International Journal of Geosciences, 2012, 3, 222-225
http://dx.doi.org/10.4236/ijg.2012.31025 Published Online February 2012 (http://www.SciRP.org/journal/ijg)
Local Magnitude Study of the Seismic Activity on
Ítalo Lopes de Oliveira, George Sand França, Cristiano Naibert Chimpliganond
Seismological Observatory, University of Brasília, Brasília, Brazil
Received November 5, 2011; revised December 14, 2011; accepted January 6, 2012
The importance of studying the local magnitude related to seismic activity occurred recently in the region of Ita-
carambi, state of Minas Gerais, is due to the fact that these were earthquakes of intraplate origin. From the study of
 and the relation between local magnitude and seismic signal duration, was performed a data analysis obtained in
the same region, on the period between October/2007 and June/2008, in which we can estimate the equation
MD = 2.153(±0.072) LogD – 1.925(±0.132) to calculate the magnitude of local duration. We can also estimate one value
for the b parameter using the equation LogN = a – bMD from a frequency-magnitude study. It was found the value of b
= 0.826(±0.020) for the general activity of Itacarambi, MG, that is within the universal range proposed by .
Keywords: Intraplate Earthquakes; Local Magnitude; Duration of Seismic Signal; Parameter b
The city of Itacarambi-MG, especially the district of Car-
aíbas, has been affected by a continuous occurrence of
earthquakes in recent years, some of considerable pro-
portions even in the case of intra-plate events. In this
study we hope to determine a formula to calculate the
local magnitude of the region, but what comes to be
magnitude and what its significance?
The magnitude is correlated with the amount of energy
released by the earthquake in the source, and calculating
it gives us an absolute value which helps in comparing
the relative size of earthquakes, in other words, give us a
better estimate of how destructive may be an earthquake.
Reference  proposed an equation to calculate local
magnitude of events occurred up to 100 km of distance
from the recorder. Based on a logarithmic scale and
seismic signals amplitude, according to Richter local
magnitude is given by:
ogA LogAM =L (1)
A represents the maximum amplitude of the signal in
μm and A0 a pre-established value. The  study, al-
though known and used worldwide, was carried out with
earthquakes from the west coast of North America,
however it is common ground that both the area and re-
corder are completely different as it portrays the formula
described by Richter for our region. Thus we sought to
obtain a similar equation obtained by Richter, but using
the local parameters and registers today.
The Itacarambi-MG region is located at the north of
Minas Gerais state, near São Francisco river, about 660
km from the metropolis, Belo Horizonte (Figure 1). In
October 2007 was installed a network with 10 seismo-
meters of short period in the region (Figure 2), to moni-
tor recent earthquakes occurred in this region . This
work will be done with data collected through this network.
Initially, studies will be conducted in the region to de-
termine the magnitude of events occurred between Oc-
tober/2007 and June/2008 from the Equation (1). And in
a second stage of the study, a relationship between local
magnitude and duration of the signal will be estimated, in
order to improve the calculation of small tremors.
Figure 1. Location of Itacarambi, MG region. Square rep-
resents cities and districts, star represents the key event
occurred in the region, of magnitude equal to 4.9 mb.
opyright © 2012 SciRes. IJG
Í. L. DE OLIVEIRA ET AL. 223
Figure 2. Arrangement of local seismographic stations. The
rectangles represent the stations by which it was not possi-
ble to measure the duration of a given seismic signal.
We have many examples of local and regional magnitude
in intra-plate areas [4-7].
The analyzed seismic data were collected in digital
form by the Seismological Observatory at the University
of Brasília. The SAC software was used for the reading
and processing of these digital seismic records .
A total of 451 seismic events were analyzed with the
objective of obtaining the values related to the seismic
signal duration and maximum length of the P-wave in the
vertical component record’s. The duration of the sig-
nal-D was obtained directly out of the original record. An
arbitrary time of ten seconds was chosen, beginning from
P-wave’s first arrival (Figure 3). Three out of the 10
available stations were unable to get the data about the
duration (Figure 2). Either a malfunctioning of the sta-
tion instruments or the noise signal might have been the
cause. In order to get the maximum amplitude, caused by
a gain in the efficiency of the instrument’s response, it
was necessary canceling the effects to get a response
equal to Wood-Anderson Seismometer (a seismometer
used by Richter to obtain the Equation (1)). Only then
was it possible to calculate ML. Such effects were can-
celled primarily through a Transference Function, which
converts data from the velocity × time’s original instru-
ment into Wood-Anderson instrument data, in which we
have some data presented in terms of displacement ×
After the data’s conversion and obtaining seismic sig-
nal’s maximum amplitude on the arrival of the first
P-wave, we used the Equation (1) to calculate the local
Figure 3. Seismic event recorded by the Jan09 station, 0802
08_1529_jan09. T0 represents the beginning of a seismic
signal (P-wave) and T5 represents obtained signal’s dura-
magnitudes. 140 events, of seven different stations, were
selected out of a 451 seismic occurrences. In the end,
three magnitude ML > 3 were discarded so a more accu-
rate formula could be obtained for the calculation of the
local magnitude, such calculation based on the maximum
amplitude of the P-wave and on the seismic signal as
well, since these signals are usually pretty much satu-
rated due to the stations’ being too close to one another.
