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The systematic discrepancies in both tsunami arrival time and leading negative phase (LNP) were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel, Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami (DART) sites and 29 coastal tide gauge stations. The results revealed systematic travel time delay of as much as 22 min (approximately 1.7％ of the total travel time) relative to the simulated long waves from the 2015 Chilean tsunami. The delay discrepancy was found to increase with travel time. It was difficult to identify the LNP from the near-shore observation system due to the strong background noise, but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean. We determined that the LNP for the Chilean tsunami had an average duration of 33 min, which was close to the dominant period of the tsunami source. Most of the amplitude ratios to the first elevation phase were approximately 40％, with the largest equivalent to the first positive phase amplitude. We performed numerical analyses by applying the corrected long wave model, which accounted for the effects of seawater density stratification due to compressibility, self-attraction and loading (SAL) of the earth, and wave dispersion compared with observed tsunami waveforms. We attempted to accurately calculate the arrival time and LNP, and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event. The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model. Taking all of these effects into consideration, our results demonstrated good agreement between the observed and simulated waveforms. We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP, which is observed for tsunamis that have propagated over long distances frequently. The travel time delay between the observed and corrected simulated waveforms is reduced to <8 min and the amplitude discrepancy between them was also markedly diminished. The incorporated effects amounted to approximately 78％ of the travel time delay correction, with seawater density stratification, SAL, and Boussinesq dispersion contributing approximately 39％, 21％, and 18％, respectively. The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event. In contrast, the seawater stratification only reduced the tsunami speed, whereas the earth\'s elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations. This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival, and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami. These results also support previous theory and can help to explain the observed discrepancies.