MOMENT TENSOR ANALYSIS OF MIDDLE AND
LARGE EARTHQUAKES IN NICARAGUAPetronila Guadalupe Flores Ayerdis∗
MEE12606

Supervisor: Bunichiro SHIBAZAKI∗∗

ABSTRACTWe determined moment tensor solutions for middle and large-size earthquakes that occurred during
the period 1990-2013 in the subduction zone, Nicaraguan forearc and Nicaraguan depression, using
inversion analysis of teleseismic waveforms. In order to understand tectonic stress state from thesubduction zone to the inland crust in Nicaragua, we estimated stress drop for each earthquake using
obtained values of seismic moment and half duration of source time function. We found that the thrustfaulting is clearly predominant in subduction zone, generating shallow earthquakes with magnitudes
up to more than Mw 7, while in the Nicaraguan forearc the faulting type is mixed including thrust andstrike-slip faulting, generating intermediate earthquakes with magnitudes between Mw 5.3-6.9. On theother hand, in Nicaraguan depression the strike-slip faulting with left-lateral motion is predominant,generating shallow earthquakes with magnitudes between Mw 5.3-6.1. Then, we examined therelationship between seismic moment and half duration of source time function, and found that thestress drop for each earthquake is nearly constant between 0.1-10 MPa with no dependence on seismic
moment. Earthquakes with a depth of 50-100 km show higher stress drop than earthquakes with adepth of 0-50 km. Our results give information for understanding of tectonics in Nicaragua.
Keywords: Moment Tensor Inversion, Seismic Moment, Stress Drop, Nicaragua

1. INTRODUCTION
Occurrence of earthquakes is affected by the stress field in a region induced by movement of tectonic
plates and the subsequent deformation field. Nicaragua is located in the western border of the
Caribbean plate, between the Cocos, North American and South American plates, constituting a very
complex region, which is characterized by being exposed to extensional and compressional stresses.
Such stresses are caused by the interaction between the Caribbean and Cocos plates.
As a result of the plate motions, in Nicaragua the seismic activity is concentrated along the
subduction zone, Nicaraguan forearc sliver and Nicaraguan depression, considering the subduction
zone as the most seismic active area. However, the seismic activity generated along the Nicaraguan
depression has caused inland earthquakes highly devastating of up to Mw 6.3 as was experienced in1972.
In this study we investigate moment tensors for earthquakes located in the subduction zone,
Nicaraguan forearc sliver and Nicaraguan depression, to present new insights about stress field in
Nicaragua. We use a program set developed by Yagi and Nishimura (2011) to obtain moment tensor
solutions by inversion analysis of seismic waveforms for middle and large-size earthquakes that
occurred during the period 1990-2013. We also estimate the stress drop for middle and large-size
earthquakes. Obtained results will give essential information for understanding of tectonics in
Nicaragua.
∗Institute of Geology and Geophysics, National Autonomous University of Nicaragua(IGG-CIGEO/UNAN-Managua).
∗∗
International Institute of Seismology and Earthquake Engineering (IISEE), BRI, Japan.

12. DATAIn this study, we analyzed only teleseismic body waves (P-waves) from 41 events for a period from 1st
January 1990 to 30 June 2013 in the range of latitude between 10.65°N and 15.1°N and longitude
between -89°W and -82°W with moment magnitude (Mw) above 5.
We obtained waveform data through Wilber IIapplication from the Data Management Center of theIncorporated Research Institution for Seismology(IRIS-DMC) via the Internet. Figure 1 shows an example of
the GSN broadband station and US array backbone station
distributions from a viewpoint of good azimuthal coveragewith distance range from 30° to 90°.

3. THEORY AND METHODOLOGY
3.1. Moment Tensor Inversion
Recently, inversion techniques have been developed using
the broadband seismic waveform, from which the synthetic
seismograms are compared with observed seismograms
Figure 1. Location map of GSN
applying iterative techniques to determine earthquakes
broadband and US array backbone
parameters. We used the program set developed by Yagi andstations (IRIS-DMC Network).
Nishimura (2011) for estimating moment tensor solutions.
Hereafter we explain the method of inversion following the paper by Yagi and Nishimura(2011). In general, the observed seismic waveform of c component at a station j due to the seismic
moment release in a source volume V is given by6~~
u cj (t ) = ∑ ∫∫∫ Gcjq (t , ξ ) ∗ M q (t , ξ )dξ + ecj′ (t )

~

v

q =1

(1)

,

~

where G is the Green’s function of basis moment tensor (Kikuchi and Kanamori, 1991), M is aspatio-temporal moment density function, and e′ is an observed error. Since the volume change~

during earthquakes is too small to detect, we can neglect the volume change component M 6 . To
estimate stable moment tensor solutions, we should assume a simple source model such as the point
source model, in which we assume the seismic waveform to be radiated from one point. Following thepoint source model, we rewrite Eq. (1) as
5~~
u cj (t ) = ∑ Gcjq (t , ξ c ) ∗ M q (t ) + ecj (t )
q =1

with

,

(2)

