Abstract - A recurring theme in studies of extensional basins has been the observation that the total amount of regional extension seen on normal faults on regional seismic lines is less than the extension indicated by the observed crustal thinning and thermal subsidence. One explanation put forward to account for the apparent discrepancies has been that small-scale faults, i.e. those below the limit of seismic resolution, are responsible for a significant proportion of the regional extension. However, this explanation has not generally found favour with earthquake seismologists, since the observed population distribution of earthquake magnitudes indicates that large earthquakes are responsible for almost all of the total seismic moment release, i.e. strain. Since earthquake moment is a direct measure of the size of the fault on which the earthquake occurs, it has been concluded that the largest faults are responsible for almost all of the fault-related strain in a deforming region.
We have measured fault-displacement populations from regional seismic profiles, and from oilfield scale 3D-seismic data and oilfield cores along the the same profiles. The observations are consistent with a single power-law relationship between fault displacement size and fault displacement density for data spanning six orders of magnitude of fault displacement, from kilometres to millimetres. A power law relationship signifies that the fault-displacement population is scale-invariant, i.e. fractal, at least within the range of displacements examined. Integration of this power-law relationship shows that a significant proportion of the total displacement along a regional seismic profile occurs on fault offsets less than the limit of seismic resolution, which is ca 50m. Typically, 10-40% of the total fault-related displacement is not observed.
Measurements of fault-displacement populations along one-dimensional
transects can be used to derive the geological moment populations of faults
within a three-dimensional volume, and these populations also have power
law distributions. The population distributions of old (inactive) faults
obtained in this way have different fractal dimensions, i.e. they scale
in a different way, to populations of active faults inferred from observations
of earthquake moment distributions. The systematic differences between
inactive and active fault populations is accounted for by evolution of
fault systems whereby some faults become inactive and stop growing, whilst
those which continue to grow constitute the active fault population at
a given time.
Nature 351, 391-393, 1991.