An improved procedure of least-squares inversion and its application in VSP record

The spectrum of a discrete Fourier transform (DFT) is estimated by generalized linear inversion, and used to produce desirable seismic traces with regular spatial sampling from an irregularly sampled data set. The essence of such an approach is to solve the DFT inverse problem with a particular constraint. This paper introduces a diagonal constrained matrix that is real and positive definition, so as to improve the resolution of model space. Application to both synthetic and real seismic data reveals the effectiveness of the technique.