Recently, co-seismic seismic source characterization based on GPS measurements has been completed in near- and far-field with remarkable results. However, the accuracy of the ground displacement measurement inferred from GPS phase residuals is still depending of the distribution of satellites in the sky. We test here a method, based on the double difference (DD) computations of Line of Sight (LOS), that allows detecting 3D co-seismic ground shaking. The DD method is a quasi-analytically free of most of intrinsic errors affecting GPS measurements. The seismic waves presented in this study produced DD amplitudes 4 and 7 times stronger than the background noise. The method is benchmarked using the GEONET GPS stations recording the Hokkaido Earthquake (2003 September 25th, Mw = 8.3).