A nearly analytic discrete method for solving the acoustic-wave equations in the frequency domain

We have developed a nearly analytic discrete (NAD) method to discretize frequency-domain acoustic-wave equations with an absorbing boundary condition. We evaluate in detail the discrete process of wave equations to derive a linear system. The sparse structure and eigenproperties of its coefficient matrix (also called the impedance matrix) were analyzed to reveal the intrinsic difficulty in solving the linear system efficiently. To accelerate the forward-modeling process in the frequency domain, we introduce a class of inexact rotated block triangular preconditioners incorporated with Krylov subspace methods to solve this linear system and test their numerical behaviors by comparing with other two commonly used preconditioners. To this end, we perform wavefield simulation by the NAD method and another two conventional numerical schemes in various media. Numerical dispersion analysis and waveform comparison are also implemented for these numerical schemes. Our results show the superiority of our proposed methods.