oa Seismic Wave Simulation based on Method of Characteristics

In this paper, we apply the CIP (Cubic Interpolated Profile) method to the simulation of elastic waves as a highly accurate and stable algorithm to solve first-order wave equations. The key idea of the CIP is that not only the physical value itself but also its first spatial derivative obeys the same equations. Using this property the solution is interpolated by cubic polynomials and interpolation coefficients can be evaluated arithmetically. We implemented this idea to the elastic wave simulation by derivation of the first-order wave equations from the basic equations of motion. The derived equations can be interpreted as the combined first-order wave equations for each mode of wave. Then, we define boundary conditions by using the merit of one-side propagation; free surface, solid-fluid boundary, irregular topography. From simulation study and the stability evaluation, we recognize the method of characteristics with the CIP is a very powerful simulation technique for the elastic wave propagation. Numerical dispersion is negligible, requiring about half the number of grid cells per wavelength than other solvers. This allows accurate, high-frequency, full-wavefield simulation in models with highly variable, random elastic contrasts with fluid-solid mixed media and complex topographic media.