# How do we measure earthquake strain energy?

I was asked a very interesting question on one of my recent LinkedIn posts that I thought deserved a slightly detailed answer. Here’s the question:

Hi David. Firstly, this is not a basic question at all. In fact, it’s one that is of considerable importance. Your question has two parts and I’ll address them individually.

How do we measure strain energy released in earthquakes?

The main way we do this is by measuring how much the ground moves in an earthquake, this can be done with high precision GPS instruments on the ground or from space based satellite measurements.

Here’s an example from the giant Tohoku earthquake, that struck Japan in 2011, of what we can do with GPS instruments. Each little arrow is a GPS station and it records how much the ground moved during the earthquake.

We can use these kind of measurements to calculate how much the ground has moved all along the fault and at depth during an earthquake. Once we have the full displacement of the fault we can relate that directly to the stress drop and strain release.

How do we measure strain energy being stored on faults?

A similar method is used to determine strain stored on a fault. The ground very slowly warps itself around a locked fault in the decades to centuries before an earthquake.

Here’s an animated model of what I mean (might need a screen refresh to play it). Imagine looking down onto the ground from above with the top half of the earth moving to the right and the bottom moving to the left.

If we can measure the degree of warping before the earthquake, again by using GPS and satellites, we can relate that to the strain energy getting stored on the fault. Here represented by the different colours, with red being the area of highest strain storage.

Ekbal

## 4 thoughts on “How do we measure earthquake strain energy?”

1. but you don’t address energy here, only strain. I remember having a discussion with James once about how moment magnitude relates to energy, and was struck that earthquake magnitudes do not scale as energy, or so I seem to remember, but as amplitude?

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2. Hi Simon, yes indeed. Actually, there are two types of ‘energy’ scales used for earthquakes. Apologies if this goes over a bit of the basics for the more general readers.

The traditional and commonly used scale is known as the moment magnitude (Mw).

The moment magnitude of an earthquake is intrinsic to the faulting geometry.
The seismic moment of the earthquake (i.e. energy) is calculated as:

Mo = μAS

where μ is the shear strength of the material (a constant), A is the rupture area on the fault and S the slip. A and S can be measured or inferred from the observation techniques I mention in the blog post.

We can convert this seismic moment into moment magnitude using:

Mw = 2/3 log(Mo) – 10.7

For example, a magnitude 7 earthquake, i.e. Mw = 7, has a moment of ~4xE19 Joules of energy.

The other scale, and the one I think you are referring to is the radiated energy from the earthquake, which is a measure of the potential for damage to man-made structures. This is an updated version of the old Richter Scale.

Theoretically, the radiated energy (E) is calculated by summing the energy flux over a broad suite of frequencies generated by an earthquake.

The radiated energy magnitude is then calculated as:

Me = 2/3 log(E) – 2.9

Although Mw and Me are both measurements of energy they describe different physical properites of the earthquake. Mw is related to the area of the rupture while Me describes the seismic potential for damage.

I hope that is a bit more clear?

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3. Thanks for the link Eric! Yes, indeed.

The original Richter scale definition of magnitude was related to the amplitude of ground motion at a single period. 20s for surface waves and 1s for body waves.

However these saturated at large earthquakes and resulted in the development of the new moment magnitude scale (which is defined at 0 period).

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