Consider the nonlinear and completely continuous scattering map \[ \mathcal{S}\big((\Omega; \lambda, \mu, V), \mathbf{u}^i\big)=\mathbf{u}_t^\infty(\hat{\mathbf{x}}), \quad \hat{\mathbf{x}}\in\mathbb{S}^{n-1}, \] which sends an inhomogeneous elastic scatterer $(\Omega; V)$ to its far-field pattern $\mathbf{u}_t^\infty$ due incident wave field $\mathbf{u}^i$ via Lam\'e system. Here, $(\lambda, s...