The linearized monotonicity method for elastic waves and the separation of material parameters

We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show that the linearized method has some additional advantages. The linearized method can in particular be used to obtain additional information on the material parameters, and is able to partially separate and identify the supports of the Lam\'e parameters.