Dear Raymond,

As you already mentioned, it depends of what you want to study. If you are a seismologist you want to know the specific area and not just the fault or the hole rupture zone which produces the earthquakes.  As a structural geologist, it depends of the scale you want to work with, for example you may consider a faulted zone as a line on a map when you work in a regional scale, but if as a structural geologist you want to study timing, kinematics or dynamics you have to focus in a scale which reaches the scale where an earthquake could be borned, e.g 1-2 km of the hole fault zone. It's logical the excistance of a relationship between length and magnitude, but this relation depends from many local factors. So, each region has its own equations describing this relation, e.g the Aegean area.

Kind regards

Ioannis Alexandridis

Thanks Ioannis,

Well, I was more thinking in terms of the portion of the fault surface that reactivates in a slip event. A conservative assumption would assume that the entire fault area could slip which would result in a very large earthquake whereas a smaller portion seems more reasonable, when looking at solutions of faults e.g. ChiChi, Thoku-Oki, etc. It seems that only a minor portion of the fault is envolved in the slip at any reactivation event, and the size of this slipping part is scale dependent, somehow. Additionally, it seems that the location of the slipping portion moves around the fault plane (logical in a sense) so that sooner or later, given enough time and many enough reactivations, the entire fault plane is sheared. It actually all boils down to this: What is the largest possible earthquake you can expect along a fault of known dimensions? Using the entire surface area would give one answer, using a portion of another (disregarding, for simplicity, jumpjng  ruptures, branching, etc).

Ray

Dear Raymond,

The length of a fault is related with the field and the magnitude of stress in a region and other parameters such as the lithology. Consider a fault as cord of a bow, you can drag it only let's say 1/10 of the total lenght of it. If you drag it more then the bow will brake. Analogous with that, if you had energy enough to activate the hole length of a fault then you should expect to see the tips of the fault moving away many times the length, so you will have an other fault.

You can't know the largest possible earthquake, but you can make statistical analysis of all the data (magnitudes-lengths-deep-regional dynamics etc) for a long period and produce equations for the specific area you had the data. For other area you should generate other equation. Then you will have reliable estimations about the magnitude you could have from a known fault. There is an equation which works for the globe:

logL=0.51Μ-1.85 ---- Papazachos & Papazachou 2002

Regards

Ioannis Alexandridis

Dear Raymond,

4 approaches occur to me: I. Seismologists and 2. Structural geologists 3. Google your subject or search Journal of Structural Geology

1. The radii of seismic slip surfaces are expected to be about 10E4 times the displacements along them (Slunga1991; and pers. comm. 2001). Nb. Assumes a circular slip surface. Slunga, R.S., 1991: The Baltic Shield earthquakes. Tectonophysics 189, 323–331. So “The large number of seismic displacements between a few dm and c. 1 m over pseudotachylites (at Skelleftehamn at least hundreds of metres long indicate earthquakes with magnitudes ML = 5–6 (Slunga1991; and pers. comm. 2001).” From Talbot, C.J., 2005: Lateral constraint rather than escape along a terrane boundary near Skelleftehamn. GFF, Vol. 127 (Pt. 2, June), pp. 99–114. Stockholm. ISSN 1103-5897.

2. Structural Geologists; See eg: Sanderson, David J. and Kim, Young-Seog (2005) The relationship between displacement and length of faults. Earth Science Reviews, 68, (3-4), 317-334. (doi:10.1016/j.earscirev.2004.06.003. Follow references on faults areas versus displacements.

Hi Raymond,

In your question, I think that you are meaning to the rupture area related to a single earthquake, aren't you?. But this is not the fault area. If you assume that the rupture area of one single earthquake is similar to the fault area you are assuming the model of "characteristic earthquake", that is, one fault prefer to break in a similar size during his seismic history (Wesnousky, 1994). However, this model is widely discussed by Kagan (2012). The interesting thing if you mean how to determine the rupture area (potential seismogenic faults), from the fault area. In that case, you need to know the fault geometry in 4D and the active stress field, among other parameters.

On the other hand, the model of earthquake rupture based on asperities and barriers (e.g. Aki, 1981, Kanamori and McNally, 1982) across the fault plane, lead us to the fault size and the earthquake magnitude, related by segments of asperities separated by barriers. It is well known the case for the subduction area. Once again, the fault size and the rupture area is not the same.

