We re-examined the slip distribution on faults of the 2004 Sumatra-Andaman (M 9.1 according to USGS) earthquake by the inversion of tsunami data with phase-corrected Green's functions applied to linear long waves. The correction accounts for the effects of compressibility of seawater, elasticity of solid earth, and gravitational potential variation associated with the motion of mass to reproduce the delayed arrivals and the reversed phase of the first tsunami waves. We used sea surface height (SSH) data from satellite altimetry (SA) measurements along five tracks, and the tsunami waveforms recorded at tide gauges (TGs) and ocean bottom pressure gauges (OBPGs) in and around the Indian Ocean. The inversion results for both data sets for different rupture velocities (Vr) show that the reproducibility of the spatiotemporal SSHs and tsunami waveforms is improved by the phase corrections, although the effects are not so significant within the Indian Ocean. The best slip distribution model from joint inversion of SA, TG and OBPG data with Vr of 1.3 km/s shows the largest slips of 16-25 m off Sumatra Island, large slips of 2-11 m off the Nicobar Islands, and moderate slips of 2-6 m in the Andaman Islands. The inversion results reproduce the far-field tsunami waveforms well at distant stations even more than 13,000-25,000 km from the epicenter. The total source length is about 1400 km and the seismic moment is Mw 9.2, longer and larger than that of our previous estimates based on TG records.