doi: 10.3319/TAO.2010.07.26.02(TibXS) * Corresponding author E-mail: cjxu@sgg.whu.edu.cn Strain Rates in the Sichuan-Yunnan Region Based upon the Total Least Squares Heterogeneous Strain Model from GPS Data Caijun Xu 1, 2, * , Leyang Wang 1 , Yangmao Wen 1, 2 , and Jianjun Wang 1 1 School of Geodesy and Geomatics, Wuhan University, Wuhan, China 2 Key Laboratory of Geo-Space Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan, China Received 20 January 2009, accepted 26 July 2010 ABSTRAcT We present crustal strain and deformation models for the Sichuan-Yunnan region based on high-precision GPS mea- surements from 1998 - 2004 using the total least squares method (TLSM). Coordinate errors as well as GPS velocity errors recorded at GPS stations are considered, but only the latter errors are considered using the conventional least squares method (LSM). In addition, the spatial pattern of a given strain field is also likely to be heterogeneous. We investigate two models with a spatially variable strain, the least squares heterogeneous strain model (LS-HSM) and the total least squares heteroge- neous strain model (TLS-HSM). Our result shows that estimated strain field parameters are more precise using the TLS-HSM than those by LS-HSM because the fitting to the data is improved, hence the TLS-HSM is preferred. The principal dilation strain rate, principal contraction strain rate, maximum shearing strain rate and surface dilation rate estimated by TLS-HSM in the northwestern Sichuan-Yunnan sub-block are 13.2526 ± 1.2624, -10.8001 ± 2.9826, 24.0527 ± 3.2381, and 2.4525 ± 3.2393 × 10 -9 yr -1 (with a confidence probability of 95%), respectively, while those in the southeastern Sichuan-Yunnan sub- block are 18.8651 ± 1.8353, -12.0875 ± 1.3926, 30.9525 ± 2.2971 and 6.7776 ± 2.3105 × 10 -9 yr -1 (and exhibiting similar probabilities), respectively. The results indicate that the sub-blocks play a key role in continental tectonic deformation in the Sichuan-Yunnan region, and that small errors in site coordinates can have a significant impact on strain estimates, especially where sites are close together. Key words: Total Least Squares (TLS), Strain rate, GPS, Uniform strain model (USM), Heterogeneous strain model (HSM) Citation: Xu, C., L. Wang, Y. Wen, and J. Wang, 2011: Strain rates in the Sichuan-Yunnan region based upon the total least squares heterogeneous strain model from GPS data. Terr. Atmos. Ocean. Sci., 22, 133-147, doi: 10.3319/TAO.2010.07.26.02(TibXS) 1. InTRoDucTIon The Sichuan-Yunnan region is located in the south- east borderland of the Tibetan Plateau and is character- ized by a complex geological structure (Fig. 1). The struc- ture is adjacent to the stable south China block to the east, and spans most of Sichuan and Yunnan provinces. There have been many, widely-distributed, shallow hypocenter and great-magnitude earthquakes in the area. For example, the 12 May 2008 Wenchuan M w 7.9 earthquake occurred along the Longmenshan fault zone. Determination of crustal deformation and its stress and strain characteristics using geodetic data is a very effective method for investigating the regularity of crustal movement, determining earthquake potential and provides direct evidence via quantitative analysis of characteristics within the geophysical meaning of crustal movement. Recently, there have been many stud- ies using GPS observation data to obtain crustal horizontal displacements and strain characteristics about the Sichuan- Yunnan region (e.g., Lü et al. 2003; Shen et al. 2005; Gan et al. 2007; Xu et al. 2007; Wang et al. 2008). Although the crustal deformation models employed in these stud- ies were not exactly the same, all used the least squares method (LSM) wherein only errors of GPS velocities were considered and not the coordinates of GPS stations. Just as importantly GPS site coordinates reveal actual errors of less than centimeters. A typical 3-D weighted root-mean- square (WRMS) misfit after transformation is 4 - 6 mm for recent GPS sites solutions, while the post transformation 3-D WRMS residuals were usually ~15 mm for 1993 and Terr. Atmos. Ocean. Sci., Vol. 22, No. 2, 133-147, April 2011