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Geodynamics

The Sassy Scientist

The Sassy Scientist – Earthquake Exoteries Nr. IV

Every week, The Sassy Scientist answers a question on geodynamics, related topics, academic life, the universe or anything in between with a healthy dose of sarcasm. Do you have a question for The Sassy Scientist? Submit your question here or leave a comment below.

In a comment on a post about the key papers in geodynamics, the Curmudgeonly Commenter asked:

Could you please point out some exceptionally important papers in geodynamics and tell us something interesting about the history of the field?

Dear CC,

After discussing the earthquake cycle last week, I think we can go into friction. Are you still following me? Is this series of blog posts in depth enough? There’s more to come, don’t worry.

Rate-and-state turmoil
During the 60’s and 70’s an additional new theory was fostered in the framework of rock mechanical experiments investigating friction, which still rocks the scientific community to this very day: rate- and state-dependent friction. I cannot get into too much detail about rate-and-state friction here for brevity and clarity — and I won’t — but I’ll leave some references at your disposal for further in-depth reconnaissance. Building on earlier work, Dieterich (1978, 1979) and Ruina (1983) describe that the shear stress on a fault plane is related to the normal stress on said fault plane — as in Byerlee — but additionally the sliding velocity on the fault and a critical slip distance (i.e., a measure of the fault interface smoothness) also come into the equation. The fault interface itself is oftentimes distributed as a fault gouge — i.e., a very fine-grained, usually unconsolidated material in a fault zone between the strong blocks. Faults without such gouge are oftentimes considered immature, and may behave fundamentally different (Marone and Scholz 1988). Putting the complexity of frictional fault slip in layman’s terms: the rate-and-state formalism states that the friction on a fault interface evolves through time, between static ‘locking’ and dynamic ‘sliding’ coefficients. This includes the possibility of healing or weakening of the fault interface (Marone 1998, Scholz 1998, Sleep 2005). Rate-and-state dependent friction provides an explanation for an abundance of observations, e.g., predicting stable, conditionally stable and unstable depth ranges of seismicity, the down-dip slip distribution and loading of a fault plane during the interseismic period, and aftershocks (e.g., Marone 1998, Scholz 1998). One — relatively recent — and exciting observation is that the rate-and-state friction formalism does not only hold for earthquakes generated at interfaces between rocks, but also along the bottom of ice masses (Winberry et al. 2013; Lipovsky and Dynham 2016). That’s just a chilling coincidence.

Just one tiny, eensy-teensy, itty-bitty, wee, slightly negative comment on rate-and-state friction; it’s a kinematic description of the observations, not a mechanical explanation of what’s actually happening at depth along a ‘fault interface’. If you can even call it that.

I think that’s more than enough for one week. Or rather, the Editor-in-Chief thinks that.

