Reconstruction of blocky impedence profiles from normal-incidence reflection seismograms which are band-limited and miscalibrated

We study the inverse problem of determining the impedance of a one-dimensional medium from reflection data which are band-limited and uncalibrated. The problem arises in seismic exploration data processing. We give a brief review of the subject and explain why there is a need to model the data more realistically. We show that if we are given, in addition to the reflection data, some a priori information about the impedance, we can in principle determine the desired unknown. The method incorporates the a priori information about the impedence profile inan optimization problem involving L¹- and L²-norms. From the character of the optima of the minimization, we are able to assess the possibility of absolute calibration of the data, and of estimating the absolute impedance of the medium. Our findings are illustrated with numerous simulations.