Before revision:  Practical implementations of PMLs often use smooth-varying attenuation coefficients to reduce the numerical reflection from PMLs and to reduce the thickness required for reaching a certain level of absorption .
After revision:  Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from PMLs and to reduce the thickness required for reaching a certain level of absorption .