Numerical Simulation of Wave Propagation in Complex Medium Using with a Staggered Finite-Difference Method

In this paper we setup a model based on complex medium (composite), which considers randomly distributed characteristics of medium. A finitedifference method (FDM) of estimating velocity for composite based on elastic-wave theory is used. The FDM wave equation using stress-particle velocity equations, and the scheme is second–order accurate in time and eight-order accurate in space, In order to improve the accuracy of the calculations, the staggered grids are generally used [1], [2] and [3]. This paper presents some examples of sound field simulation; the recorded forward full waveforms are processed by Fast Fourier Transform (FFT) and statistics method processing method to determine the Pwave velocities of composites [4]. The simulation results show there is a corresponding relationship between the P-wave velocity and the volume fraction (porosity) when the wavelength is greater than the size of the scatterers. When the scatterers impedance of media is smaller than that of the homogeneous media, the P-wave velocity has a regular decreasing and vice versa. We also compare the simulation results with simple time-average model results, there are obvious difference, the results from simulation are much more reasonable.