An improved convolution perfectly matched layer for elastic second-order wave equation

A convolution perfectly matched layer (CPML) can efficiently absorb boundary reflection in numerical simulation. However, the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly to the second-order elastic wave equation. In view of this, based on the first-order CPML absorbing boundary condition, we propose a new CPML (NCPML) boundary which can be directly applied to the second-order wave equation. We first systematically extend the first-order CPML technique into second-order wave equations, neglecting the space-varying characteristics of the partial damping coefficient in the complex-frequency domain, avoiding the generation of convolution in the time domain. We then transform the technique back to the time domain through the inverse Fourier transform. Numerical simulation indicates that the space-varying characteristics of the attenuation factor have little influence on the absorption effect and increase the memory at the same time. A number of numerical examples show that the NCPML proposed in this study is effective in simulating elastic wave propagation, and this algorithm is more efficient and requires less memory allocation than the conventional PML absorbing boundary.