# Iterative Interferometric Denoising Filter for Traveltime Picking
## 3 Synthetic Example  
In this section, we created synthetic data using a two-layer model, shown in Figure 2a. The velocities of the first and second layers are constant at 500 m/s and 1500 m/s, respectively. We used fourth-order space and second-order time finite-difference staggered-grid algorithms to calculate the acoustic wave equation [45]. To avoid virtual reflection from numerical boundaries, we implemented an auxiliary differential equation of the complex-frequency-shifted perfectly matched layer (ADE CFS-PML) as the absorbing boundary [46]. A 30 Hz central frequency Ricker wavelet was employed as the source wavelet. We calculated 5200 time steps with 0.25 ms step intervals. The calculated 20 th common shot gather (CSG) is shown in Figure 2b. This synthetic example has 121 sources and receivers with 5 m source and receiver intervals. The noiseless data were muted by a tapered window around the trial's initial first-arrival traveltime. Figure 3 shows a common shot gather (CSG) and a corresponding zoom-in on the seismic data. Figure 4a shows the same CSG (Figure 3) after adding noise. Here, a set of Gauss numbers, with a maximum value of 50% of the normalized seismic data amplitude peak, were generated and then added to the muted seismogram as incoherent noise. Figure 4a represents the 20 th noisy CSG and a zoom-in on the part of the seismogram in the blue box; it is obvious that this type of noise will lead to trouble during first-arrival traveltime picking. In real applications, this type of problem will cause high labor costs and uncertainty in the picked traveltimes; even tomography results in degradation. The 20 th CSG after one iteration of the proposed method and the corresponding zoom-in of the blue box are displayed in Figure 4b. We can see that the incoherent data noises were eliminated, mainly because this type of data noise does not have a symmetrical character and is suppressed. This processed result will allow geophysicists to conveniently pick a traveltime and the subsequent traveltime tomography inversion. Figure 3: The muted 20 th CSG without noise and the related zoom. Figure 2: (**a**) The velocity model used to create synthetic data. (**b**) The 20 th common shot gather (CSG) of the synthetic data without noise. The 70 th trace of the 20 th CSG before and after applying the IDF is shown in Figure 5a,b; it is noticeable that the dynamic information is distorted through our proposed method with pseudo-WDF. We utilized the Fourier transform to obtain the amplitude spectrum before and after iterative IDF for frequency domain analysis, and the processed results are shown in Figure 5c. It is apparent that the peak frequency of the wavelet increased compared to that of the original wavelet because incoherent noise was eliminated, so our method's ability to keep kinematic characteristics was demonstrated. This comparison indicates that, after the proposed IDF method, the head wave could support inversion methods based on traveltime information, such as traveltime tomography [3] and wave equation traveltime inversion [6], but it would not be suitable for FWI, which fits waveform information [47]. Figure 4: (**a**) The muted 20 th CSG with noise and the related zoom. (**b**) After applying IDF, the muted 20 th interferometric CSG, and the corresponding zoom. Figure 5: (**a**) Trace no. 70 of the noisy seismic data. (**b**) The same trace after applying IDF. (**c**) The amplitude spectrum of seismic data before (black line) and after (blue line) IDF process. We used in-house software to pick the first-arrival traveltime information for this set of synthetic data. We found that the processed data were much easier to pick than noisy data. The corresponding traveltime difference between manually picking information on original noiseless and interferometric noisy data was minimal (Figure 6).