Joint Advanced Student School (JASS) 2009 Dynamic inverse problem in acoustic media

Solution of inverse problem is one of the most important questions in many fields of science and knowledge. Only a small range of simple inverse problems could be solved by mathematical means. In geophysics and other sciences there exist a number of kinematic and dynamic inverse methods which inherently assume preliminary knowledge of the reference medium. In order to construct the regular reference medium the author suggests Gelfand-Levitan-Moses method. The method is based on mathematical theory and allows reconstructing the solution of inverse dynamic problem for a simplest models. The model parameters are estimated from the recorded dataset. As far as such an estimation of a reference model has fully mathematical basis it is automatically more regular than empirical. Numerical examples for 2D case illustrate the potential of the method and give a direction for further investigations. The method could be used in applied geophysics or may have different applications in fields where one must deal with inverse problems