Category Archives: Seismic Source Theory

Calaveras fault mystery!

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As science is defined by philosphers as the procces of discovering patterns, however, sometimes those patterns break down revealing new exception! In fact, with time those exceptions form a new pattern.

In lithospheric dynamics, is well known that earthquakes occure in the brittle part of the crust, while creep occurs in ductile part of crust. That is not the case in Hollister in California where creep can be found on the surface!! However, geoscientists have different explinations for such phenomena. Check the following link which is a report  made by USGS summerized most of the geophysical findings in Calaveas fault creep in Hollister.

http://search.proquest.com.ezaccess.libraries.psu.edu/docview/1641132558?pq-origsite=summon

Aftershock triggering model using revised rate and state friction law

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The rate- and state- dependent friction laws (RSF) are empirical relations based on laboratory experiments that have been used to model a variety of earthquake behaviors, including the mechanics of a seismic cycle, episodic aseismic slip, and triggered seismicity (Kame et. al, 2013). These laws describe variations in friction based on the loading rate and state of the sheared zone. There are several forms of the RSF laws. The paper summarized below is based on the RSF law proposed by Dieterich (1979) and a more recently revised version proposed by Nagata et al. (2012).

In 1994, Dieterich modeled aftershock seismicity after an imposed stress step using his RSF model. His model can predict the observed 1/t decay of aftershock rate but there are two major observational gaps: (1) The model under predicts the amount of aftershock productivity and (2) The model predicts too long a delay time before the onset of decay. In a recent paper, Kame et al. (2013) hoped to address these gaps by running similar models using the Nagata RSF law.

Dieterich’s model considered a fault of fixed size embedded in an elastic medium. He was able to solve for the aftershock rate analytically. Kame et al. (2013) applied the Nagata law, which contains a stress weakening effect, to a similar model but found that the problem required a numerical solution.

Main observations from Kame et al. (2013) study:

1) Although the revised model produced greater seismicity and shortened delayed times, these improvements were only by a small factor compared to the disparities with natural observations that span several orders of magnitude.

2) Unlike the Dieterich model , in which a stress step always advances the timing of an earthquake, the revised model showed two different types of behavior. In most cases, the timing of the earthquake was advanced. However, if the stress step occurred at a specific time in the loading history of the fault , oscillatory slow slip cycles began, effectively delaying  the onset of the earthquake.

For more details on this study see:

Kame, Nobuki, et al. “Effects of a revised rate-and state-dependent friction law on aftershock triggering model.” Tectonophysics 600 (2013): 187-195.
http://www.sciencedirect.com/science/article/pii/S004019511200755X

Other sources:

K. Nagata, M. Nakatani, and S. Yoshida. A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data, 2012.
http://onlinelibrary.wiley.com/doi/10.1029/2011JB008818/abstract

J.H. Dieterich. A constitutive law for rate of earthquake production and its application to earthquake clustering, 1994. http://onlinelibrary.wiley.com/doi/10.1029/93JB02581/abstract

J.H. Dieterich. Modeling of rock friction 1. Experimental results and constitutive equations, 1979.
http://onlinelibrary.wiley.com/doi/10.1029/JB084iB05p02161/abstract

What’s all this talk about earthquakes? Part I

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The detection and source characteristic of glacial earthquakes or “icequakes”.

Cryoseismic events are distinct from the earthquakes we have been characterizing and modeling so far in class. This wasn’t recognized until the latter part of the last century when a number of earthquakes were giving unusual results due to their atypical amplitude spectra.

What was obvious in these events, however, was their lack on high-frequency energy. As earthquakes scale in magnitude, typically the larger events lack in high-frequency signal; these smaller events, though, were breaking the rules. The answer to the puzzle was actually quite simple. The reason larger events lack the high-frequency energy is due to their long duration. Small events with short durations are very efficient at releasing short-period energy. Think about the Fourier Transform of an impulse function as an extreme. While these events (4.6 < M < 5.0) weren’t scaling up in magnitude, they were in duration.

As it turns out, a typical duration of an icequake is between 30 and 60 seconds – much longer than even many large earthquakes, which is great at quelling the high-frequency signal and the reason these events weren’t caught on traditional monitoring equipment using previous methods.

Later, attempts were made by Ekström et al. to invert the seismograms using the global-moment-tensor method to characterize the slip event. As expected, they ran into hurdles and the inversions were unstable. Their solution was to parameterize their inversion in terms of a centroid single force (CSF). A centroid single force model is a distribution of single forces equal but opposite of the slip direction. This is related to the event energy source being gravitational potential energy as opposed to elastic strain energy. Centroid single forces are also used in the characterization of landslides. CSF analysis can provide the product of mass and sliding distance, but neither independently.

Can anyone give a better description of a CSF?

Reference:   Ekström, Göran, Meredith Nettles, and Geoffrey A. Abers. “Glacial earthquakes.” Science 302.5645 (2003): 622-624.

Splay faulting during the 2010, Mw 8.8 Maule, Chile Earthquake

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The authors describe their use of off-shore observations to demonstrate the existence of splay faulting in the shallow regions of the Chilean Subduction Zone involved in the Mw 8.8, 2010 Maule, Chile earthquake. A splay fault is a relatively steep fault that connects the plate boundary interface with the seafloor that when activated during a large earthquake, can enhance tsunami excitation. Based on previous work noted in the paper, the most likely location of splay faults is along the boundary between outer and inner wedges, which is where the authors, Liessr and others, observed the seismic activity in the Chile study.

Specifically, the authors deployed a 30-station ocean-bottom seismometer network for three months and analyzed the offshore data in concert with observations from another 33 land-based seismic stations. They used a a 2.5 dimensional velocity model derived from seismic reflections profiles and previous local earthquake studies to locate the aftershocks.

Good data coverage provides a road to good results, which in this case includes several interesting outcomes. The aftershock locations illuminate a 50 km long linear structure extending from the plate boundary interface to the seafloor that coincides with a splay fault outcrop (on top of the wedge). The P-wave speed distribution (estimated from active-source and tomographic results) suggests that the splay fault begun to branch off with an angle of 7⁰-8⁰ from the plate boundary interface at ~20 km depth and ~67 km away from the deformation front. Finally, it’s important to mention that the southern part of the study area it does not appear that the main shock experienced any activity associated with a splay fault.

Please see the papers for details:  http://geology.gsapubs.org/content/41/12/e309.full

Thamer

Moment-Tensor Decomposition

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While the moment tensor makes relating seismograms to seismic sources more convenient, it adds a non-unique interpretational step once you have the Mij values. You have to decompose the moment tensor into double-couples, CLVD sources, isotropic sources, etc.  Here is a link to a script I wrote for Matlab to do the decomposition.

mtensor_decomp.m