Lecture index: Fault scaling relationships between variables. / Fractal distributions of fault variables. / Fluid flow through faults.
Readings: Note that these readings are from the primary literature. There may be aspects of the article you don't understand yet. Read carefully and get what you can out of these. Focus on the graphs and diagrams. Ask questions.
Other references for extending your understanding of faulting:
While this topic is typically not treated at much length in undergraduate structural geology textbooks, much has been learned in the last few decades, and it is useful knowledge in the practice of geology. For these reasons, and just because it is interesting, we will take a look at them.
Scaling - in a multivariable system a mathematical relationship between the magnitude of one variable versus another variable. The powerful example in geology is the relationship between the size and frequency of an event (such as floods or earthquakes).
Possible geometric aspects of faults that scale against each other:
This is explored some in your readings. It is also important to consider amount of deviation from the scaling relationship, which in geologic situations can be significant. That deviation influences the error associated with a prediction based on scaling relationships.
This photograph of a normal fault zone truncating a horizontal sandstone layer in the hanging wall is from the Arikaree Group in NW NE. Note the well developed fault breccia, along with thin white calcite slickensides at the base of the fault zone. Offset could not be measured for this outcrop since matching strata on both sides could not be identified. Could one estimate the amount of offset on this fault on the basis of the thickness of the fault zone (and with what amount of confidence)? Scaling relationships could provide at least some basis for doing so.
Interestingly most of the examples in the literature focus on normal faults. Arrays of strike-slip faults may also show scaling relationships. Thrust faults often do not seem to follow these scaling relationships (or it may be difficult to get that information). However, some thrust fault zones with abundant movement on them are very thin and so the fault zone thickness seems to bear little relationship to the amount of slip. Therefore, a key consideration is to know when and when not to use scaling relationships.
Astronaut image of part of the East African rift zone. Image source: NASA Visible Earth - https://visibleearth.nasa.gov/view.php?id=77566 . Some of the fault scarps, which appear as shadows, are identified. The topographic relief controlling the shadows is a direct function of the amount of vertical offset. Faults of a variety of lengths exist here and the longer faults have widershadows suggesting some type of relationship between surface length of a fault and the amount of offset. What exactly that relationship might be and why it exists is an example of fault scaling studies.
Fractal perspective: Scaling relationships can also be found in the distribution of a single fault descriptor, and these can exhibit a fractal character. The reason for this is discussed in Turcotte's book - Fractals and chaos in geology and geophysics (Cambridge University Press). The best documented such relationship is for fragmented rocks, i.e. breccias.
Map of Cenozoic faults in Mojave Desert area, southern California. If one focuses on fault length there appears to be many shorter faults and fewer longer faults. Does the length frequency follow a mathematical relationship, and is it fractal in specific can be asked. When doing so one can also consider the bias of finding shorter faults versus longer faults. One can also consider this is a linked fault network accomodating large scale crustal strain. Image from USGS site - Cenozoic tectonics of the northern Mojave Desert: https://geomaps.wr.usgs.gov/neotectonics/ .
Power law distributions also occur.
Why are scaling relationships useful?
Evidence faults effect fluid flow:
This is a USGS image where the colors represent subsidence due to "fault-controlled deformation from the dissipation of residual ground-water pore-fluid pressure changes in response to past underground nuclear weapons testing." in the Yucca Flat area. Note how the white lines, representing faults, compartmentalize the pattern of subsidence. The faults are acting as barriers to fluid flow in this case. Source: http://pubs.usgs.gov/fs/fs06903/
These are sandstones of the Brule Formation in the White River Group at Slim Buttes, South Dakota. Two sub-vertical fins can be seen to cut through the strata. These are due to differential (increased cementation), and the localization along the small fault and associated fractures suggests that the faults acted to direct fluid flow, with the cement representing a fluid-rock interaction.
Hot springs along a fault on the flank of the Jemez Mountains in New Mexico (along with UNO field trip participants). The layered deposits are calcium carbonate tufa deposits, and some of the hot spring waters can be seen seeping out of the interior underneath the feet of Dr. Engelmann to the right. These deposits are a demonstration of the long term flow of fluids upwards along this fault. Many hot springs occur along structural controlled fluid path ways, often faults.
Processes that effect the geohydrology of a fault:
Upper image: Fault breccia zone in the French Alps (in Vanoise National Park) that extends for miles. Lower image: Close up of silicified breccia where the original clasts were marble, and the area between and some of the angular clasts have been silicified. Given some estimate of the amount of silica that might be dissolved in the waters one can estimate how much water had to pass through in order to accomplish this amount of silica replacement, and the answer is generally a large amount. One can also appreciate the amount of dilatancy that had to occur to provide the initial pore space between the clasts. This is evidence that this fault behaved as a very significant hydrothermal conduit at some time, but one that might have been self sealing (i.e. a mechanism of fault hardening that would cause the fault breccia zone to widen with development).
Water, the seismic cycle, and seismic pumping:
Oxidizing vs. reducing waters - possible indicator of direction of fluid flow. Structural topography and direction of flow (normal faults vs. thrust faults).
This is an image of a brittle fault within amphibolite basement mylonitic gneisses that are both part of the long-lived Billefjorden fault zone in Spitsbergen Norway. Note the multiple slip surfaces that both parallel and cut and offset the gneissic layering along with the breccia with the reddish matrix just below the walking stick. The view is looking down into the ground. Can you tell which direction the fault moved? The red coloration follows the faults and is the result of fluids that migrated along the fault fracture network modifiying and precipitating minerals. Since they are red a first assumption may be that they are iron oxides and the migraitng waters were oxidizing. However, care must be taken, because the red coloration could also be due to modern weathering of sulfides. However, these rocks show no other signs of weathering, and so the mineralogy may reflect the fluids that were moving along the fault.
Sealing faults vs. porous faults, and the significance in petroleum exploration, carbon sequestration, geothermal systems, and bedrock geohydrology.
The importance of damage zones versus fault cores.
Chart showing data and model for how the permeability varies across a fault core and damage zone for the Nojima fault (which caused the 1995 Kobe, Japan earthquake). Note how if this is the persistent structure along the fault you have two high permeability channels separated by a lower permeability core. Image source: http://earthquake.usgs.gov/research/physics/lab/nojima.php
Additional references for reading for the interested:
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