Automatic GSDF Method
Automatic GSDF method is an update version of traditional Generalized Seismological Data Functionals (GSDF) method that was developed by [Gee and Jordan, 1992], combining Helmholtz tomography developed by [Lin and Ritzwoller, 2011]. In this method we measure the phase difference between all nearby stations and use these measurements to reconstruct the wavefield of surface wave that propagates through a dense array. 
The advantages of this method includes:
  • Automatic: No human interacting required. No phase picking, automatic data quality control.
  • Fast: For a mid size array with 40 stations, only takes 1-2 hours to process 2 years data.
  • Robust: No cycle skipping problem, more accurate than FTAN
  • Multi-platform: Code is developed in MATLAB, no extra library required.
The limitations of this method are:
  • Dense Array: the station distance should be smaller than 2-3 wavelength of your highest interested frequency band
  • Major phase: the measured phase (Rayleigh or Love) has to be the largest phase within the time window defined by 5km/s to 2km/s
Method Description
After the earthquake waveforms are downloaded and the instrument responses are corrected, the group delays of all frequency bands of interest are estimated by tracking the peaks in the narrow-band filtered envelope functions for each station. Then group delays of all stations are fitted by a linear function of average group velocity and time offset for each frequency band. These estimations are used to build a time window to isolate the energy of fundamental-mode surface wave (Figure 1). We then calculate multi-channel broadband cross-correlation functions of the isolated waveforms from nearby stations, and fit narrow-band filtered cross correlations with a five-parameter wavelet [Gee and Jordan, 1992] to retrieve the phase difference at a range of frequencies. The amplitude of this cross-correlation function can be used to estimate the coherence of the waveforms from the station pair, which together with SNR are the key factors to exclude poor measurements. The phase difference measurements between all the nearby station pairs for each event at each frequency band are then used as the input to an Eikonal tomographic inversion [Lin et al., 2009] for two-dimensional estimates of apparent phase velocity. We measure the amplitude of each station by adapting the same process on the auto-correlation function and perform Helmholtz tomography [Lin and Ritzwoller, 2011] to estimate and remove interference (focusing / defocusing) effects (Figure 2). For each earthquake, maps of apparent phase velocity, amplitude corrected structural phase velocity, amplitude distribution, and wave propagation direction at each frequency bands can be generated as shown in Figure 2. Finally, we stack the structural phase velocity of each individual event to get the final phase-velocity tomogram in each frequency band (Figure 3).
This method is applicable to both Rayleigh wave and Love wave by using the vertical and the tangential component as the input data, respectively.

The whole process can be described as the following steps:
  1. Automatically generate a time window includes only fundamental surface wave based on group delay measurement.
  2. Cross-correlate the windowed waveform with the waveforms from nearby stations.
  3. Window around the peak of cross-correlation waveform.
  4. Apply narrow-band filters.
  5. Fit the waveform with a five-parameter wavelet, which is a cosine function multiplied by a Gaussian envelop.
  6. Correct cycle skipping and get the phase delay between each station pair.
  7. Use phase difference measurement to perform Eikonal tomography.
  8. Apply amplitude correction based on Helmholtz tomography
  9. Stack the result from difference events
More details and examples (coming soon)
Github Link
  1. Jin, G., and J. B. Gaherty (2014), Surface Wave Measurement Based on Cross-correlation, Geophys. J. Int, submitted.
Gee, L. S., and T. H. Jordan (1992), Generalized seismological data functionals, Geophysical Journal International, 111(2), 363–390.
Lin, F.-C., and M. H. Ritzwoller (2011), Helmholtz surface wave tomography for isotropic and azimuthally anisotropic structure,
Geophysical Journal International, 186(3), 1104–1120, doi:10.1111/j.1365-246X.2011.05070.x.