Fault scaling relationships, and fluid flow through rocks.

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.

• Schlishe et al., 1996, Geometry and scaling relationships of a very small rift-related normal faults; Geology, 24, 683-687 - geology.rutgers.edu/~schlisch/microfaults.pdf
• Sibson, R. H., 1987, Earthquake rupturing as a mineralizing agent in hydrothermal systems; Geology, 15, 701-704. Good introduction into one aspect of fault-fluid flow behavior.

Other references for extending your understanding of faulting:

Fault scaling relationships between variables.

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:

• fault length (typically map length) vs. maximum displacement.
• fault zone thickness vs. slip amount.
• fault slip rate vs. net slip (do larger faults get large by a greater slip rate or by being longer lived?).

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.

Map from USGS showing array of faults (red lines) in the Arbuckles of Oklahoma. What scaling relationships might exist here? What do you notice about the pattern of faulting? Source: http://ok.water.usgs.gov/arbsimp/

Fractal distributions of fault variables

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.

• A fractal distribution is often evident as a log-log linear relationship between frequency and size.
• Features that can show a fractal distribution:
• maximum slip amount in a fault set.
• the length of faults.
• frequency of various size clasts in fault breccia.
• Link to a simple geometric model for formation of a breccia. If two adjoining faces are of equal size we can specify that one of them will break. As a result, if we break a cube into smaller cubes, only two diagonal cubes will survive.
• Break it into 8 cubes. Each of these will have a side length of h/2.
• Repeat the process for each cube except for two diagonal cubes which survive. We then have 2 cubes of size h/2.
• Repeat the above process for each of the cubes of size h/2, i.e. for all cubes that have facing sides that are of the same area.
• Every time you repeat this step only 6 out of the 8 blocks will participate in fracturing. The number of new cubes is equal to the the number existing before x 6. Most importantly, for each one of these boxes, 2 will survive the next reiteration. Therefore there will be (6^N) x 2 boxes of size H/(2^N), where N is the number of reiterations.
• Plot log size vs. log # of clasts and you will see a straight line plot with a slope of 2.58.
• Challenge with application to natural breccias is the varying clast shape.
• Could fault or fracture line density in map view be fractal in character?

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?

• They can be used to extrapolate behavior and patterns with them. In other words, they provide a basis for extrapolating from an observed temporal or spatial scale to a larger or smaller unobservable scale. A crucial related question is - over what scales does the fraqctal relationship hold?
• They can be used to review maps and draw more realistic patterns.
• The relationship can be used to quantitatively model behavior, such as fluid flow through breccias.
• Breaks in scaling relationships (bifractals) can provide useful insight also. To repeat, it is important to be think about the scale range over which the fractal distribution may exist.

Fluid flow through faults

Evidence faults effect fluid flow:

• abundant vein material and associated alteration in fault zones gives clear evidence of enhanced fluid flow along faults. Estimates of fluid-rock ratio can yield minimum fluxes.
• changes in water tables and spring behavior associated with earthquake events along active fault zones.
• see gas "reflections" in an oil field in position consistent with leakage along a reactivated fault (e.g. Wiprut & Zoback, 2000)

Quartz veins concentrated in fault hanging wall. They could be considered as part of a damage zone. Source: http://geology.wr.usgs.gov/parks/olym/olym7.html

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:

• brecciation, microcracking and production of new pore space and dilatancy (preserved in damage zone?).
• alteration by fluids (hydrolitic weakening), clay gouge formation and fault core barrier to flow.
• hydrothermal precipitation: rupture-seal processes and mineral precipitation and fault hardening.
• smearing of clays in wall rock units along the fault and the production of local across-fault-flow seals.
• solution (some fault rocks are associated with volume loss), can reduce or increase porosity.

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:

• The sucking behavior of dilational jogs.
• what is a dilational jog (see image to the right)?
• the cracking and associated volume dilation during seismic events serves as pumping device sucking water from nearby areas that then can travel along the fault conduit.
• significance of vertical orientation of dilational jogs for strike-slip faults?
• Consider the history of pore pressure with stick-slip rupture and dilatancy.
• Will return to when we look at the effect of pore pressure on stresses.
• Larger earthquakes and greater degree of veining and hence inferred dilation is associated with the brittle-ductile transition. It may follow then that these large earthquakes tend to draw water down to deeper levels. Thinking of faults along strike, it also follows that the fluid flow behavior will vary with the segmentation of the fault.
• Sudden dilation and pressure drop can create steam and rapid mineral precipitation.

Oxidizing vs. reducing waters - possible indicator of direction of fluid flow. Structural topography and direction of flow (normal faults vs. thrust faults).

• Simplistic thinking - oxidizing waters associated with flow from surface down along fault, while reducing waters may come from below. One can think of situations where you would expect differences.
• With thrust faults one might expect up-dip fluid flow. Springs are seen at the toes of detachments in accretionary wedges, suggesting the detachment can act as a conduit.
• Normal faults may at times act as conduits for fluid flow descending along the fault.
• Osmotic barriers may exist in systems with waters of contrasting salinity.

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