Seismic waveform data are generally contaminated by noise from various sources, which interfere with the signals of interest. In this study, we implemented and applied several noise suppression methods using data recorded by the regional network of the University of Utah Seismograph stations. The denoising methods, consisting of approaches based on nonlinear thresholding of continuous wavelet transforms (CWTs, e.g., Langston and Mousavi, 2019), convolutional neural network (CNN) denoising (Tibi et al., 2021), and frequency filtering, were all subjected to the same analyses and level of scrutiny. We found that for frequency filtering, the improvement in signal‐to‐noise ratio (SNR) decreases quickly with decreasing SNR of the input waveform, and that below an input SNR of about 32 dB the improvement is relatively marginal and nearly constant. In contrast, the SNR gains are low at high‐input SNR and increase with decreasing input SNR to reach the top of the plateaus corresponding to gains of about 18 and 23 dB, respectively, for CWT and CNN denoising. The low gains at high‐input SNRs for these methods can be explained by the fact that for an input waveform with already high SNR (low noise), only very little improvement can be achieved by denoising, if at all. Results involving 4780 constructed waveforms suggest that in terms of degree of fidelity for the denoised waveforms with respect to the ground truth seismograms, CNN denoising outperforms both CWT denoising and frequency filtering. Onset time picking analyses by an experienced expert analyst suggest that CNN denoising allows more picks to be made compared with frequency filtering or CWT denoising and is on par with the expert analyst’s processing that follows current operational procedure. The CWT techniques are more likely to introduce artifacts that made the waveforms unusable.