~
M q (t ) = ∫∫∫ M q (t , ξ )dξ(3),
where ξ c is the location of the centroid, and e contains observed and modeling errors. We assumed
that the focal mechanism is kept constant during an earthquake, and approximated the shape of thesource time function to be an isosceles triangle with half duration of t r . Based on the assumption of
the constant focal mechanism and the simple source time function, we can rewrite Eq. (2) asv

5u cj (t ) = ∑ mq × Gcjq (t , t r , ξ c ) + ecj (t )
q =1

with

~
Gcjq (t , t r , ξ c ) = Gcjq (t , ξ c ) ∗ T (t , t r )

2

,

,

(4)

(5)

where T is a source time function with half duration of t r . In general, we apply low-pass filters to
observed data for mitigating the aliasing effect in re-sampling procedure, the effect of the complicatedseismic source process and the effect of the heterogeneity of the local velocity structure. Therefore,
relationship between the observed seismic waveform and data waveform is represented by(6)
d cj (t ) = B(t ) ∗ u cj (t ),where B is the function of the low-pass filter. Substituting Eq. (4) into (6), we then rewrite in thefollowing simple vector form:(7)d = A (t r , ξ c )m + e,
where d and e are N-dimensional data and error vectors, respectively; m is a 5-dimensional model
parameter vector; A is a N x 5 coefficient matrix. The solution of the above matrix equation is
obtained by the least square approach if we assume the duration of the source time function t r and thecentroid location ξ c . Also, we assumed that the horizontal location of the centroid can beapproximated to the epicenter, estimated optimal depth of the centroid and half duration using the
grid-search method, which minimizes normalized L2-norm as d − A(t r ξ 0 )m d .
3.2. Stress Drop
Stress drop is one of the most important parameters in the description of earthquake source properties.
This parameter is determined by the source size and seismic moment. In order to evaluate the stress
drop, we assume a circular crack model. Using the Brune’s formula that relates seismic moment Mo
and stress drop Δσ:

MO =

16
Δσa 3
,
7

(8)

where a is the radius of the fault, which is assumed to be expressed using rupture velocity Vr andsource duration t d :a = Vr t d(9),
Substituting Eq. (9) into (8), we obtain

MO =

16
3
Δσ (Vr t d )
,
7

(10)

Therefore, stress drop can be estimate as

Δσ =

7 MO
16 (Vr td )3 ,(11)

where Vr is assumed to be 2.5 km/s.

4. RESULTS
4.1. Moment Tensor Inversion
Using a program set developed by Yagi andNishimura (2011), we analyzed 41
earthquakes from 1990 to 2013 to obtain
moment tensor inversion of seismic
waveforms and find out the best depth andsource time with the minimum variance. We
determined moment tensor for 30 events,

Figure 2. Example of moment tensor solutions
obtained for the 1996 March 03 Mw 6.5. Upper left
and middle figures show the focal mechanism and thesource time function of the solution. Upper rightshows information of source parameters. Lower
figures show observed (black lines) and synthetic (redlines) waveforms.

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because the waveforms of the others events did not have good S/N ratio to obtain solutions. Figure 2
shows an example of a solution for the 1996 March 03 event with Mw 6.5.
We compare theobtained seismic moments andthose of GCMTs (Figure 3) and
we found that obtained seismic
momentsaregenerally
consistent with those of Global
CMT results. However, someseismic moments of our results
were different from those of
Global CMT; one of the reasonsis that we used body waves
although Global CMT isdetermined using long-period
waves.
We plotted the focal
Figure 3. Comparison of seismic moments (dyne-cm) between mechanisms obtained in thisobtained moment tensor solutions and Global CMT solutions study and we found that the
momenttensorsolutionsbased on type of earthquakes.
demonstratethedifferent
features of the tectonic setting in Nicaragua and suggest that a large number of earthquakes show
moment tensor solutions clearly dominated by thrust faulting, in some cases varying their mechanism
to oblique thrust and low-angle thrust faulting (Figure 4). This type of faulting produces shallow
earthquakes (0-50 km) and deep earthquakes(80-130 km) with moment magnitudes up to
more than 7 (purple circle in Figure 5), which
are generated due to subduction process
between the Cocos and Caribbean plates,
proving that the subduction zone is the mostseismic active area in Nicaragua.
According to historical records the
1992 Nicaragua tsunami earthquake is theevent with larger magnitude occurred in the
subduction zone, which corresponds with thelarger earthquake analyzed in this study(92/09/02 in Figure 5). The magnitude of the
1992 earthquake is Mw 7.2 in our solution
although that of Global CMT is Mw 7.6. Thismay be due to the method using body waves in
our analysis.
As is dominant in the subduction
zone, the seismic events generated show thrust
Figure 4. Focal mechanism solutions of moment
faulting with exception of some events fortensor inversion. Abbreviations: SZ-Subduction
example the 1996 March 27 and 2004 April 28
Zone; NF-Nicaraguan Forearc; ND-Nicaraguan
events that show normal faulting. These
Depression.
earthquakes are located very near to the Middle
America Trench (96/03/27 and 04/04/28 in Figure 4).
A moderate number of the earthquakes are located in the Nicaraguan forearc. These
earthquakes show moment tensor solutions that include interplate earthquakes with thrust faulting andintraplate earthquakes with strike-slip faulting (Figure 4). These types of faulting generateintermediate earthquakes (30-70 km) with moment magnitudes between 5.3 and 6.9 (green diamond in
Figure 5), which are generated as a consequence of the subduction of the Cocos plate beneath the4Caribbean plate; however it also includes the local faulting system along the Pacific coast ofNicaragua.
The largest historical earthquake in this zone occurred in 1956 and it had a magnitude ofMw 7.3. In this study the 2013 June 15 event is considered to be the largest earthquake with a moment
magnitudeofMw
6.4(13/06/15 in Figure 5).
Finally,afew
number of earthquakes show
momenttensorsolutionsrepresentedbystrike-slip
faulting,
withleft-lateralmotion mainly along theNicaraguan depression (Figure4). This type of faulting
generates shallow earthquakes(0-40 km) with moment
magnitudes between 5.3 and
6.1 (pink triangle in Figure 5).
In this area, highly
devastating
inland earthquakes
Figure 5. Relationship between moment magnitude and depth ofhave
occurred
historically,
obtained moment tensor solutions based on type of faulting.
with magnitude up to Mw 6.3
as was experienced in 1972. In this study, the 2005 August 03 event is considered to be the largest
shallow inland earthquake within the Nicaraguan depression (05/08/03 in Figure 5).

