The eigenvalues are critical to the determination of the right eigenvectors and left eigenvectors, your product accompanied by the initial conditions determine the parameters in the solution weighted seismic system
I understand and say, The seismic inverse is used for soil studies, teacher you have seismic data, and obtains the eigenvalues of the data set, and want to know which means each eigenvalue as a function of soil behavior?, Problems of this type are attacking techniques such as wavelet-gabor and imaging techniques. It may be that an eigenvalue may represent soil behavior.
From explicit data state variable can calculate its first derivatives and second derivatives. (slope and curvature), also from the discrete equation of a dynamic system can estimate the transition matrix (inverse problem) and then determine its eigenvalues and eigenvectors determine them right and left and from there the weighting