Interstation correlation is the basic operation in seismic noise and coda‐wave interferometry for signal extraction in imaging and monitoring applications. Conventional cross‐correlations evaluate the similarity between two signals along lag time, and they are efficiently computed by the fast Fourier transform (FFT), valuable to manage the large data volumes that ambient noise applications demand. The phase cross‐correlation (PCC) method contributes to increase convergence, a key issue in seismic ambient noise imaging and monitoring; however, it is much more computationally demanding. PCC evaluates similarity by subtracting the modulus of the sum and difference of the instantaneous phase of two signals. We introduce solutions to dramatically reduce the high‐computational cost of PCC. We show that PCC can be rewritten as a complex cross‐correlation and computed by the FFT when the moduli are raised to the power of 2, and we demonstrate PCC can improve waveform coherence and increase convergence compared with the default processing flow of 1‐bit amplitude normalization and standard cross‐correlation. Moreover, we develop a graphics processing unit implementation to accelerate computations when using powers other than 2 and particularly when using the power of 1. Finally, we extract Rayleigh‐ and body‐wave signals from many years of data from seismic stations distributed worldwide using PCC without a significant increase in computational cost compared with conventional cross‐correlation.

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