4.2. Stress Drop
From equation (10), we obtain the following equation:log M o = 3 log t d + log

16
3
ΔσVr
.
7

(12)

We examined the relationship between log M o and log t d as shown in Figure 6. Three blue lines
indicate cases with stress drop of
0.1, 1 and 10MPa and types offaulting are also indicated. We
found that log M o is in
proportion to log t d and stressdrops range from 0.1MPa to
10MPa, namely there is no
systematic dependence of stressdrop on seismic moment. As canbe seen in Figure 6, somestrike-slip earthquakes show highstress drops with ranges between
1MPa and 10MPa. These eventsareintermediate
depth
earthquakes. Thrust earthquakes
show a clear tendency thatlog M o is in proportion to

Figure 6. Relationship between seismic moment and half durationof obtained moment tensor solutions based on type of faulting
and stress drop.

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log t d .
We also examined the relationship between the seismic moment and half duration withdifferent depth ranges (Figure 7) and we found that stress drop of intermediate depth (50-100 km)
earthquakes are larger than those of shallow depth earthquakes (Figure 7).

5. CONCLUSIONSTo determine the behavior of
middleandlarge-size
earthquakes in Nicaragua, we
obtained
momenttensorsolutionsinandaroundNicaragua. We used the program
set developed by Yagi andNishimura(2011)
fordetermining moment tensor
solutionsusing
teleseismic
waveforms.
We
obtainedsolutions of 30 events from 1990
Figure 7. Relationship between seismic moment and half duration to 2013. We compared the resultsof obtained moment tensor solutions based on classification ofwith the solutions from Global
depth and stress drop.
CMT. Some differences are seen
in centroid depth and seismic moments between our results and Global CMT solutions, which may be
due to the difference in method for determining moment tensors.
Regarding moment tensor solutions obtained in this study, the thrust faulting is clearly
predominant, generating shallow earthquakes with moment magnitude up to more than 7 in the
subduction zone, while in the Nicaraguan forearc the faulting are mixed including thrust and strike-slip
faulting that generate intermediate earthquakes with moment magnitudes between 5.3 and 6.9. On theother hand, in Nicaraguan depression the strike-slip faulting with left-lateral motion is predominant,generating shallow earthquakes with moment magnitudes between 5.3 and 6.1.
Using Brune’s formula we estimated stress drop for each earthquake, which is nearly
constant between ranges from 0.1MPa to 10MPa. From these results we found no dependence of stressdrop on seismic moment but an increase of stress drop with depth.
It is necessary to work more with this methodology to obtain a better understanding of thetectonic setting and tectonic stress field for subduction earthquakes and inland earthquakes around
Nicaragua.

ACKNOWLEDGEMENTS
I am extremely thankful to Professor Yuji YAGI (Tsukuba University) who kindly provided me theprogram and technical guidance for moment tensor analysis.

REFERENCES
Kikuchi, M., and Kanamori, H., 1991, Bull. Seism. Soc. Am., Vol. 81, No.6, pp. 2335-2350.
Madariaga, R., 1979, Journal of Geophysical Research, Vol. 84, No. B5, pp. 2243-2250.
Ruff, L.J., 1999, Pure and Applied Geophysics, v. 154, pp. 409-431.
Yagi, Y., and Nishimura, N., 2011, Bull. of Inter. Inst. of Seism. and Earthq. Eng., 45, pp. 133-138.

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