COMPARISON OF SOME INVERSE METHODS FOR WAVE-PROPAGATION IN LAYERED MEDIA

The one-dimensional wave equation in a layered medium is considered. The inverse problem consists of computing the acoustic impedance of the layered medium from the reflection response measured at the surface. For a discrete medium consisting of homogeneous layers of equal travel time, the Levinson algorithm is used to compute the reflection coefficients at the interfaces between the layers. For a medium with continuously varying parameters, an iterative frequency-domain method based on the Riccati equation is used. When these methods are applied to band-limited synthetic seismic data, the result is a filtered version of the acoustic impedance. When the noise level is increased, both methods diverge. For a medium consisting of homogeneous layers of unknown thickness, the reflection coefficients and the travel times are estimated simultaneously by using a detection scheme combined with a numerical solution of the wave equation. The performances of three different methods were compared using synthetic data. All three detection methods proved to have superior performance compared to the classical method using the Levinson algorithm or the iterative frequency-domain method.