Equation of triangulation method to locate earthquake epicenter

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Seismic101
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Equation of triangulation method to locate earthquake epicenter

Post by Seismic101 »

Hello, I am doing some research about how to locate earthquake epicenter using triangulation (or trilateration?) method. I am trying to convert this concept into a Matlab code. My friends told me there is an equation that uses the P and S wave arrival times separation to calculate the radii of the circles that intersect at the epicenter location. Anyone knows the equation or the science behind so I can maybe derive myself?

in other words, how is the S-P separation converted into distances here? http://www.geo.mtu.edu/UPSeis/locating.html. I know how to use the chart. I want to know how those numbers were estimated.

Peace & Love everyone xoxo

GuyM
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Re: Equation of triangulation method to locate earthquake epicenter

Post by GuyM »

http://eqseis.geosc.psu.edu/~cammon/HTM ... erior.html
We can measure that difference from a seismogram and if we also know the speed that the waves travel, we could calculate the distance by equating the measured time difference and the expression. For the distance range 50 to 500 km, the S-waves travel about 3.45 km/s and the P-waves around 8 km/s. The value in parentheses is then equal to about (1/3.45 - 1/8) or about 1/8. Thus the simple rule of thumb for earthquakes in this distance range is the distance is about eight times the arrival time of S-wave less the arrival time of the P-wave.
The rule of thumb I knew was that p-waves are about three times faster than s-waves (hey, I'm a reflection seismologist!) but the above seems to be what you are after....

Seismic101
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Re: Equation of triangulation method to locate earthquake epicenter

Post by Seismic101 »

How do you think they obtain P and S velocity information in earthquake seismology? IS that done in a similar manner to what we do in reflection seismology?

GuyM
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Re: Equation of triangulation method to locate earthquake epicenter

Post by GuyM »

As far as I know its tomography and modelling from a combination of active and passive source seismology -so the same kind of thing.

The experiments my colleagues have worked on are things like this one :

Media version : http://www.radionz.co.nz/national/progr ... e-boundary
Nature paper : http://www.nature.com/nature/journal/v5 ... 14146.html

This combined 12 x 500kg land shots with two marine survey lines into onshore and offshore detectors spanning the North Island of New Zealand; the recorders run 24x7 during the project so they can also include any natural seismic events at the same time.

There's been a number of these : NIGHT (North Island GeopHysical Transect) in 2001, and SIGHT (South Island GeopHysical Transect) in 1996 for example; the latter managed to image the lithospheric loading under the Southern Alps, which was pretty cool.

Wide-angle refractions are modeled in the same way as near-surface statics - that is to say events are picked and then usually inverted using Colin Zelt's RayInver modelling code in order to build up structural models. (see http://www.otago.ac.nz/geology/research ... yinvr.html )
They use multi-component receivers so can measure P, S and P-S mode converted waves.

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