Evaluation of sampling in the subsurface

The evaluation of sampling is presented in the form of a sampling error defined as a difference between the true average and the sampled average of the measured process over the sampling domain. The sampling error is quantified as a product between the process point variance (defined at the scale of a sampling device's support volume) and the sampling variance function, which quantifies the reduction of uncertainty due to the sampling activity. The sampling variance function is expressed analytically as a function of the scale of fluctuation of the measured process. For a single sampling point the sampling variance function defines the reduction in the process point variance as a result of sampling over a certain support volume. The presented evaluation of the sampling performance can be used for designing the monitoring activity and for measurement conditioning of stochastic theories. The presented examples demonstrate the use of sampling evaluation for the purpose of conditioning on the concentration measurements.