## Dalles, Oregon, M 3.6 Earthquake of September 24, 2007

#### Two-Station Location with AS-1 Data

This small earthquake was well recorded by AS-1 stations located in Corvallis and Portland, OR.  This IRIS site:  http://www.iris.edu/quakes/make_event_search_map.pl?USER_DEF=Y makes it easy to locate an event using the S-P interval method.  I've assumed that the distance to a station is approximated by multiplying the time between the P and S phase arrivals by 8 km/s.  This is a rough rule of thumb for nearby earthquakes.

 UPOR (sac file) University of Portland, Portland, Oregon 45.34N 122.43WS minus P time = 7.6 seconds CHOR (sac file) College Hill, Corvallis, Oregon. 44.57N 123.29WS minus P time = 8.2 seconds

 Station (S-P) Seconds Distance, km, ~ (S-P)*8 Distances, corrected for 22.2 km depth UPOR 7.6 60.8 61.6 CHOR 8.2 65.6 56.6

Circles uncorrected for earthquake depth.  The star is located at the catalog epicenter.

The circles above can be corrected for the depth provided by the catalog location, 22.2 km.  Consider the diagram below.  We estimate that the earthquake is located at a distance R from a station.  This defines a hemisphere centered on the station.  If the depth is Z, then the radius, R', of the circle on which the event is located is related to Z and R by:

R**2 = Z**2 + R'**2  Solving for R'

R' = sqrt(R**2 - Z**2)

Circles corrected for earthquake depth of 22.2 km.  The triangle marked EQ is located at the catalog epicenter.

For this case, knowing the depth provides enough added constraint to get a rough location with just two stations.