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The perfectly matched layer (PML) absorbing technique has become popular in numerical modeling in elastic or poroelastic media because of its efficiency in absorbing waves at nongrazing incidence. However, after numerical discretization, at grazing incidence, large spurious oscillations are sent back from the PML into the main domain. The PML then becomes less efficient when sources are located close to the edge of the truncated physical domain under study, for thin slices or for receivers located at a large offset. We develop a PML improved at grazing incidence for the poroelastic wave equation based on an unsplit convolutional formulation of the equation as a first-order system in velocity and stress. We show its efficiency for both nondissipative and dissipative Biot porous models based on a fourth-order staggered finite-difference method used in a thin mesh slice. The results obtained are improved …