## 1 Introduction
Reference [10] used SPOT (Satellite Pour l'Observation de la Terre) images and interpreted the coseismic slip as shallow and detected more displacement on the hanging-wall than the footwall. Also, they estimated that the deeper part of the fault was not activated during the event and the western front of the area should produce a \(M_{w}\) 7 to 7.5 event every 150-250 years. Reference [11] used aerial photos which gave understanding of the hanging-wall to build a high-resolution map of the horizontal coseismic deformation. However, Reference [6] pointed out that non-negligible residuals were presented in Reference [10] and Reference [12] GPS based models. The residuals between each model and InSAR observations are estimated at 17 cm for Reference [10] and 7 cm for Reference [12]. One explanation for this difference is the geometry used: Reference [12] uses a point source method while Reference [10] uses a plane dislocation [13]. Mainly based on GPS but also combining data sets (InSAR, SPOT or Aerial photos), a few models were designed. Reference [14] built a four segment model based on GPS including a ramp geochemical system at depth with a lateral ramp at the northern end. The main part is of about 70 km from the south to the north from Chushan to Fengyun, then an 8 km long segment bending to the east and finally a 25 km segment trending up to Shuangchi. Using GPS and InSAR, [PERSON] [15] constructed a model with triangular elements, a more realistic dislocation method to represent the curved three-dimensionalfault surface without introducing overlaps and gaps. It shows similar slip pattern to GPS based models, but the magnitude of the fault slip is smaller and the slip pattern smoother. The results of Reference [10] based on SPOT imagery pointed out a shallow 20-35\({}^{\circ}\) east dipping ramp with a low dipping decllement at a depth of 6 to 8 km. However, a more recent paper, Reference [16], concluded a decllement at a depth of about 12 km, more consistent with the hypocentral depth of the mainshock and the distribution of aftershocks. According to them, the maximum slip is between 10 and 15 km on the shallow northern part of the fault with a moment of 3.6 \(\times\) 10\({}^{20}\) N\(\cdot\)m but most of the moment was released at shallow depths (between 0 and 5 km). In addition, the area ruptured by the main shock was fully locked before the earthquake. The slip is mainly aseismic for depths above 10 km [16]. No earthquake similar in magnitude to [PERSON]'s is known to have occurred in recent centuries in central western Taiwan. Figure 1: (**A**) Geodynamic map of Taiwan. The Chelungpu thrust fault is shown in red (National Taiwan University) and the other faults in yellow (National Taiwan University). Focal mechanism of the Chi-Chi earthquake on the inset map (USGS: 23.772\({}^{\circ}\)N 120.982\({}^{\circ}\)E). Seismicity (from 1998 to 2000, source National Taiwan University) over Taiwan. GPS displacement vectors ([9]) shown by black arrows. Green dashed box shows the location of the ERS-2 scenes from descending track 232, orange dashed box shows the location of the SPOT satellite images used in this study. The purple dashed box is the location of the benchmark data, results are presented in (**B**) for the football displacements and in (**C**) for the hanging-wall displacements (notice the different scale). Finally, the blue dashed box is the location of the levelling data, results are presented in (**D**). In this study, we use five types (Figure 1) of geodetic observations (GPS, levelling, benchmarks of urban planning, InSAR and SPOT offsets) in a joint inversion in order to estimate the slip distribution with and without precise estimation of the relative weights. In previous models, non-negligible residuals are present due to lack of information (density of the GPS network and no coherence on the hanging-wall for InSAR). This study focuses on showing the importance of combining and using complementary data sets rather than improving the model geometry.