Numerical Inverse Elastic Scattering Problems

The elastic wave propagation problems have a wide range of applications, particularly in geophysics, nondestructive testing and seismology. The associated inverse problems arise from the use of transient elastic waves to identify the elastic properties as well as to detect flaws and cracks of solid speciments, especially in the nondestructive evaluation of concrete structures (see e.g. [55, 58]). Moreover, the problem of elastic pulse transmission and reflection through the earth is fundamental to both the investigation of earthquakes and the utility of seismic waves in search for oil and ore bodies (see, e.g., [1, 20, 21, 36, 57] and the references therein). The scattering of elastic waves are very complicated due to the coexistence of compressional and shear waves propagating at different speeds. There is a vast literature on the inverse elastic scattering problem as described above. We refer to the theoretical uniqueness results proved in [24, 47, 49–54] and, the sampling-type reconstruction methods for impenetrable elastic bodies developed in [3, 7] and those for penetrable ones in [13, 56].