Furthermore, the station close to center of the array
wasn’t used in calculations and considering that the epi-
central distance is on the order of 5 km, thus we don’t
why to incorporate distance dependence in our duration
magnitude formula and derive duration magnitude using
the following equation:
On acquiring data for the maximum amplitude and the
duration of the seismic signal, we performed an analysis
to each station correspondent data. These generated ML ×
LogD graphs for all stations used, as shown in Figures 4
and 5 for stations Jan03 and Jan06 respectively.
Making some calculations to get all the linear regres-
sion equations averages, we were able to determine a
general equation which allows us to make an estimate of
the region’s local magnitude and any possible errors as-
sociated to it:
M2.1530.072 LogD1.9250.132 (3)
From the Equation (3), we calculated the magnitude
for all 137 events selected and by performing an analysis
with the aid of the graphics, the linear regression equa-
tions for each station, along with the errors related to
them (the stations), we noticed that the stations present
some variation in the record of both the maximum
Copyright © 2012 SciRes. IJG
Í. L. DE OLIVEIRA ET AL.
Figure 4. Graph ML × LogD at station Jan03.
Figure 5. Graph ML × LogD at station Jan06.
amplitude and the duration of the signal for a same-nat-
ured event. An magnitude analysis makes this fact pretty
obvious, this discrepancy in the records also produces
some variation in the magnitude of an event recorded by
several stations. Some examples in the Table 1 below
represent such variations, and allow us to sort out the
stations used for our study into three groups which share
similar behaviors: Jan03 and Jan05; Jan02 and Jan07;
Jan06 and Jan09.
These different behaviors could be explained by some
factors such as the distance between the group of stations
and the event’s epicenter. This situation applies very well
for the contrast among the first group and the others.
Moreover, another factor that may justify that difference
of behavior, mainly between the last two groups, is the
geological setting. Stations Jan02 and Jan07 are localized
nearby a carbonate geology river while stations Jan06
and Jan09 are in a more complex geology region. Never-
theless, the station Jan01 doesn’t fit into either groups.
Table 1. Comparison of the magnitudes obtained from dif-
With the analysis of each station result, we arrived at a
ferent stations for the same seismic event.
Date_Hour_StationAmp. P (m)ML Dur.
041107_1529_jan011.64E–051.216 50.746 1.7051.747
041107_1529_jan031.02E–051.007 25.966 1.4141.120
041107_1529_jan051.14E–051.059 33.837 1.5291.368
041107_1529_jan065.32E–051.726 61.203 1.7871.922
080208_1529_jan021.38E–051.139 30.993 1.4911.286
080208_1529_jan064.37E–051.640 51.077 1.7081.753
080208_1529_jan074.66E–051.668 25.758 1.4111.113
080208_1529_jan091.22E–042.088 48.924 1.6901.713
Amp. P: P-wave amplituhte m; Dr
eneral equation that enables us to make some estimate
de; ML: Ricr’s localagnitudeur.: Duation of
seismic signal; LogD: Logarithm of duration; MD: Magnitude of local dura-
as to the local magnitude, based on the duration of each
seismic signal for the earthquakes in the Itaracambi-MG
M2.1530.072 LogD1.9250.132 (3)
D is the signal’s duration in seconds. It’s worth
, we can draw a
ning that all the seismometers and registers used were
of the DM24 type (GURALP brand).
Having as a reference the works of
mparison between the Richter’s ML magnitude and the
MD magnitude obtained by Equation (3). In Figure 6
these magnitude’s data have been plotted and indicate
that the adjustments made are sufficiently reliable, the
standard deviation from MD to ML for the seismic activi-
ties of our choice being equal to:
From the magnitudes estimated by the Equation (3)
can estimate, on the basis of a frequency-
d from the date on which the events took place, we can
come up with a magnitude × time histogram which can
be used to make an estimate of the region’s seismic oc-
agnitude study, a value for the parameter b using the
Equation (5) according to , establishing a correlation
between the number of earthquakes (N) and the duration
of their magnitude (Figure 7). The result obtained for the
parameter b ended up being within the universal range
As next steps of this study, we will estimate the mag-
nitude through the frequency domain .
Copyright © 2012 SciRes. IJG
Í. L. DE OLIVEIRA ET AL.
Copyright © 2012 SciRes. IJG
Figure 6. Correlation between the ML magnitude and the
Figure 7. Logarithm of the number of events (N) × magni-
ish to thank Ibama (Parque
G.S.F. wishes to thank CNPq-3003529/2010-5.
gical Society of America,
tude (M). Dashed line re presents the Equation (3), b = 0.826
The authors of this study w
das Cavernas Peruaçu), Mr. Evandro and the city-hall of
Itacarambi-MG for their support in the course of the field
work, Ruan R. Alves and Cesar G. Pavão for several
suggestions that improvement the manuscript. I.L.O.
wishes to thank CNPq for the funding via PIBIC
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