In this work, we successfully applied an alternative formulation of the perfectly matched layer (PML), the so-called nearly PML (NPML), to acoustic wave propagation modeling. The NPML formulation shows great advantages over the standard complex stretched coordinate PML. The NPML formulation deviates from the standard PML through an inexact variable change, but this fact only affects the wave behavior in the NPML layer, which is outside the region of interest. The equivalence of the wave-absorbing performance between these two PML formulations (the standard complex stretched coordinate PML formulation and the NPML formulation) in 3D Cartesian coordinates for acoustic wave propagation modeling is proved mathematically in this work. In time-domain methods, the advantages of the NPML over the standard PML were explained by both the analytical analysis and the numerical simulations in terms of implementation simplicity and computational efficiency. The computation time saving is up to 17% for the 2D example used in this work. For 3D problems, this computational saving is more significant. After theoretically analyzing the numerical reflections from the NPML and the standard PML, we concluded that these two PML formulations have exactly the same performance, even after spatial discretization. This conclusion is validated by numerical experiment. Finally, we tested the NPML in the Marmousi velocity model and found its wave-absorbing rate is high enough, even for this realistic structure.
