This paper addresses a multivariate sampling problem. Assuming that the sampling procedure can be modelled as a multivariate random walk in R P with absorbing barriers, the ergodic limit of the error-covariance matrix is found using Wald’s equality. It is shown that false correlation or non independent errors could be induced in the data by the sampling procedure. Theoretical expressions of the error covariance matrices for different granulometric distributions have been obtained from a Monte Carlo simulation and a case study. The advantages of these theoretical equations are (i) the possibility of calculating the a priori sampling error; (ii) the evaluation of the error covariance matrix (nugget effect); (iii) the optimization of sampling procedures.