In this paper, we consider a multi-carrier and multi-relay underwater acoustic communication (UWAC) system and investigate the relay selection problem. Our channel model is built on an aggregation of both large-scale path loss and small-scale fading. For path loss modeling, we use the publicly available ray-tracing algorithm Bellhop software to precisely reflect the characteristics of an underwater geographical location (such as the sound speed profile, sound frequency, bathymetry, type of bottom sediments, depths of nodes, etc). For relay selection, we consider different selection criteria which rely either on the maximization of signal-to-noise ratio (SNR) or the minimization of probability of error (PoE). These are used in conjunction with so-called per-subcarrier, all-subcarriers, or subcarrier grouping approaches in which one or more relays are selected. We present an extensive Monte Carlo simulation study to evaluate the error rate performance of the UWAC system with different relay selection schemes under consideration and point out differences with terrestrial radio-frequency (RF) systems.