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Predicting shear (Vs) and compressional (Vp) wave velocities is crucial for seismic interpretation and reservoir characterization. However, Vs logs are frequently missing or unreliable in legacy datasets. While machine learning (ML) offers strong predictive power, it can yield physically implausible results when extrapolating. This study introduces a novel hybrid workflow integrating rock physics with ML to ensure robust, physically consistent Vp and Vs predictions offshore Egypt. A calibrated rock physics model guides feature engineering and generates training data, constraining the ML model to avoid non-physical outputs. The results are incorporated into geostatistical simulation (SGS) to produce high-resolution, probabilistic 3D realizations of elastic properties, honoring well data and quantifying spatial uncertainty. This approach provides reliable synthetic logs for derisking exploration in the Mediterranean.