Sampling Grid Shifting Algorithm: A Non-ergodic Spatial Bootstrap
Technique for Regular and Irregular Sampling Patterns
Abstract
Accounting for uncertainty in statistical model parameters is an
essential part of geostatiscal reservoir characterization. While
parameter uncertainty may be assessed in its ergodic form; the
non-ergodic is a better characterization of the variability in the
random field. Assessing non-ergodic parameter uncertainty requires
re-sampling (bootstrapping) techniques. Existing techniques for such
non-ergodic re-sampling are plagued with some limitations/complications.
This paper therefore presents a spatial bootstrap algorithm that
overcomes the limitations/complication. For a discretized field, the
algorithm implements simultaneous displacements (shiftings) of all
sampling points through the same distance vector. The shiftings are done
across the dimensions of the field subject to the dimensionality of the
sampling. In each dimension, the sampling points are shifted
successively through a distance equivalent to the gridblock length in
that dimension. At each shifting, a shifted sampling grid, of similar
configuration as the original sampling grid, is generated. Using the
shifted sampling grid, the algorithm re-samples a full-grid simulated
realization of the field. The assumption of second-order stationarity
implies that a sample from a shifted sampling grid is considered a
repeated sample of the original sample. The algorithm has been scripted
in R statistical computing environment and applied to an
irregularly-sampled 3-D field with satisfactory results.