Regarding the earthquake geologists and paleoseismology, fault size is defined by the fault trace, dip and depth of the fault, measurements obtained from field work and geophysic survey. Rupture area is realted to earthquake size, surface rupture and fault displacement. Nevertheless, one single fault is determined by several fault segments, each responsible of one single event. In exceptional cases, the total rupture of the fault could trigger the greatest earthquake related to this fault. In this framework, geologists use the Wells and Coppersmith 1994 relationship for fault size and earthquake rupture. There are a lot of works with minor variations (e.g. Stirling et al., 2002), including paleoseismic evidence for empirical relationship between fault parameters and earthquake size.

As you can see, there are different models regarding different assumptions: earthquake occurrence in time, subduction areas, paleoseismic evidence, etc.

As a conclusion, the area A, is the fault area capable to trigger a single earthquake of magnitude M (rupture area). The equation of Hanks and Kanamori 1979 is a good approximation for the physical phenomena related to the geometry of faults and earthquakes. On the other hand, If you decide to use the empirical relationships for fault area and rupture area, you have to classify the type of fault: reverse, normal and strike-slip. If you are looking for the unify model of fault rupture and fault area, there is a long way to walk so far.

Therefore, a fault could be understood as a set of rupture areas capable to trigger earthquakes in a time distribution as a power law (Aki, 1981, Bak and Tang, 1989). As a particular case, the fault area could be the fault rupture.

Best regards

References

Aki, K. (1981). A probabilistic synthesis of precursory phenomena. In Earthquake Prediction (Maurice Ewing Series, 4) (D. Simpson and P. Richards, eds.) 566–574. American Geophysical Union, Washington, DC.

Bak, P. and Tang, C. (1989). Earthquakes as a Self-Organized Critical phenomenon. J. Geophys. Res. B94, 15635.

Hanks, T. C. and H. Kanamori (1979). A moment-magnitude scale, J. Geophys. Res. 84, 2348-2350.

Kagan et al., (2012). http://arxiv.org/ftp/arxiv/papers/1207/1207.4836.pdf.

Kanamori, H. and McNally, K.C., (1982). Variable rupture mode of the subduction zone along the Ecuador-Colombia coast. Bull. Seismol. Sot. Am., 72: 1241-1253.

Stirling, M., D. Rhoades, and K. Berryman (2002). Comparison of earthquake scaling relations derived from data of the instrumental and pre-instrumental era, Bull. Seism. Soc. Am., 92, 812-830.

Wesnousky, S. G. (1994). The Gutenberg–Richter or characteristic earthquake distribution, which is it?, Bull. Seismol. Soc. Am. 84, 1940–1959.

Wells, D. L., and K. J. Coppersmith (1994). New empirical relationships among

magnitude, rupture length, rupture width, rupture area, and surface displacement,

Bull. Seism. Soc. Am. 84, 974-1002.

The Raymond's question is very intriguing because it implies not only the explication of the difference between rupture and fault area, but mainly the underlying conceptual model from which we start to describe our observations.

I appreciate the very clear, concise and correct response of Raul which describes the different meaning of the two terms. Basically the discussion is how starting from "different conceptual models" to integrate and interpretate our observational data (magnitude, surface displacement, etc).

Another aspect, evidenced in the previous answers, is that some conceptual models are not developed only to describe and "predict" the physics of the fault system, but also to approach the risk reduction (more properly the definition of the hazard (deterministic and/or probabilistic, i.e. the "characteristic earthquake" for an area).

In other words we assimilate in the conceptual model a phenomenological description of the 4D physical fault system to attempt a definition of "a useful model to assess the hazard". In this sense the general "geological" concept of a fault should include the "seismological" concept of rupture model.

The underlying question is really the "unified conceptual model of fault rupture and fault area" as claimed by Raul.

In my opinion the main way to reach this is to concentrate our efforts on the knowledge of the rheological-thermodinamic status of the system.

More than the fault system (geological-physical) it could be better to speak of the stress and strain attractors, intended as a dynamic system, (not only the (geological) faults or its (rupture) parts but in general a distribution of rheological parameters) which evolve with a dynamic that is higly non linear (e.g. Bak and Tang and SOC and similar models).