Yours truly,

The Sassy Scientist

PS: This post was written in some state at some rate.

```References:
Dieterich, J. H. (1978), Time-dependent friction and the mechanics of stick-slip. Pure and Applied Geophysics, 116, 790–805
Dieterich, J. H. (1979), Modeling of rock friction: 1. Experimental results and constitutive equations. Journal of Geophysical Research, 84, 2161–2168
Lipovsky, B. P. and Dunham, E. M. (2016), Tremor during ice-stream stick slip. The Cryosphere, 10, 385–399, doi:10.5194/tc-10-385-2016
Marone, C. J. (1998), Laboratory-derived friction laws and their application to seismic faulting. Annual Reviews of Earth and Planetary Science, 26, 643–696
Marone, C. J. and Scholz, C. H. (1988), The depth of seismic faulting and the upper transition from stable to unstable slip regimes. Geophysical Research Letters, 15, 621–624
Ruina, A. (1983), Slip instability and state variable friction laws. Journal of Geophysical Research, 88, 10359–10370
Scholz, C. H. (1998), Earthquakes and friction laws. Nature, 391, 37–42
Sleep, N. (2005), Physical basis of evolution laws for rate and state friction. Geochemistry, Geophysics, Geosystems, 6, 11, doi:10.1029/2005GC000991
Winberry J. P., S. Anandakrishnan, D. A. Wiens, and Alley, R. B. (2013), Nucleation and seismic tremor associated with the glacial earthquakes of Whillans Ice Stream, Antarctica. Geophysical Research Letters, 40, 312–315, doi:10.1002/grl.50130```

The Sassy Scientist – Earthquake Exoteries Nr. III

Every week, The Sassy Scientist answers a question on geodynamics, related topics, academic life, the universe or anything in between with a healthy dose of sarcasm. Do you have a question for The Sassy Scientist? Submit your question here or leave a comment below.

In a comment on a post about the key papers in geodynamics, the Curmudgeonly Commenter asked:

Could you please point out some exceptionally important papers in geodynamics and tell us something interesting about the history of the field?

Dear CC,

We can finally get into the interesting stuff. Let’s forget about the descriptions of earthquake kinematics last week and look at actual earthquake cycles now.

Beyond an elastic half-space… towards an earthquake cycle
Slip along fault planes is not restricted to earthquakes (i.e., co-seismic displacements) only; Smith and Wyss (1968) describe additional differential surface motion in the years following the 1966 Parkfield earthquake. So elastic half-spaces are all fun and games, but something else is happening. What about the underlying asthenosphere (Barrell 1914)? Doesn’t this — low-magnitude (Haskell 1935) — viscous material affect surface motions? Indeed. Nur and Mavko (1974) elaborated that the co-seismic phase is followed by a phase of transient, time-dependent deformation, dubbed the post-seismic phase. Thatcher and Rundle (1979) provide elaborate evidence for surface-breaking events that the earthquake cycle should include significant post-seismic surface motion, without the need for exotic fault or rock properties. What could these post-seismic processes be? Is it just viscous flow of rock layers at depth (e.g., Freed and Lin 2001), or do we need to look for other mechanisms, such as a combination of the presence of water inside rock pores at depth (Nur and Booker 1972; Peltzer et al. 1998), and a-seismic or micro-seismic slip on the same fault plane after a major event (Perfettini and Avouac 2004)?

Stick-slip and earthquake statistics
In terms of understanding earthquake nucleation rather than describing the after-the-fact surface deformations, Brace and Byerlee (1966) provided the next step to better explain the earthquake source: stick-slip. Stick-slip states that the differential motion on a fault plane between two blocks does not occur smoothly, but rather ‘jerky’, i.e., the roughness of the surface ensures that the two block stick together and when the fault ‘strength’ is overcome the fault fails and an earthquake occurs. Burridge and Knopoff (1967) subsequently provided a wonderfully simple analogue that simulates the statistics of earthquakes with both small-magnitude and major earthquakes, noting similar statistics as the empirical Gutenberg-Richter (1956) and Omori (1894) laws (Utsu 1961). Burridge and Knopoff (1967) conclude that a viscous component is necessary to produce aftershocks. Byerlee (1978) — yes, the guy from the law — relates the normal stress to the shear stress on the fault plane — quite an important inference, and a step beyond the Mohr-Coulomb failure law. In this, the smoothness of the surface and therefore the presence of asperities — i.e. friction — is paramount. Asperities — domains on fault interfaces that are locked (Lay et al. 1982) — and, especially, their spatial distribution control the seismogenic nature of a particular fault interface.

So, we’re actually getting somewhere. I think I’ve whetted your apatite, but you will have to wait another week before I start explaining how friction works.

Yours truly,

The Sassy Scientist

PS: This post was written after being stuck for a while, then released quickly through a sudden burst of energy, and then some transient editing of the text. I’ll put this on repeat for the forthcoming posts in this series.

```References:
Barrell, J. (1914), The strength of the crust, Part VI. Relations of isostatic movements to a sphere of weakness — the asthenosphere. Journal of Geology, 22, 655–683
Brace, W.F. and Byerlee, J.D. (19660, Stick slip as a mechanism for earthquakes. Science 153, 990–992
Burridge, R., and Knopoff, L. (1967), Model and theoretical seismicity. Bulletin of the Seismological Society of America, 57, 3411
Byerlee, J.D. (1978), Friction of rock. Pure and Applied Geophysics, 116, 615–626
Freed, A.M., and Lin, J. (2001), Delayed triggering of the 1999 Hector Mine earthquake by viscoelastic stress transfer. Nature, 411, 180–183
Gutenberg. B. and Richter, C.F. (1956), Magnitude and energy of earthquakes. Annals of Geophysics, 9, 1-15
Haskell, N. A. (1935), The motion of a fluid under a surface load, 1. Physics, 6, 265-269
Lay, T., Kanamori, H. and Ruff, L. (1982). The asperity model and the nature of large subduction zone earthquakes, Earthquake Prediction Research, 1, 3-71
Nur, A. and Booker, J.R. (1972), Aftershocks caused by pore fluid flow? Science 175, 885–887
Nur, A. and Mavko, G. (1974), Postseismic viscoelastic rebound. Science, 183(4121), 204–206. https://doi.org/10.1126/science.183.4121.204
Omori, F. (1894), On after-shocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7, 111-200
Peltzer, G., Rosen, P., Rogez, F. and Hudnut, K. (1998), Poro-elastic rebound along the Landers 1992 earthquake surface rupture. Journal of Geophysical Research, 103, 30131–30145
Perfettini, H. and Avouac, J.P. (2004), Stress transfer and strain rate variations during the seismic cycle. Journal of Geophysical Research, 109, B06402. https://doi.org/10.1029/2003JB002917
Smith, S.W. and Wyss, M. (1968), Displacement on the San Andreas fault initiated by the 1966 Parkfield earthquake. Bulletin of the Seismological Society of America, 58, 1955-1974
Thatcher, W. and Rundle, J.B. (1979), A model for the earthquake cycle in underthrust zones. Journal of Geophysical Research, 84(B10), 5540–5556. https://doi.org/10.1029/JB084iB10p05540
Utsu, T. A. (1961), Statistical study on the occurrence of aftershocks. Geophysical Magazine, 30, 521-605```

