The search for the optimum model of the structure of a layered medium based
on experimental reflectivity data is considered. A new modification of the
successive-descent method is developed for minimizing the functional descr
ibing the discrepancy between the observed and the calculated reflectivity
profiles. The significance of the model parameters is established as a resu
lt of the test of simple statistical hypotheses. The efficiency of the meth
od developed is illustrated on an experimental reflectivity profile measure
d earlier by Wiesler and Majkrzhak [2].