An investigation of time-frequency domain phase-weighted stacking and its application to phase-velocity extraction from ambient noise's empirical Green's functions

The time-frequency domain phase-weighted stacking (tf-PWS) technique based on the S transform has been employed in stacking empirical Green's functions (EGFs) derived from ambient noise data, mainly due to its superior power in enhancing weak signals. Questions such as the induced waveform distortion and the feasibility of phase-velocity extraction are yet to be thoroughly explored. In this study, we investigate these issues by conducting extensive numerical tests with both synthetic data and USArray transportable array (TA) ambient noise data. We find that the errors in the measured phase velocities associated with waveform distortion caused by the tf-PWS depend largely on the way of how the inverse S transform (IST) is implemented. If frequency IST is employed in tf-PWS, the corresponding errors are generally less than 0.1 per cent, sufficiently small that the measured phase velocities can be safely used in regular surface wave tomography. On the other hand, if a time IST is used in tf-PWS, then the extracted phase velocities are systematically larger than those measured from linearly stacked ones, and the discrepancy can reach as much as similar to 0.4 per cent at some periods. Therefore, if tf-PWS is used in stacking EGFs, then frequency IST is preferred to transform the stacked S spectra back to the time domain for the stacked EGFs.