The Sassy Scientist – Earthquake Exoteries Nr. II

Every week, The Sassy Scientist answers a question on geodynamics, related topics, academic life, the universe or anything in between with a healthy dose of sarcasm. Do you have a question for The Sassy Scientist? Submit your question here or leave a comment below.

In a comment on a post about the key papers in geodynamics, the Curmudgeonly Commenter asked:

Could you please point out some exceptionally important papers in geodynamics and tell us something interesting about the history of the field?

Dear CC,

As explained in last week’s post, we will start from the very beginning: a time and place where everything was still considered elastic.

Elastic rebound theory
After millennia of attributing earthquakes to gods and mythical beasts (what a wondrous time that must’ve been), and a plethora of decades since the design of the first western seismographs, with a poor understanding of the source mechanism behind an earthquake, H.F. Reid (1910) proposed a theory on the occasion of the great 1906 San Francisco earthquake. The elastic rebound theory states that elastically stored energy is released suddenly during an earthquake on a pre-existing fault plane that resides in the solid crust. There is no need to generate a new fracture interface. Benioff (1949, 1954, 1964) — yes, the one comprising half of the name of the Wadati-Benioff zone — championed this theory and concluded that at least the shallow and intermediate-depth earthquakes could be attributed to this mechanism. Benioff considered deeper earthquakes (>300 km), posing less of a seismic hazard at the surface, to result from volumetric changes; no fracturing nor fault slip on a plane. A further refinement of the elastic rebound theory was necessary though in order to explain e.g., the low-magnitude stress changes that arise in the lithospheric medium as a result of earthquake ruptures.

Elastic dislocation theory
Whereas the nucleation of earthquakes was one line of inquiry, another was to use actual surface observations to infer fault slip at depth. There’s nothing better than guessing from afar what’s actually happening below the surface, right? Building on Volterra’s (1907) theory of distortions in elastic bodies — you know, by atomic off-sets in crystal structure — Steketee (1958) and Chinnery (1961) provided elementary steps forward in determining the surface deformation that result from motion on dislocations that reach the surface. Later, Savage and Burford (1970, 1973) and Okada (1985, 1992) elaborated and expanded elastic dislocation theory to include a complete set of analytical expressions of (surface) deformation due to slip on a (buried) fault (segment) in an elastic half-space. To this day still, these simple analytical expressions are widely used, both for fault slip inversions (e.g., Bagnardi and Hooper 2018), and elastic block models (e.g., Meade and Loveless 2009). In the elastic realm of the lithosphere, static stress changes are transferred and may trigger new earthquakes on other faults (King 1994; Stein 1999). This is already getting dangerously close to actual dynamics, instead of only finding descriptions of surface kinematics. What a waste …

Unfortunately, that’s all we have time for this week. Next week, I promise we will finally get into a bit more of the dynamics. Let’s discuss the earthquake cycle for instance.

