# Inversion of Rayleigh Wave Dispersion Curve Extracting from Ambient Noise Based on DNN Architecture
## 3 Data Application Example in Yellow River Delta  
Considering the good performance of synthetic data, we applied our approach to real dispersion data to demonstrate how it works well in inversion. In October 2021, we employed the centerless circular array (CCA) for observation (Figure 10) and collected the  
Figure 8: Average error of different learning rates.  
Figure 9: Average error of different DL network layers.  
ambient noise data at an offshore beach in the Yellow River Delta [33]. The ambient noise survey was a completely new method; its measurement was relatively straightforward, and the process did not need an active source [34; 35]. This method can overcome a number of obstacles that make traditional geophysical technologies difficult or impossible to implement in some special areas, such as weakly consolidated soils offshore where it is difficult to maintain the quality of the borehole and hence impossible to conduct in-hole S-wave velocity testing [5].  
In testing, we set up two stations, S1 and S2, located 1.2 km apart. Each station utilized six identical vertical component velocity detectors (PS-2 Hz) referred to as ST1, ST2, ST3, ST4, ST5, and ST6. These six detectors were evenly distributed on a circular array centered at each station, with a radius of one meter. We employed this CCA array to collect random noise data and subsequently processed the obtained raw data. Through resampling and calculating the coefficients of principal component analysis, we obtained the dispersion curves for stations S1 and S2 stations [33] (black line in Figure 11).  
Figure 11: Comparison of observed and predicted dispersion curves. (**a**) S1 station; (**b**) S2 station.  
Figure 10: Map of the centerless circular array (CCA). (**a**) Schematic of CCA; (**b**) field photograph.  
Since the output depth range needs to vary with the periodic range of the input Rayleigh wave dispersion velocities, to invert these dispersed data using DNN, the dispersion data must be preprocessed first. The frequency range of the measured dispersion curve was 2.08-12.5 Hz (0.08-0.48 s), but the spacing between each dispersion point was not uniform. For this reason, we used an interpolation algorithm to resample these data into 101 points at equal intervals to ensure consistency with our network structure; these data would be used for S-wave velocity inversion.  
In part 1.1, we generated lots of random velocity models. However, the S-wave velocity range of these velocity models was between 300 and 1200 m/s, while the velocity range of the testing area in the Yellow River Delta was 80-350 m/s above a 100 m depth. The weights trained with the synthetic dispersion data could not accurately predict S-wave velocities because DL did not learn the features of the measured dispersion curve. To this end, we recalculated the velocity models with a range of 80 m/s to 350 m/s and the corresponding dispersion data over 8000 pairs. After training these datasets (~15 s), we obtained the weights, and then the 1D \(V_{S}\) models (blue dashed line in Figure 12) of the two stations were inverted.  
In order to compare the inversion results, we also used the VFSA-DHSM method [36] to invert the dispersion curve. The results are presented in Figure 12 (black solid line). As seen from the figure, DL results are in good agreement with that of the VFSA-DHSM. In addition, [PERSON] et al. [37] gave statistics on the S-wave velocity in the Yellow River Delta area. They listed the S-wave velocity at every 10 m interval within a depth of 100 m; unfortunately, no more detailed logging information is available. Here, we tabulated the data and our inversion results in Table 1. Again, we found consistency among them and further confirmed the validity of our DNN method.  
Figure 12: Comparison of inverted \(V_{S}\) model from DL and VFSA-DHSM method for observed dispersion data. (**a**) S1 station; (**b**) S2 station.