High-precision acoustic modeling with second-order staggered difference

Since the precision of spatial derivative of wavefield calculated by staggered difference is superior to that by central difference, the formula of second-order staggered differential coefficient with 2N-order precision is constructed via mathematical deduction on combination of first-order differential coefficient on each grid point, and its validity is verified by numerical simulation in constant velocity media. With the staggered mesh, the maximum peak frequency of Ricker wavelet which does not generate numerical dispersion may be increased by 10–15 Hz, thus the vertical resolution of simulated seismograms may be enhanced. In order to eliminate the boundary reflection which is characterized as high frequency, the absorbing boundary condition of perfectly matched layer with staggered mesh is utilized in numerical simulation of scalar-wave equation, and the suppression effect is superior to that of the central difference. The precision of simulated records may be improved when staggered mesh is adopted in calculation of the second-order spatial derivative, and the ringing phenomena appeared before the first break may be avoided. The computational cost of second-order staggered difference increased by only 25% on 3.60 GHz Intel Core i7–4790 processor when the precision of simulated records is same as that simulated by second-order central difference.