# Simulation of Wave Propagation Using Finite Differences in Oil Exploration
### Literature Review
\begin{table}
\begin{tabular}{c c c} \hline
**Method** & **Description** & **Disadvantages** \\ \hline \multirow{4}{*}{Finite element method [25]} & \multirow{4}{*}{A numerical method for solving partial differential volumes and applying conservation laws to each volume.} & It requires more computation and memory to construct and solve the system of equations compared to the finite difference method. It may be more challenging to implement and adjust due to the complexity of creating the interpolation functions for each element. The finite difference method may need a more accurate representation of complicated geometries. \\ \cline{1-1} \cline{2-3}  & & Compared to the finite difference method, it requires more memory and computational time to construct and solve the system of equations. Implementing and adjusting may be more challenging due to the need to discretize the domain into finite volumes. It may need to be more accurate in representing gradients of the solution at the edges of finite volumes. \\ \hline \multirow{4}{*}{Contour element method [27]} & \multirow{4}{*}{A numerical method for solving partial differential equations that involves discretizing only the boundary of the domain and approximating the solution at the border using interpolation functions.} \\ \cline{1-1} \cline{2-3}  & & It may be less accurate than the finite difference method in the solution in the domain’s interior since only the boundary is discretized. It may be more challenging to implement and tune due to the complexity of constructing the interpolation functions for the border. It may require a more significant amount of memory and computational time than the finite difference method to build and solve the system of equations. \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the optimization methods potentially applicable to the problem. Table 1 presents a comprehensive range of methods to obtain a numerical solution for partial differential equations within a specific domain. This study, in particular, meticulously examines three prominent methods: the finite element method, the finite volume method, and the boundary element method. The papers collectively suggest that finite difference methods are commonly used for wave propagation simulation in oil exploration due to their high precision, flexibility, and cost-effectiveness. However, the simulation of these phenomena demands a high computational cost and large amounts of available memory. To solve this problem, some researchers propose using GPU-based solvers for wave propagation problems [9; 28]. Additionally, [PERSON] [29] reviews finite difference methods for elastic wave motion modeling, discussing issues, such as finite schemes, source problems, boundary conditions, and numerical dispersion. Finally, [PERSON] [30] compares the accuracy of various monolithic methods for wave propagation in the presence of a fluid-solid interface, finding that a first-order velocity-stress formulation could be used to treat fluid-solid interfaces without necessarily using staggered grids. Overall, the papers highlight the importance of finite difference methods in wave propagation simulation for oil exploration, while also identifying unresolved problems, such as the high computational cost and incorporation of proper boundary conditions. Further studies suggest that algorithms are available to simulate wave propagation in oil exploration. [PERSON] [31] proposes two wave propagation models based on deep neural networks that use seismic attributes and rock physical properties to estimate seismic properties. [PERSON] [32] suggests optimization strategies for a wave propagation model for many kernel systems, including improved cache utilization, vectorization, and locality in the memory hierarchy. [PERSON] [33] proposes a reduced-order modeling method that uses modal forms of the model to decrease the computational cost of wave propagation modeling for applications such as inverse time migration.