  The perfectly matched layer(PML) is commonly used in wave propagation,
radiation and diffraction problems in unbounded space domains. A new
implementation scheme of PML is presented. The PML formulation is pre-defined,
and the wave field absorption is achieved by calculating the residual between
the PML equation and original equation through backward induction. Two forms of
the Residual PML (RPML) are presented: RPML-1, which defines the residual as
the difference between the original and PML equations, and RPML-2, which
defines the residual as the difference between the original and PML wave
fields. RPML-2 is the simplest and easiest to extend, as it does not alter the
original equation and only has one time partial derivative term in the residual
equation. Additionally, since the residual equation has no spatial partial
derivative term, high-order spatial difference discretization is unnecessary,
which results in higher accuracy and computational efficiency. Furthermore,
simulating a wave field in TTI media requires a high absorption effect and
stability of PML. The numerical simulation demonstrates that RPML-2 provides
better absorption performance and stability compared to ADEPML and NPML. To
meet the needs of wave field simulation for complex media, a multiaxial complex
frequency shifted RPML-2 (MCFS-RPML-2) is introduced, which employs double
damping profiles and complex frequency shift technology to achieve higher
stability and absorption effects.
