| Abstract: | The acoustical impedance distribution of the substratum, or equivalently, the reflection coefficient sequence, is determined from VSP data. This nonlinear inverse problem is solved by a least-squares method. As the wavelet is unknown, the impedance distribution and the Neumann boundary condition (which characterizes the excitation of the medium) are simultaneously identified. The inversion method is applied to synthetic and field VSP's; the result is satisfactory, even when strong noise corrupts the data, provided that a suitable constraint on the impedance distribution is introduced in order to ensure the stability of the inverse problem. The reliability of the inversion result in the case of field VSP, is confirmed. Some ways in which this result may be used are illustrated (calibration of the seismic surface data, multiple identification, prediction ahead of the bit). |
