Non-parametric identi cation of geological models

Marc Schoenauer1, Andreas Ehinger2 and Bertrand Braunschweig3 (1) : CMAP, CNRS-URA 756, Ecole Polytechnique, Palaiseau, France (2) : Geophysics and Instrumentation, IFP, Pau, France (3) : Computer Science and Applied Mathematics, IFP, Rueil-Malmaison, France E-mails : [email protected], fandreas.ehinger,[email protected] Abstract Many problems to be solved in geophysical processing can be expressed in terms of identi cation of spatial geological models : given a function applied to a geological model , producing a result R, the problem is to nd such that ( ) = R , where R is the expected result : a seismogram, a pressure curve, a seismic cross-section etc. The presented research deals with the joint use of evolutionary algorithms and Vorono diagrams to address some non-parametric instances of identi cation problems in geophysics, i.e. without a priori hypothesis about the geometrical layout of possible solutions. In this paper, a rst application in velocity determination for seismic imaging demonstrates the ability of this approach to identify both the geometry and the velocities of the underground from experimental seismograms.