This paper focuses on a tight carbonate reservoir in a giant field in Abu Dhabi by identifying shortcomings in conventional modeling strategies for geomechanics and demonstrating the benefits of continuous core data to build more reliable 1-D Mechanical Earth Models (MEM). A 1-D MEM was built from the sonic wireline log, which shows significant difference with a profile of ultrasonic P-wave velocity (Vp) measured on cores. However, results of rock mechanical tests (RMT) on plug samples (including ultrasonic Vp measurements at different stress conditions, and stress-strain curves from triaxial tests) are consistent with the core-based Vp profile. We investigate the impact of stresses, resolution and fluid saturation on sonic velocities to reveal the possible shortcomings of sonic wireline logs as an input for geomechanical models and the greater relevance of using core based ultrasonic velocities measured on dry cores for the upscaling of static elastic moduli. Finally we propose an empirical relation to correct sonic wireline logs for geomechanical modeling in offset wells. The following conclusions can be drawn from this study: 1. The core based Vp profile, which is highly consistent with the RMT results, ultimately leads to opposed trends in the in-situ horizontal stresses predictions compared to those of a 1-D MEM based on the non-calibrated wireline sonic log. 2. Only unrealistic reservoir stress conditions could reconcile ultrasonic Vp measured on plugs at different stress states with wireline sonic velocities; 3. Using a low resolution Vp profile at reservoir stress conditions (combining Vp from plug samples and core based continuous Vp profile), we show that differences in stress only partially explain the discrepancy between velocities measured on plugs and wireline sonic velocities.