into account reflected phases, e.g., the *Pm* phase. The speed of the inversion is acceptable due to the use of optimized matrix calculations. The package has been used to re-locate the Lushan earthquake series which occurred in Sichuan, China, from April 20 to April 22, 2013. The results obtained with the package show that the Lushan earthquake series defines the dip of the Guankou fault, on which most of the series occurred, to be 39° toward the NW. Further, the surface projection of the Lushan earthquake series is consistent with the regional tectonic strike which is about N45° E.

## Keywords

Earthquake re-location 1D velocity inversion Jacobi matrix Constrained LSQ optimization## Notes

### Acknowledgments

The project “Deep geological survey of the structural belt along the Longmenshan” directed by the Chinese Geological Survey sponsored this work. The Beijing Gangzhen Corp., Limited is thanked for providing the Chinese instruments for the fieldwork, while the Geophysical Instrument Pool of the Deutsches GeoForschungsZentrum Potsdam – GFZ is acknowledged for providing the German instruments. The Sichuan Province Land Resource Institute is thanked for providing support for the work as are the local people who guarded the instruments during the fieldwork. The routine “eqplot” from hypoDD was used with some small modifications to plot Figs. 2, 5, 6, 7, and 8. We also acknowledge the detailed suggestions of two reviewers for better presentation of this approach.

## References

- Boggs PT, Tolle JW (1996) Sequential quadratic programming. Acta Numerical 4:1–51CrossRefGoogle Scholar
- Bratt SR, Bache TC (1988) Locating events with a sparse network of regional arrays. Bull Seismol Soc America 78:780–798Google Scholar
- Crotwell HP, Owens TJ, Ritsema J (1999) The TauP toolkit: flexible seismic travel-time and ray-path utilities. Seismol Res Lett 70:154–160. doi: 10.1785/gssrl.70.2.154 CrossRefGoogle Scholar
- Dennis JE Jr, Gay DM, Welsch RE (1981) Algorithm 573-NL2SOL: an adaptive nonlinear least-squares algorithm. ACM Trans Math Softw 7:348–368CrossRefGoogle Scholar
- Han SP (1976) Superlinearly convergent variable metric algorithms for general nonlinear programming. Math Program 11:236–282CrossRefGoogle Scholar
- Jin W, Tang L, Yang K, Wan G, Lü Z (2010) Segmentation of the longmen mountains thrust belt, Western Sichuan Foreland Basin, SW China. Tectonophysics 485:107–121CrossRefGoogle Scholar
- Kennett BLN, Engdahl ER (1991) Traveltimes for global earthquake location and phase identification. Geophys J Int 105:429–465CrossRefGoogle Scholar
- Kissling E, Ellsworth WL, Eberhart-Phillips D, Kradolfer U (1994) Initial reference models in local earthquake tomography. J Geophys Res 99:19635–19646CrossRefGoogle Scholar
- Knapmeyer M (2004) TTBox: a MatLab toolbox for the computation of 1D teleseismic travel times. Seismol Res Lett 75:726–733. doi: 10.1785/gssrl.75.6.726 CrossRefGoogle Scholar
- Levenberg K (1994) A method for solution of certain nonlinear problems in least squares. Q Appl Math 2:164–168Google Scholar
- Li Y, Jia D, Wang M, Shaw JH, He J, Lin A, Xiong L, Rao G (2014) Structural geometry of the source region for the 2013 Mw 6.6 Lushan earthquake: Implication for earthquake hazard assessment along the Longmen Shan. Earth Planet Sci Lett 390:275–286CrossRefGoogle Scholar
- Liu S, Zhang S, Ding R, Ren J, Liu H, Jiang D, Xie F (2015) Upper crustal folding of the 2013 Lushan earthquake area in southern Longmen Shan, China, insights from Late Quaternary fluvial terraces. Tectonophysics 639:99–108CrossRefGoogle Scholar
- Long F, Wen XZ, Ruan X, Zhao M, Yi GX (2015) A more accurate relocation of the 2013 M
_{s}7.0 Lushan, Sichuan, China, earthquake sequence, and the seismogenic structure analysis. J Seismol. doi: 10.1007/s10950-015-9485-0 Google Scholar - Nash SG (1998) SUMT revised. Oper Res 46:763–775CrossRefGoogle Scholar
- Su J-R, Zheng Y, Yang J-S, Chen T-C, Wu P (2013) Accurate location of the Lushan, Sichuan M7.0 earthquake on 20 April 2013 and its aftershocks and analysis of the seismogenic structure. Chinese J Geophys 56:425–434CrossRefGoogle Scholar
- Waldhauser F, Ellsworth WL (2000) A double-difference earthquake location algorithm: method and application to the northern Hayward fault, California. Bull Seismol Soc America 90:1353–1368CrossRefGoogle Scholar
- Xu ZJ, Song X (2010) Joint inversion for crustal and Pn velocities and Moho depth in Eastern Margin of the Tibetan Plateau. Tectonophysics 491:185–193CrossRefGoogle Scholar