A k-space method for coupled first-order acoustic propagation equations.

A k-space method for large-scale simulation of ultrasonic pulse propagation is presented. The present method, which solves the coupled first-order differential equations for wave propagation in inhomogeneous media, is derived in a simple form analogous to previous finite-difference methods with staggered spatial and temporal grids. Like k-space methods based on second-order wave equations, the present method is exact for homogeneous media, unconditionally stable for "slow" [c(r) < or = c0] media, and highly accurate for general weakly scattering media. In addition, unlike previous k-space methods, the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer (PML) nonreflecting boundary conditions. Numerical examples illustrate the capabilities of the present k-space method. For weakly inhomogeneous media, accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite-difference and pseudospectral methods. The low dispersion of the k-space method allows accurate representation of frequency-dependent attenuation and phase velocity associated with relaxation absorption. A technique for reduction of Gibbs phenomenon artifacts, in which compressibility and exponentially scaled density functions are smoothed by half-band filtering, is introduced. When employed together with this smoothing technique, the k-space method provides high accuracy for media including discontinuities, high-contrast inhomogeneities, and scattering structures smaller than the spatial grid resolution.