Using a Hankel function expansion to identify stiffness for the boundary impulse input experiment

Motivated by the fact that the Green’s function for the Helmholtz equation in 2D space is the Hankel function, we modified the traditional ansatz of geometrical optics by replacing the exponential function with the Hankel function. With the new ansatz, the leading order amplitude in the asymptotic expansion captures the amplitude change of the solution more accurately than the traditional one in the case where there is a point source on the boundary. This allows us to extend the inverse algorithm developed in Ji and McLaughlin ([7]) for the recovery of the Lamé parameter μ from the shear wave displacement field to the case where the shear wave propagation can be modeled by a simplified 2D wave equation and the boundary source becomes a point source in the simplified 2D space.