# Inversion of Rayleigh Wave Dispersion Curve Extracting from Ambient Noise Based on DNN Architecture
## 1 Introduction  
Rayleigh wave exploration based on ambient noise is an important method for investigating near-surface shear wave velocity (\(V_{S}\)) structures. It is widely used in fundamental geological surveys [1; 2], geostechnical engineering [3], geological hazard early warning [4; 5], hydrogeological surveys [6], and other fields. In particular, it has incomparable advantages for urban subsurface surveying and measuring the VS of weakly consolidated soils in offshore areas because other geophysical methods are easily susceptible to noise [7] or do not allow for borehole testing to be carried out. Achieving the subsurface S-wave velocity profile by inverting the Rayleigh wave dispersion curve is a key step in surface wave analysis [8]. However, similar to most geophysical inversion problems, dispersion curve inversion has the characteristics of high nonlinearity, multiparameter, and multi-extremum [9], and the accuracy of inversion results is affected by the two main aspects. One is the choice of the initial model; ingeneral, the inversion problem exists relative to the forward problem and may generate different inversion results for the same physical process. Another is the dimension of the inverted parameters. The phase velocity of Rayleigh waves depends on the compression wave velocity (\(Vp\)), S-wave velocity (\(V_{S}\)), density (\(\rho\)), and layer thickness (\(h\)) of strata. However, the S-wave velocity has a deterministic effect on the surface wave dispersion, so dispersion curve inversion usually refers to inverting the S-wave velocity and layer thickness (\(h\)). In recent research, the local optimization inversion method assumed that the subsurface is subdivided into a reasonable and fixed number of layers, and the number and thickness of each layer could be defined by the user [10]. In fact, this method transforms the problem into a single parameter dispersion curve inversion (only for \(V_{S}\)). In case of simple stratigraphic structures, such a method can provide a reliable estimation of the S-wave velocity. However, due to the influence of natural and human factors on the near surface, the seismic wave velocities usually change abruptly with depth or local structural reversals, such as the subsurface cavities, weak interlayers, etc. In such a case, it is difficult to give a reasonable estimation of \(V_{S}\) by simply increasing the number of layers. Moreover, accurate depths of layers are critical for many applications. A promising approach is to invert \(V_{S}\) and h simultaneously. However, an increase in unknown parameters may cause problems. [PERSON] et al. [11] proposed a method to perform multiple inversions with a global search approach, in which the layer thickness (\(h\)) is parameterized with a \"stratified ratio\", and its value can be determined via user experience. Subsequently, many global optimization algorithms, such as the Monte Carlo method, the genetic algorithms, and the simulated annealing, have appeared in many studies [12; 13; 14]. The global optimization algorithms have been widely adopted because they do not rely on the initial model and do not require calculating directional derivatives. However, due to the larger amount of computation, low efficiency, and easy premature convergence, the application of the global optimization method is limited. Artificial intelligence (AI) and cloud computing technology have entered many areas, such as national defense and military [15], economic construction [16], and social development [17], impacting our world on many levels. AI is a general field that encompasses machine learning and deep learning (DL) but also includes many more approaches that do not involve any learning. With machine learning, we input data as well as the answers expected from the data, and the output comes from the rules. These rules could then be applied to new data to produce original answers [18].