Sampling of fault populations using sub-surface data: A review

In favourable circumstances, seismic reflection data can give an unrivalled view of faulted rocks in the sub-surface, imaging features down to the seismic resolution (typically 20-30 m). The lack of finer detail can, in part, be addressed by analysing well cores through the same rock volume. Samples of fault populations from such data often exhibit power-law size distributions where 'fault size' can be trace-length or fault-displacement. Analysis of a synthetic fractal model (the 'fragmentation model') demonstrates that changing the dimension of the sampling domain (e.g. volume to plane, plane to line) changes the power-law exponent of the sample's size distribution. The synthetic model also suggests how best to treat faults that extend out of the sample area, and illustrates potential problems in comparing samples from very different scales (e.g. regional and detailed mapping). Analysis of a variety of interpreted seismic-reflection data sets has provided a range of power-law exponents for different sample types: (i) fault-trace lengths (two-dimensional samples): -1.1 to -2.0; (ii) fault-trace maximum displacements (two-dimensional sample): -1.0 to -1.5; (iii) 'arbitrary' displacements (one-dimensional sample): -0.5 to -1.0. Fault-trace lengths are very sensitive to truncation (resolution) effects, and rip regions should be re-assessed using displacement gradients. Maximum displacements, and displacements obtained by line-sampling, are much more robust attributes. Well data are useful in constraining the extrapolation of populations to smaller scales. Fault populations scale differently than earthquake populations, because the latter represent only the instantaneous deformation, whereas fault populations represent the deformation accrued over geological time. A valuable dataset to clarify these relationships would be a true three-dimensional sample of faults in an actively-deforming area.