Accelerometer-based seismometer?

[moonman239]

Here's what I want to do: take a few "snapshots" of the accelerometer data then find the median value of the said data. (That part I can do.) I will then calculate the magnitude of an assumed earthquake on the Richter scale. Then I will subtract any measurement error (ie, if the typical error in measurement is .5, and I calculate a magnitude of .7, I will just subtract .5 from .7, so according to my calculations the actual magnitude of a theoretical earthquake should be .2).

But, how do I calculate the magnitude of the earthquake?

 

[Faloren]

Here's what I want to do: take a few "snapshots" of the accelerometer data then find the median value of the said data. (That part I can do.) I will then calculate the magnitude of an assumed earthquake on the Richter scale. Then I will subtract any measurement error (ie, if the typical error in measurement is .5, and I calculate a magnitude of .7, I will just subtract .5 from .7, so according to my calculations the actual magnitude of a theoretical earthquake should be .2).

But, how do I calculate the magnitude of the earthquake?

It's not as simple as you think. The determination of the magnitude is dependent on a number of factors, not least the distance from the hypoentre. Generally the classification is worked out by comparing readings from a number of different locations and presumably by computers which triangulate the position of the earthquake; i say triangulate, it's not quite the same, but the principle is there.

Think about it, if you're at the centre of a small earthquake, it will feel to you the same as if you were on the outskirts of a large earthquake. Astronomers face similar difficulties when determining stellar parameters - is it a big star far away, or a small star close up? Indeed, the Richter scale was supposedly inspired by the absolute magnitudes astrophysicists refer to when discussing brightness.

So that's it really, you need to know where the quake is in order to define how big it is - the primary purpose of a proper seismograph is location finding, magnitudes are secondary. What you need to do is measure the P and S waves as they arrive (and also determine that they are indeed P and/or S waves) - with very precise timing. From that you can work out a circle of points where the earthquake could be.

Once you know where the quake happened, or at least how far away it happened, you can then work out the corrected magnitude. On paper-based seismographs that you can buy in stores, one works out the timing by hand and then compares the amplitude of the trace to a lookup table with distance-amplitude-magnitude readings. The original Richter scale is defined using the amplitude of the trace on a particular seismograph so all other instruments must be calibrated accordingly.

To do this electronically, you'll need a minimum of two amplitude readings, ideally as many as you can, including a zero reading which you can compare to known magnitudes. After you have a few such measurements, you can plot graph of them to interpolate your live results. Remember that the Richter scale is log-10 based, so when you work out your calibration equation, it will be logarithmic, not a linear or polynomial fit.

http://www.geo.mtu.edu/UPSeis/locating.html

If you want to simulate an earthquake, then you could cheat a little and hard code an earthquake distance so that all your amplitudes are corrected for that distance. You'll still need to calibrate the accelerometer, however, to know how your shaking correlates to actual earthquakes.

Also, with regards to errors, you shouldn't simply subtract. Measurement errors are generally quoted as ± so if you measured magnitude 0.7 with a measurement error of 0.2, your actual quake would be 0.7±0.2. If, with your example your error was 0.5, and that was an upper bound, you could say that your magnitude was somewhere between 0.2 and 1.3. What you should be aiming towards is a statistical statement like "I am 95% confident that this Earthquake was between 0.5 and 0.9". If, however, you had a systematic error of magnitude +0.5 then you could subtract it; this is the case, for instance, with CCD cameras that add a bias level to the number of photons they count. In this case, you're more likely to be removing background vibrations so it makes more sense to work out the maximum "no earthquake" magnitude and then ± that from your final calculation.

 

[moonman239]

Okay, new plan:

I shall use a network of accelerometer-equipped laptops and mobile devices (cellphones, PDA's, tablets, etc.), scattered around an earthquake fault, to determine the magnitude of the earthquake. Much like that network that the guys at Stanford University are running, only with the addition of mobile devices to the equation.

 

[Faloren]

You'll still need to calibrate each individual device for amplitude readings. Multiple devices will let you pinpoint the location of the quake, but you still won't be able to determine how large the quake was unless you've got some previous data to give your results some context.

 

[moonman239]

You'll still need to calibrate each individual device for amplitude readings. Multiple devices will let you pinpoint the location of the quake, but you still won't be able to determine how large the quake was unless you've got some previous data to give your results some context.

What exactly do you mean by "previous data"? Are you talking about local (city/state/zipcode) data?

I saw an app in the iPhone App Store that uses the built-in accelerometer to calculate the magnitude of an earthquake.

 

[Faloren]

What exactly do you mean by "previous data"? Are you talking about local (city/state/zipcode) data?

I saw an app in the iPhone App Store that uses the built-in accelerometer to calculate the magnitude of an earthquake.

I mean what I said earlier. Simply taking an acceleration reading tells you nothing about the actual magnitude of the quake itself. It tells you the size of the quake at your location. Combining location and amplitude will give you a 'weighted' measurement, but that's still useless without a calibration curve.

Without knowing what acceleration, at a certain distance, corresponds to what magnitude you will be unable to tell what the magnitude is. You can certainly conclude that your measured earthquake has a median amplitude of, say, 2000% of a non-earthquake reading, but you won't be able to turn it into a Richter measurement. To do that you'd need to take some data during earthquakes of known magnitude and then work out how acceleration, distance and magnitude are related for your device.

You could alternatively use a scale like the Shindo,

http://en.wikipedia.org/wiki/Japan_Meteorological_Agency_seismic_intensity_scale,

but note that it's not a linear relationship, although conditional statements in software would be fine for classification into the ranges given in the table. This would be the easiest to implement with your software, requiring you to simply measure the acceleration at each of your monitoring stations which then spit out a location, using their combined results, and a magnitude. The magnitudes will, therefore, vary for each node in your network.

I suspect the app you mentioned (iTemblor?) works out the magnitude for zero distance which conveniently knocks out the hard parts of the equation.

Have a read through http://earthquake.usgs.gov/learn/topics/measure.php, it explains things pretty well.

 

[davenn]

also any "Richter scale" type magnitude usually uses a velocity sensor ie. V/ms-1. An accelerometer is going to measure "G" force is as a % of g

Also as a side note when Richter developed his magnitude scale is was based on
1) a specific type of seismometer
2) for local/regional events out to ~ 150km
3) for ground type in the California region
4) and for low to moderate strength events <M6.0 (All of the older scales start failing at M6 and above and hence the advent of the Mw scale discussed below

It constantly makes me laugh and cringe as the constant misuse of the Richter scale by the media.

The standard scale used by the USGS/NEIC and other international acencies these days is the Mw (Moment Magnitude). The moment magnitude takes into account the area of the fault plane that ruptured and gives a better indication of the total amount of energy released in the event

others like the Mb = Body Wave; Ms = Surface Magnitude tend to top out (overload) with the large events and its difficult to "accurately" estimate the size of the event

cheers
Dave