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The acoustic tools widely used in borehole well logging and being developed in borehole acoustic reflection imaging do not have the function of azimuthal measurement due to a symmetric source, so they can not be used to evaluate the azimuthal character of borehole formation. In this paper, a 3D finite difference method was used to simulate the acoustic fields in a fluid-filled borehole generated by a traditional monopole source and a phased arc array. Acoustic waveforms were presented for both cases. The analysis of the simulated waveforms showed that different from the monopole source, the acoustic energy generated by the phased arc array transmitter mainly radiated to the borehole in a narrow azimuthal range, which was the key technique to implement azimuthal acoustic well logging. Similar to the monopole source, the waveforms generated by the phased arc array in the fluid-filled borehole also contain compressional (P) waves and shear (S) waves refracted along the borehole, which is the theoretical foundation of phased arc array acoustic well logging.