The multiaxial perfectly matched layer (M‐PML) is a stable and effective nonreflecting boundary condition for many problems in computational seismology. As in the case of the classical perfectly matched layer when the system of M‐PML equations is discretized, the absorbing layer is no longer perfectly matched, and a small spurious numerical reflection manifests itself at the interface between the physical domain and the M‐PML. More reflections originate at the rigid outer boundary of the M‐PML, where waves that are not completely damped out bounce back and return to the physical domain.
In this work we present a plane‐wave analysis to demonstrate that the M‐PML is perfectly matched in the case of the continuum on the condition that the damping profile is zero at the interface between the physical domain and the M‐PML. We also performed a quantitative assessment of the numerical reflection introduced by the discrete M‐PML when the latter is implemented to truncate a computational domain over which the elastodynamic wave equation is discretized using the spectral element method. By means of numerical experiments, we show that such numerical reflection depends on the actual M‐PML width, the damping profiles, and the wavelength, and it does not decrease indefinitely when damping is increased. The effectiveness of the M‐PML to reduce reflections is illustrated with comparisons with well‐known analytical solutions.