## 1 Introduction  
Earthquake early warning, which is the rapid detection of an ongoing earthquake, prediction of the expected ground shaking based on information extracted from the early arriving P-waves, and transmission of a useful warning prior to the onset of damaging ground shaking, is considered to be an effective, pragmatic, and viable tool for the earthquake emergency response and seismic hazard mitigation [1,2]. In the standard approaches, earthquake early warning systems have historically been based on seismic sensors. Such systems have been implemented in seismically active seismic regions, e.g., Japan, Mexico and California [3; 4; 5].  
Earthquake-induced cooseismic displacement is the essential information required for rapid source and rupture inversion. However, due to the rotation, tilt, drift and saturation problem of seismic instruments (strong motion sensors and broadband seismometer) and imprecision in the numerical integration process, the integrated displacements are not reliable in real-time [6]. Recent advances in the performance of real-time high-rate GPS, estimates of permanent displacement directly, mean that its use can potentially be complementary to the seismic-based methodologies for earthquake early warning [1; 7; 8; 9; 10]. The main weaknesses of current GPS measurements are the lower sampling rates (1\(\sim\)50 Hz) and the larger high-frequency noise contribution [11], and so the GPS-derived dynamic motions are not accurate enough to identify the first arrival wave (P-wave). While strong motion sensors are able to sample at very high rates (e.g., 200 Hz) and perform very well in the high-frequency range as it is much more sensitive to ground motions than GPS receiver, especially in the vertical direction. The complementary nature of GPS and seismic sensors for station displacement estimation and P-wave detection is well recognized and the integrated processing of the two dataset is a hot topic in GPS seismology for obtaining more accurate and reliable displacements and P-wave arrival time [12; 13].  
Several loosely-integrated approaches have been proposed to fuse accelerometer with collocated GPS displacement data [14; 15; 16; 17; 18]. As the GPS coordinates are already estimated prior to integration with the accelerometer, the precise dynamic information provided by accelerometers cannot be used to enhance the GPS-only solutions in these integration algorithms. In order to combine all the advantages of both sensors, [PERSON] _et al_. [19] proposed an approach of integrating the strong motion data into the ambiguity-fixed precise point positioning. A tightly-integrated filter is developed to estimate coseismic displacements from raw GPS phase and pseudorange observations and raw strong motion data. In this filter, seismic data can improve the GPS estimates in terms of ambiguity fixing, besides, and the tightly-integrated filter can also provide displacements with better accuracy compared to the loosely-integrated approach [13; 19].  
In this study, we apply the tightly-coupled integration to analyze collocated GPS and seismic data collected during the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquakes. Time and frequency domain analysis show that the integrated displacement and velocity waveforms are more accurate than GPS-only or seismic-only results. The integrated displacement waveform can capture both transient phenomena (waves) and permanent or static deformation. From the integrated results, we detect the P-wave arrival, locate the epicenter, and extract the permanent offsets for static slip inversion and magnitude estimation.