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Rock Fractures and Fluid Flow

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Main research fields

Statistical physics

We use the principles of thermodynamics and statistical physics to analyse and forecast the properties of geological (and some human-made) probability distributions. The analysed structures include size-distributions of crater cones and volcanoes, but the main focus has been on the distributions of various fracture parameters (fracture length, displacement, aperture, strike, and dip) of populations such as fissure swarms, dyke swarms, fault zones, and sedimentary basins. For example, we calculated the power-law scaling exponents and the (Gibbs/Shannon) entropies of tectonic fractures, ranging in length by five orders of magnitude, from four networks at the plate boundary in Iceland.

The results show a strong linear correlation between the population scaling exponents, the fracture length ranges and average lengths, and the calculated entropies. The correlation is partly explained by the entropy (and the scaling exponent) varying positively with the length range (the difference between the longest and the shortest fracture) of the populations in each network. Currently, we are working on how to relate the calculated entropies to the thermodynamic principles that control fracture initiation and propagation (the theory of Griffith). We have applied the same method to analysing other lineament patterns, such as streets in cities of various shapes and sizes, as well as building-size distributions.

We also use entropy considerations to assess likely distributions of various fracture parameters in the subsurface – such as in fractured reservoirs – with a view of forecasting fracture porosity and permeability. Here we use the existing data at the extremes of the probability distribution, that is, large-scale faults from seismic data and small fractures from well data, and use the entropy method to forecast or complete the ‘missing part’ of the probability distribution.


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Length-size distributions of 221 tension fractures and normal faults, in the Holocene lava flows of the rift zone in Southwest Iceland, power law. On a log–log (bi-logarithmic) plot the data are seen to be with a break, so that a double power law fits the distribution better than a single power law.

See the following PDF file:
Tectonophysics - Lengthdisplacement scaling and fault growth

Aerial view of tension fractures and normal faults in the rift zone of Southwest Iceland.

See the following PDF file:
Relations between the scaling exponents, entropies, and energies of fracture networks



Contact: rf3@es.rhul.ac.uk


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