Abstract
It is shown that the density and the two Lamé profiles of a layered elastic medium can be uniquely determined from the impulse responses due to obliquely incident SH plane waves at two precritical angles of incidence and a normally incident P plane wave. A direct (noniterative) inversion algorithm is developed which construct the three elastic profiles of the layered medium from the reflection data. The equation of motion for an obliquely incident SH plane wave is transformed to the Schrödinger equation whose potential is related to the density profile, shear modulus profile, and the angle of incidence. The Gelfand–Levitan theory is used to recover the potential of the Schrödinger equation from the impulse response. When the impulse response is available at two angles of incidence, the shear modulus and density profiles can be separately obtained as a function of depth. It is further shown that the incompressibility profile can be obtained from the impulse response due to a normally incident P plane wave and the density and shear modulus profiles.
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