Introduction to Seismology
Exercise: Magnitude determination
Introduction
Goal of this exercise is making you familiar with the measurement of seismic amplitudes and
periods in seismograms and the determination of magnitude values for local and teleseismic
earthquakes.
The following general relationship is used for magnitude determination:
A 
M  log T    , h 
T 
AT is the maximum ground motion amplitude in μm (10-6 m) or nm (10-9 m), T is the period
associated with the cycle of the measured maximum amplitude in seconds. Figure 1 shows a
seismogram and explains how to determine the positive and negative part of the maximum
amplitude (A) as well as the period. To get the true ground motion in μm or nm the amplitude
has to be divided by the amplification factor, Mag(T), at the relevant frequency of the recording
seismometer:
AT 
A
Mag T 
The attenuation of the amplitudes along the travel path is compensated by the function
y R    log A0
 (, h)   log A0 is the calibration function of the magnitude, also referred to as Q(, h) or
P(, h) for teleseismic body waves. The epicentral distance, ∆, is given in degrees for
teleseismic events (> 1000 km), 1° corresponds to 111.19 km, and R in km for local
earthquakes (< 1000 km). The calibration information for this exercise can be found in the
datasheets of the New Manual of Observatory Practice 2 (NMSOP2), chapter DS 3.1.
According to Richter's (1935) original definition of the local magnitude ML only the maximum
amplitude A in mm, recorded with a standard Wood-Anderson seismograph (WA), is to be used:
M L  log AWA  log A0 R 
No period, T, is measured and the amplitude is not converted to true ground motion. If the
calibration function for the local magnitude is applied to the maximum amplitude, A, in mm,
recorded on a different seismograph than a Wood-Anderson seismograph with a differing
amplification Mag(T), the amplification has to be corrected for a frequency related difference:
M L  log ASM   log Mag WA  log Mag SM   log A0
Data
Use the figures and tables on the following pages to solve the tasks of this exercise.
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Fig. 1: Examples for measurements of trace amplitudes A and periods T in seismic records for magnitude
determination: a) the case of a short wavelet with symmetric and b) with asymmetric deflections, c) and d) the
case of a more complex P-wave group of longer duration (multiple rupture process) and e) the case of a dispersed
surface wave train. Note: c) and d) are P-wave sections of the same event but recorded with different
seismographs (classes A4 and C) while e) was recorded by a seismograph of class B3.
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Fig. 2: Vertical component records of a local seismic event in Poland at the stations CLL and MOX in Germany at
scale 1:1. The magnification values Mag(SM) as a function of period T for this short-period seismograph are given
in Table 1 below.
Tab. 1: Magnification values Mag(SM) as a function of period T in s for short-period seismograph used for the
records in Figure 2 together with the respective values Mag(WA) for the Wood-Anderson standard seismograph
for ML determinations.
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Fig. 3: Analogue record at scale 1:1 of a Kirnos-type seismograph from a surface-wave group of a teleseismic
event. Scale: 1 mm = 4 s; for displacement Mag = V see inserted table.
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Fig. 4: Display of the long-period (10 to 30 s) filtered section of a broadband 3-component record of the Uttarkasi
earthquake in India (19 Oct. 1991: h = 10 km) at station MOX in Germany. The record traces are, from top to
bottom: E, N, Z. Marked are the positions, from where the computer program has determined automatically the
ground displacement amplitudes A and related periods T for the onsets (from left to right) of P, PP and S. For S
the respective cycle is shown as a bald trace. The respective values of A and T for all these phases are saved
component-wise in the data-pick file. They are reproduced in the box on the right together with the computer
picked onset-time difference S - P and the epicentral distance ∆ as published for station MOX by the ISC.
Fig. 5: As for Figure 4, however short-period (0.5 to 3 Hz) filtered record section of the P-wave group only. Note
that the amplitudes are given here in nm (10-9 m).
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Task 1, 6 pts
Identify the Pn-, Pg- and Sg-wave arrivals in the seismograms in Figure 2 (Remember: that Pnamplitudes are smaller that Pg!) and determine the S-P time, τ. Use the following rule of thumb
to calculate the hypocentral distance, R, for both stations CLL and MOX:
 S
g
 Pg
 8  R
with τ in s and R in km. Note, that for shallow earthquakes the hypocentral distance and
epicentral distance, R and ∆, are practically the same.
Task 2, 2 pts
Determine the maximum amplitude A(SM) and the associated period, T, for both stations CLL
and MOX (Figure 2). Calculate the equivalent logarithmic amplitude by using the following
relation:
log AWA  log ASM   log Mag WA  log Mag SM 
Task 3, 2 pts
Use the following equation and your results from Task 2 to determine the magnitude of the
earthquake in Figure 2 for both stations:
M L  log AWA  log A0  
To calibrate -log A0 use:
 Table 1 in DS 3.1 - Richter (1985) for California
 Table 2 in DS 3.1, vertical component - Kim (1998) for Northeast America
 Table 2 in DS 3.1, vertical component - Alsaker et al. (1991) for Norway
Task 4, 3 pts
Discuss the differences in terms of:
 differences in regional attenuation in the three regions from which ML calibration
functions were used
 amplitude differences within a seismic network
Task 5, 3 pts
Measure the maximum amplitudes of the horizontal and vertical component of the ground
motion, A, in mm and the corresponding periods, T, in s in the seismograms in Figure 3. Use
the following equation to vector average the horizontal amplitudes:
AH 
A
N
2
 AE
2

Task 6, 2 pts
Use the Table enclosed in Figure 3 to find the period dependent amplification factor of the
seismometer and calculate the maximum horizontal and vertical amplitudes of the true ground
motion AH_T and AV_T in μm.
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Task 7, 3 pts
Determine the surface wave magnitude MS. Use these function for calibration:
 σ(∆) from Richter (1958) - Table 3 in DS 3.1, horizontal component
 σ(∆) for H and V following the Prague-Moskow-Sofia-Group - Table 4 in DS 3.1
 σ(∆) from the Prague-Moskow-Formula
 A
M S  log   1.66 log   3.3
 T  max
Differentiate between the magnitudes from horizontal and vertical records!
Task 8, 3 pts
In 1991 an earthquake occurred near Uttarkasi in India at depth of 10 km. Seismograms of this
event are shown in Figures 4 and 5. The International Seismological Centre (ISC) determined
an epicentral distance for station MOX of ∆ = 52.76°. Use the equation
   S  P  2 *10
with ∆ in degrees and τ in minutes, to estimate the epicentral distance yourself. Compare the
results.
Task 9, 3 pts
Calculate the body wave magnitude mb from the short period seismograms in Figure 5:
 Q(∆,h) from Figure 1a in DS 3.1 for the vertical component of P
 P(∆,h) from Figure 2 in DS 3.1
Discuss the differences between the both magnitudes.
References
Richter C.F. (1935) An instrumental earthquake magnitude scale.
Bull. Seism. Soc. Am., 25, 1-32
Richter C.F. (1958) Elementary seismology, W.H. Freeman and Company, San Francisco and
London, VIII + 768 pp.
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