The application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint wave propagation problems. An important challenge is to design an infinite domain truncation method suitable for accurately truncating an infinite domain governed by second order elastic wave equations in displacement and able to efficiently absorbing normal to near-grazing incident surface waves and body waves. Furthermore, it should be suitable be implemented with high-order finite element methods in order to treat steeply varying medium interfaces and free surface with topography while remaining computationally efficient. In this report, we will show how to construct complex-frequency-shifted PML (CFS-PML) for time-domain adjoint methods. Then we show its implementation with high-order finite element method. Finally, based on numerical test, we show that our formulation and implementation is absorbing efficient for normal to near-grazing incident body waves and surface waves. The advantage of using CFS-PML in time-domain adjoint methods have also been analysed and illustrated.