System identification of distributed parameter systems applied to seismic inverse problem

A system identification technique is developed for a class of second-order hyperbolic equations and applied to solve an inverse problem in seismic interpretation. The system model is represented by a wave equation, which is excited by a point source and observed also at a point which are placed at any arbitrary depth. The system identification problem is formulated as an optimal control problem to minimize a weighted least squares of the errors between measurements and simulated responses. A variational approach is used to solve the problem and a necessary condition is obtained. The computational algorithm is developed by using the Fourier method for solving state and costate equations.