Predicting the three-dimensional population characteristics of fault zones: a study using stochastic models

Major fault zones are surrounded by damage zones composed of minor faults that, in siliclastic rocks, often form significant barriers to fluid flow. Information on fault damage zone architecture is usually available only as 2D maps, or as 1D line samples or well logs. However, the accurate determination of the 3D fault population characteristics is crucial for flow prediction. In this paper, stochastic models of fault damage zones are generated by incorporating the statistical properties of fault populations (power law length and throw distributions, orientation distribution) and different spatial distributions, including randomly located, simple and hierarchical clustering of faults. These damage zone models are used to investigate the characteristics of 2D and 1D samples, which were found to depend on the 3D power law length exponent, D3, and the spatial distribution of the parent 3D population. Observed 1D samples may fail to show power law characteristics and, therefore, a lack of power law behaviour need not imply a non-power law parent population. The simple rules in which observed 2D and 1D samples follow power laws with exponents D2=D3−1 and D1=D3−2, respectively, are not always obeyed. Clustering tends to reduce the difference between these exponents to less than their simple integer values, most markedly for the simple clustering model. The hierarchical clustering model, in which small faults are clustered around larger faults throughout the fault damage zone and which most closely resembles nature, suggests that the simple rule D2=D3−1 is obeyed with only small deviations but that 1D samples may depart from the simple rule, D1=D3−2, by as much as 0.25.