I conclude for analogy that in this respect we should learn from the historical evolution of meteorological forecast. "Is a long way to walk so far" because the earth interior, is less accesible than the atmosphere (in observational strictly sense), and it has different spatial and time scales. At present, I have the feeling of being, as a meteorologist still in the era of the measurements with the pluviometer and barometer at earth surface!

Dear Colleagues, sorry for not having reacted until now, simply slipped my mind...

I am happy that  my original question was "finally" understood as I intended. Indeed, Rauls last sentence summarises the issue elegantly:

"Therefore, a fault could be understood as a set of rupture areas capable to trigger earthquakes in a time distribution as a power law (Aki, 1981, Bak and Tang, 1989). As a particular case, the fault area could be the fault rupture."

with, perhaps, the clarification of "...time-space distribution as powerlaw..."

And Roberto nailed the problem nicely: "In this sense the general "geological" concept of a fault should include the "seismological" concept of rupture model."

Indeed, the "rheological-thermodynamic" status ought be of fundamental importance, but, unfortunately, not aplicable for paleoseismic analyses. And for SHA, we inevitably bump into the problem of mixing paleoseismic "data" with modern data. Which place us at square one in the sense that magnitude estimates of paleoseismic events only have (net) slip and trace length, sometimes fault area, at its disposal. To obtain a magnitude therefore, the rupture area is assumed equal to the fault area. I think its  is reasonable to assume that the rupture area is smaller than the fault area in most cases, perhaps equal in some extreme cases, which lead us to estimates of magnitudes of paleoseismic events that should, generally, be essentially smaller than often reported. But how much smaller? 

If we would have statistics on, say, rupture area vs fault area (which is similar, but not equivalent, to slip versus trace length a la coppersmith, Leonard and others) we could perhaps use averages with uncertainty bonds as basis for magnitude estimations of paleoseismic events, raher than the "maximum possible magnitude compatible with its dimensions". Perhaps the ratio is different between intraplate and interplate earthquakes (probably it is, but how large is the difference)? Thrusts vs Strike-slip vs normal? Many intriguing questions.

Regardless. Should you bump into something that could enlighten us further in these matters, please post it here. And with this I wish to thank all of you who spent your valuable time on my thread.

Sincerely,

Raymond

Dear Raymond,

I am sorry I have found these Q&A some years late, even sorry as I think we do not have a good aswer yet (e.g. data collection focussed to address the questions you raise).

If the argument is still in your interests, here some "old" stuff, we (the Fault2SHA community) were running, and stil are running, around this topic, expecially after the Central Italy earthuquakes in 2016. Search also my presentation in the workshop materials online folder here https://fault2shablog.wordpress.com/2017/06/23/workshop-materials-online/

I will be happy to know if you moved some steps forwards in the meantime.

thanks and all the best

Dear Laura,

Thank you for your kind answer and attached material. The "family tree" is especially useful (and informative).

In a sense, I am glad that there are not any clear answers yet, as it justifies my original question somewhat. Lets hope "someone" nails it before I retire...

Sincerely,

Raymond

Seismology is a science derived from Geology and Mathematics concerning with Geodynamics. The term “rupture” may be inherited from Mathematics. Literally, “Rupture” means fractures with/without displacement (faults/joints). Generally, “rupture” resulted when something explode, break, or tear”.

Structural geologists, use the term “shear zone” for surface and sometimes for subsurface if it extends. Seismologists use the term “rupture area” for Earth’s interior during seismic events, and sometimes they use the term “fault zone” and occasionally” shear zones”. Structural geologists, use the term “shear zone” for surface and sometimes for subsurface if it extends. Shear zone is a deformed zone between undeformed zones; brittle (fracturing) and ductile (folding) shear zones. “Rupture area” is a brittle shear zone.

Integration of close sciences will produce specific unifying terms, which may take time. It is not important to standardize the term, but the most important is to define the term accurately. Seismologists accurately expressed the meaning of the term “rupture” as you mentioned in your question “Seismologists commonly express the fault size in terms of "rupture area". Literally “size’ is the relative extent of something; a thing's overall dimensions or magnitude, this mean the zone is the area. So fault size means fault area or fault zone.

Yes, there is an acceptable "rule of thumb" to relate these entities; rupture area, fault size, and deformation called shear zones. The term “shear zone” is preferable for all deformation zones, then it can be classified according to an accurate definition.