PHY198S

Physics at the Cutting Edge (2020-21) -- PHY198S

Week 7 preparation

Victor Tsai's recent work

These are listed in order of priority:

New Earthquake Math Predicts How Destructive They'll Be: the pinball model of a slipping fault line borrows from the mathematics of avalanches, Quanta Magazine (21 April 2020)
The Seismic Signature of Debris Flows: Flow Mechanics and Early Warning at Montecito, California, by Voon Hui Lai, Victor C. Tsai, Michael P. Lamb, Thomas P. Ulizio, and Alexander R. Beer (2018) [**]
Elastic Impact Consequences for High‐Frequency Earthquake Ground Motion, by Victor C. Tsai and Greg Hirth (2020) [**]

[**] Don't worry too much about the technical details, or derivations of any formulas in these articles; just try to get the general gist. See Terminology: below for explanations of some of the jargon.

Additional resources

General stuff about earthquakes:

FAQ on earthquakes, by Natural Resources Canada
Earthquakes, by GNS Science of New Zealand (a.k.a. the Shaky Isles)
Types of faults, by US Geological Survey

Terminology:

P-wave is short for pressure waves (or primary waves), and S-wave is short for shear (transverse) waves (or secondary waves). P-waves can happen in solids, liquids, and gases, but S-waves can only propagate in solids or in liquids with high viscosity. P-waves and S-waves generally propagate at different speeds, with P-waves being faster than S-waves in rock, so we feel them first in an earthquake. Animations: P-wave, S-wave. [Note: these terms have nothing to do with electronic s and p orbitals in atoms.]
Strain on a chunk of a continuous material (say, rock) refers to the derivative of the i-th component of its displacement in the j-th direction. Since this involves two directions in space (i and j) that can be the same or different, strain is referred to as a tensor, which is like a vector but with two arrows instead of one.
Stress refers to the force on a chunk of a continuous material, coming from internal forces from neighbouring chunks (and from external forces like gravity). Stress is also a tensor, because if you pick a plane in the material with a normal vector in the i-th direction emanating from the chunk of interest, the force can in principle point in any direction j.
Stress drop refers to the difference between the stress on rocks across a fault before and after an earthquake.
When you push/pull/twist something (e.g. a solid), it is useful to quantify how much it gets displaced in response to a given input. The modulus is basically the ratio of the stress to the strain, and it measures stiffness. Example: Young's modulus Y refers to how stiff something is when you pull it. Steel has a higher value of Y than wood: around 200 GPa versus around 10 GPa along the grain.
Poisson's ratio ν (Greek nu, pronounced new) refers to the how much a material bulges in a perpendicular direction if you squeeze it along some axis. Put more precisely, it is the ratio of the transverse strain to the axial strain. Rubber has a pretty high value of ν of almost 0.5; by contrast, cork has a ν of about zero, which is why it is preferred for wine bottle stoppers.
Seismic moment is a way of quantifying the size of an earthquake. The scalar seismic moment M is given by M=μAD, where μ is the shear modulus, A is the area of the fault, and D is the average amount of slip (how far the two sides of the fault got displaced).
Rayleigh waves are a kind of acoustic wave that travel along the surface of a solid, e.g. seismic waves created by earthquakes.
Seismic power spectral density refers to the spectral energy distribution per unit time, as a function of frequency.
Elastic collisions are ones in which there is no net loss of kinetic energy.
Stochastic means randomly determined. If something is a stochastic process, it has a random probability distribution or pattern that you can analyze statistically but you may not be able to predict outcomes precisely.