AbstractNone of the processes of estimation currently available is fully acceptable to the geophysicist. Firstly, they all assume that the variable, be it seismic reflection time, rms velocities, Bouguer anomaly, etc.… is random, amenable to pure statistical considerations, and the processes all disregard the relationships which link the values of the variable in the different points of the domain under investigation. Secondly, they do not provide the geophysicist with any guideline for smoothing his data, as smoothing and estimation are considered two separate operations. Thirdly, they fail to offer a valid criterion of estimation and a measure of the estimation error.The krigeage process overcomes the above mentioned difficulties. It synthesizes the structural or “geostatistical’ characteristics of the variable by using a function called the variogram (variances of the increases of the variable with respect to distance and direction). It smoothes the variable, when necessary, as a function of the “nugget effect’ (value at the origin of the experimental variogram). It yields an optimum estimation of the variable by minimizing the estimation error, and it computes a measure of the reliability of the estimation, the variance of krigeage.The process is demonstrated herein with three examples of variograms on seismic and gravity data and an example of contouring of velocities, reflection times and depths of a productive layer in an oil field, with detection and correction of irregular data, smoothing of velocities, migration of depth points, and display of estimat