Интерполяционные сплайны в обратной задаче сейсмометрии с произвольными начальными условиями

Abstract

Direct and inverse problems of “classic” seismometry with arbitrary initial conditions are considered. A general analytical solution of the direct problem expressed through characteristic numbers of the primary matrix for a pendulum galvanometer system is suggested. A solution of the inverse problem is constructed for the situation where the record is assigned by its values in nodes of some (generally speaking, nonuniform) net. Spline structures as a tool of approxi- mation of the record function are used; the role of boundary conditions is analyzed. The results can be used for the computation of theoretical accelerograms and the processing (interpretation) of earthquake records.