Considerations for the Use of Sequential Sampling Techniques

Abstract

Sequential sampling is a well-known and efficient method to generate probabilistic realisations of models that are constrained by two-point statistics. These two-point statistics consist of second-order moments that are defined by a variogram. The statistics describe the lateral continuity behaviour of the models. It can be shown that the sequential sampling method correctly generates samples from a probability density function (pdf), when this pdf honours only the statistics that define the lateral continuity constraints. In Bayesian statistics, this is named a prior pdf. The sequential sampling method is also used to generate models from a probability density function that is constrained by observations, similar to those that are derived from seismic data. This is known as a posterior pdf. To justify this approach, some assumptions have to be made that are not strictly valid and the result is often a significant error. The errors will be investigated using a realistic synthetic example. The probabilistic seismic inversion programme that has been developed by Shell contains a module that is able to account for lateral continuity. In this module, an alternative approach has been used to mitigate the problems with the sequential sampling method. To realise this, each location needs to be visited