Simultaneous Determination of Source Wavelet and Velocity Profile Using Impulsive Point-Source Reflections from a Layered Fluid

The determination of source signature is a major calibration problem in reflection seismology. This deconvolution problem is conventionally approached by way of statistical methods, by direct measurement, or by the location of a clean reflection in an otherwise quiet part of a reflection section. We show that a quasi-impulsive, isotropic point source may be recovered simultaneously with the velocity profile from reflection data over a layered fluid, in linear (perturbation) approximation. Our approach is completely deterministic, and does not depend on the presence of an isolated reflection in a quiet part of the section, as we illustrate with a numerical example. After describing the algorithm and a numerical implementation, we give a complete mathematical treatment, which shows that our estimates of source wavelet and velocity profile are stable in a certain sense. Because of this stability property we conjecture that our approach to simultaneous estimation of source and medium parameters actually applies to a much broader class of models than that treated here. Sponsored in part by grants from the National Science Foundation NSF-DMS84-03148, NSF-DMS86-03164 and the Air Force Office of Scientific Research grant AFOSR-84-0252. Prepared in cooperation with California Univ., Los Angeles, Dept. of Mathematics, Iowa State Univ., Ames, Dept. of Mathematics, Delaware Univ., Newark, Dept. of Mathematical Sciences; and Institut Francais du Petrol, Rueil-Malmaison Cedex, France.