  The perfectly matched layer is very important for the elastic wave problem in
the frequency domain. Generally, the formulas of the elasticity tensor in the
perfectly matched layers are derived from the transformed momentum equation. In
this note, we proved that the transformed elasticity tensor derived in this way
lost its symmetry. Therefore, these formulas are inconsistency in theory and
it's hard to explain its numerical performance. We present a new symmetrical
formula of elasticity tensor from the weak form. So the theory of elasticity is
still applicable in the perfectly matched layers.