Yours truly,

The Sassy Scientist

PS: This post was written with all things elastic in my mind. Is your mind as flexural as mine?

```References:
Bagnardi, M. and Hooper, A. (2018), Inversion of surface deformation data for rapid estimates of source parameters and uncertainties: A Bayesian approach. Geochemistry, Geophysics, Geosystems, 19, 2194–2211. https://doi.org/10.1029/2018GC007585
Benioff, V.H. (1949), Seismic evidence for the fault origin of oceanic deeps. Bulletin of the Geological Society of America, 60, 1837-56
Benioff, V.H. (1954), Orogenesis and deep crustal structure—additional evidence from seismology. Bulletin of the Geological Society of America, 65, 385-400
Benioff, V.H. (1964), Earthquake source mechanisms. Science, 143, 1399-1406
Chinnery, M.A. (1961), The deformation of ground around surface faults. Bulletin of the Seismological Society of America, 51, 355-372
King, G.C., Stein, R. and Lin, J. (1994). Static stress changes and the triggering of earthquakes. Bulletin of the Seismological Society of America, 84(3), 935–953
Meade, B.J. and Loveless, J.P. (2009), Block modeling with connected fault network geometries and a linear elastic coupling estimator in spherical coordinates. Bulletin of the Seismological Society of America, 99(6), 3124–3139
Okada, Y. (1985), Surface deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 75, 1135-1154
Okada, Y. (1992), Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 82(2), 1018–1040
Reid, H.F. (1910), The California Earthquake of April 18, 1906. Volume II. The Mechanics of the Earthquake. Washington DC: Carnegie Institution of Washington, Publication No. 87
Savage, J.C. and Burford, R.O. (1970), Accumulation of tectonic strain in California. Bulletin of the Seismological Society of America, 60, 1877–1896
Savage, J.C. and Burford, R.O. (1973), Geodetic determination of relative plate motion in central California. Journal of Geophysical Research, 78, 5, 832–845
Stein, R.S. (1999), The role of stress transfer in earthquake occurrence. Nature, 402, 605–609
Steketee, J.A. (1958), On Volterra's dislocation in a semi-infinite elastic medium. Canadian Journal of Physics, 36, 192-205
Volterra, V. (1907), Sur l'équilibre des corps élastiques multiplement connexes. Annales scientifiques de l'École Normale Supérieure, 24, 401-517```

The Sassy Scientist – Earthquake Exoteries Nr. I

Every week, The Sassy Scientist answers a question on geodynamics, related topics, academic life, the universe or anything in between with a healthy dose of sarcasm. Do you have a question for The Sassy Scientist? Submit your question here or leave a comment below.

In a comment on a post about the key papers in geodynamics, the Curmudgeonly Commenter asked:

Could you please point out some exceptionally important papers in geodynamics and tell us something interesting about the history of the field?

Dear CC,

I can call you CC, right? To satisfy your needs, I’ll take on a topic that is unquestionably home to the geodynamics territory, but people are not always aware of the history behind it. I’ve chosen one that resides in the (relatively) short-timescale corner of possible topics, with many other fields contributing fundamental observations and processes: the earthquake cycle. After all, I have already discussed mantle and lithosphere dynamics at length.

The major contributions to understanding earthquakes in the past originated through several lines of inquiry with seismology, rock mechanics and geodesy providing a variety of observations. The latest contributions arise from numerical modelling (and sure… some analogue modelling too) with e.g. dynamic rupture modelling and the embedding of the earthquake cycle in long-term, evolutionary geodynamic models. To accommodate your desire for some historical provenance on the topic, these posts will be somewhat more serious than you’re used to. Bear in mind I still can only cover some aspects. Apparently, some people have thought about this over the past century… I’ll insist that at least the basics in this little story should be common understanding for those involved in the field of geodynamics. With this I mean… everyone! If that’s not the case for you, you’ve got some reading to do.

Now, I had prepared a lengthy post to impress you with my knowledge on all things earthquakes, but my …lovely… Editor-in-Chief stepped in and straight-out forbid me to publish it as it is (well, was). The nerve! Apparently she thinks people wouldn’t read long blog posts. I guess you would like to prove her wrong, right? Unfortunately, my hands are tied. As a faithful, but desperately subjugated, Sassy Scientist, the answer to your question is now split up into multiple posts. With a heavy heart, you’ll get to experience my response to your question over multiple weeks. Isn’t that fantastic? I know I think it is…

So, next week, I’ll actually start going in depth and teach you all abound elastic rebound and dislocation theory. You’re welcome.

Yours truly,

The Sassy Scientist

PS: This post was written reluctantly, despite another, well-written, just a wee bit longer, literary magnificent response to your question, CC. Do you like Editor-in-Chiefs as much as I do?

PS2: As Leonardo Da Vinci once said: “Nothing strengthens authority so much as silence.” I’ll thus shut up about this in the forthcoming series of posts.

PS3: However; “The Sassy Scientist remembers”. And also; “A Sassy Scientist always pays his debts”.

PS4: …