# Inversion of Rayleigh Wave Dispersion Curve Extracting from Ambient Noise Based on DNN Architecture
## 1 Introduction
The core of deep learning is called the neural network model, a process of distributed storage of information and parallel collaborative processing of a nonlinear system, and it can implement complex nonlinear mapping. From this perspective, it is analogous to the geophysical inversion problem. Therefore, in recent years, geophysicists have gradually introduced it into the fields of seismic data processing and interpretation [19], lithology identification of logging data [20], and magnetotelluric inversion [21]. [PERSON] et al. [22] proposed a multilayer perceptron neural network for the inversion of Rayleigh wave data, but they did not describe how to select the training dataset. [PERSON] et al. [23] obtained the Bayesian posterior distribution of the S-wave velocity at each layer of the model with a mixture density network (MDN), but the number of layers and velocity range of each layer must be known. They also did not explain how to obtain the prior models to train the MDN. [PERSON] et al. [24] utilized convolutional neural networks (CNN) to derive 1D S-wave velocity from surface wave dispersion and pointed out that CNN can solve more complex nonlinear inversion problems compared with densely connected neural networks. However, the training process of CNN is slower, and the training dataset is derived from the general geophysical inversion method. Moreover, the neural network structure must be recreated when processing new data, which makes it difficult to promote in the application. The successful applications mentioned above demonstrate that DL can invert Rayleigh wave dispersion curves into shear wave velocity models. Current research aims to improve the accuracy of inversion by exploring different neural network models and generating more representative training data. However, most existing studies focus on deep geological structures, with inversion of layer thicknesses ranging from tens of kilometers to even more. In contrast, this study focuses on the more complex near-surface geological structures. The main difference between our research and previous neural network inversion methods lies in the construction of a more refined, layered shear wave velocity model, incorporating a Markov chain (MC) with ergodic properties in the random process. As a result, the synthesized training data are more representative. In this study, we first established the method to construct a \(V_{S}\) model based on the constrained MC, and then the forward calculation of Rayleigh wave dispersion was employed to obtain the corresponding phase velocities. All these data provide the training dataset required by deep learning. Next, a multilayer deep neural network (DNN) architecture was constructed to implement the training process. We discussed the DNN performance in relation to loss function and accuracy, as well as the influence of the number of neural network layers and parameter adjustment on the inversion accuracy using a synthetic dataset. Further, we tested the DNN with field data collected in the Yellow River Delta and compared the result with the very fast, simulated annealing method and the downhill simplex method (VFSA-DHSM) approach and statistical data in the Yellow River Delta. Our purpose was to realize an easy and applicable method for Rayleigh wave dispersion curve inversion.