We revisit the problem of inversion of post-stack seismic data with a new application and a new approach to regularized inversion. Inversion of post-stack seismic data generally yields reflection coefficients or impedance as a function of two way time. In our application, we have post stack seismic data and density logs at selected locations along a 2D seismic line and we are interested in estimating seismic velocities. This problem causes additional complexity in the model parameter estimation problem in that changes in velocity cause changes in two way travel time and hence, non-linearity is introduced into the problem. We solve the inverse problem using an iterative least squares approach in which a smooth error functional comprising a data and a model misfit, is minimized using a conjugate gradient scheme. The data covariance matrix C (sub D) and the a priori model covariance matrix C (sub M) introduce stability and robustness and thus have strong influence on the quality of final inversion solution. Based on the preconditioned conjugate gradient algorithm, we have developed effective methods to determine the constant diagonal elements or the weights to model and data norms using a variant of an L-curve technique. Our experiments demonstrate that there exists a small area in the sigma (sub d) sigma (sub m) plane in which the low cost function values lie. For model smoothing, a second derivative-weighting factor is used. The synthetic examples demonstrated the fast converge properties (less than 10 iterations) and excellent data fittings. For the field data case, the whole inversion process includes two steps of model smoothing and data fitting. Our results show that almost every identified reflector of seismic data is matched by final synthetics very well. The density and calculated velocity profiles can allow identification of major stratigraphic boundaries.