Application of the Multiaxial Perfectly Matched Layer to Near‐Surface Seismic Modeling with Rayleigh Waves

Abstract

Perfectly matched layer (PML) absorbing boundaries are widely used to suppress spurious edge reflections in seismic modeling. When modeling Rayleigh waves with the existence of the free surface, the classical PML algorithm becomes unstable when the Poisson’s ratio of the medium takes values greater than about 0.38. Numerical errors can accumulate exponentially and terminate the simulation due to computational overflows. Numerical tests show that the divergence speed of the classical PML has a non-linear relationship with the Poisson’s ratio. Generally, the higher the Poisson’s ratio, the faster the classical PML diverges. the multiaxial PML (M-PML) attenuates the waves in PMLs using different damping profiles in orthogonal directions. If the proportion coefficients of the damping profiles are set appropriately, the M-PML algorithm is stable for high Poisson’s ratio earth models. Through numerical tests of 40 models with Poisson’s ratios that varied from 0.10 to 0.49, we find that a constant proportion coefficient of 1.0 is sufficient to stabilize the M-PML for all isotropic elastic cases. Wavefield simulations indicate that the instability of the classical PML is strongly related to the wave phenomena near the free surface. When applying the multiaxial technique only in the corners of the PML near the free surface, the original M-PML technique can be simplified without loosing its stability. the simplified M-PML works efficiently for both homogeneous and heterogeneous earth models with high Poisson’s ratios. the analysis reported on here was based on 2-D finite difference modeling in the time domain that can easily be extended into the 3-D domain with other numerical methods.