Adomian Decomposition Method for Numerical Solution of 1-D and 2-D Seismic Wave Equations

Abstract

The concept of real seismic wave equations has several applications through physics, geology, geophysics, and engineering. A precise and effective technique for simulating seismic wave propagation in the Earth's media must be developed to ascertain the Earth's structure. Over the past few decades, wave field simulation has developed into a potent instrument in seismological research, enabling researchers to better understand seismic events and improve predictions of earthquake impacts on various geological structures. The current study employs the well-known Adomian decomposition method (ADM) to solve the one- and two-dimensional seismic wave equations directly to obtain approximate and exact solutions without converting the seismic wave equations into ordinary differential equations (ODEs). The graph of each exact solution of seismic wave equations was plotted to show the movement of various types of seismic wave equations. The obtained results show the applicability and usefulness of the Adomian decomposition method to approximate solutions of seismic wave equations, making it suitable for geophysical applications such as exploration and subsurface imaging.