Estimating the Magnitude of the El Salvador 2001 Earthquake

During the El Salvador 2001 earthquake, the AS_1 seismograph was located in the Geophysical Lab, on the second floor of the School of Earth and Atmospheric Sciences, Georgia Tech.

The figure below shows the full record of that earthquake.

How to measure the magnitude?

General information how to measure the magnitude can be found on http://www.eas.purdue.edu/~braile/edumod/as1mag/as1mag.htm

For the record shown above the magnitude has been defined using the P-wave arrivals and the surface wave amplitudes.

Ř Using the P-wave arrivals to determine the body wave magnitude.

v Zoom in on the P-wave (extract the early part of the seismogram). The result is shown on the figure below

Determine the maximum amplitude for the highest frequency. Here this is the ninth cycle amplitude (you can find it on the figure, it is bordered by a dashed green rectangular). The measured values:

T_{p}=2.1s (the measured
period of the ninth cycle, from zero to zero)

A^{max}_{p}=779counts
(the maximum amplitude for that frequency cycle in counts, from zero to pick)

Gain=85counts/mm (the gain or also displacement amplification determined from the AS_1 Particle Displacement Response, see fig.2 at http://quake.eas.gatech.edu/MagWeb/CalReptAS-1.htm)

A_{p }= A^{max}_{p}/
Gain = 9.2mm
(the amplitude of the displacement in mm)

D=22.02deg. (the epicentral distance….)

Formula used:

M_{b}L_{g}2=log(A_{p}/T_{p})
+ 1.66*log(D) + 3.3

It works for 5deg<D<30deg and T~1s

The result: M_{b}L_{g}2=6.2

Ř Using
the surface waves to determine the surface wave magnitude (M_{s})

v Zoom in on the surface-wave packets (it can be distinguished by its lower frequency, about 20s). The result is shown of the figure below.

v Determine the maximum amplitude for the T=20s cycle (you can find it on the figure, it is bordered by a dashed rectangle). The measured values:

T_{s}=20s (it is not at the
very beginning of the packet)

A^{max}_{s}=700counts
(the maximum amplitude for that cycle in counts, from zero to peak)

Gain=0.6counts/mm (the gain or also displacement amplification determined from the AS_1 Particle Displacement Response, see fig.2 at http://quake.eas.gatech.edu/calib/CalReptAS-1.htm)

A_{s }= A^{max}_{s}/
Gain = 1167mm
(the amplitude of the displacement in mm)

D=22.02deg. (the epicentral distance….)

Formula used:

M_{s}=log(A_{s}/T_{s})
+1.66*log(D) + 3.3

It works for 20deg<D<160deg and T~20s

The result: M_{s}=7.3