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Earthquake frequency-magnitude distribution and fractal dimension in mainland Southeast Asia


The 2004 Sumatra and 2011 Tohoku earthquakes highlighted the need for a more accurate understanding of earthquake characteristics in both regions. In this study, both the a and b values of the frequency-magnitude distribution (FMD) and the fractal dimension (D C ) were investigated simultaneously from 13 seismic source zones recognized in mainland Southeast Asia (MLSEA). By using the completeness earthquake dataset, the calculated values of b and D C were found to imply variations in seismotectonic stress. The relationships of D C -b and D C -(a/b) were investigated to categorize the level of earthquake hazards of individual seismic source zones, where the calibration curves illustrate a negative correlation between the D C and b values (D c  = 2.80 - 1.22b) and a positive correlation between the D C and a/b ratios (D c  = 0.27(a/b) - 0.01) with similar regression coefficients (R2 = 0.65 to 0.68) for both regressions. According to the obtained relationships, the Hsenwi-Nanting and Red River fault zones revealed low-stress accumulations. Conversely, the Sumatra-Andaman interplate and intraslab, the Andaman Basin, and the Sumatra fault zone were defined as high-tectonic stress regions that may pose risks of generating large earthquakes in the future.


Various statistical techniques assessing the seismicity, frequency-magnitude distribution (FMD; Gutenberg and Richter 1944), and fractal dimension (D C ) (Wyss et al. 2004) are regarded as effective approaches used to understand the local seismotectonic activities. Both the b value of the FMD and the D C value are significantly related to, and therefore directly controlled by, the seismicity and tectonic stress levels in that region (Scholz 1968; Öncel et al. 1996). During the past few decades, the relationship between the b and D C values has been successfully calibrated (Hirata 1989; Öncel and Wilson 2002; Wyss et al. 2004), and the D C /b ratio has been used as an indicator of earthquake hazards (Bayrak and Bayrak 2012).

After the devastation caused by the M w -9.0 earthquake on December 26, 2004, the mainland Southeast Asia (MLSEA; Figure 1) has been recognized as one of the most seismically active regions in the world. Both interplate and a number of intraplate regimes are defined as hazardous earthquake sources. More than 45 major earthquake events (M w  ≥ 7.0) have been reported during 1962 to 2013 within the MLSEA. Accordingly, evaluation of the FMD a, b, and D C values of all earthquake sources recognized in the MLSEA is important and is therefore the primary focus of this study. The results of this study may be useful for seismic hazard assessments for countries in the Association of Southeast Asian Nations (ASEAN).

Figure 1
figure 1

Map of mainland Southeast Asia (MLSEA) and the 13 designated seismic zones (A to M). The map shows epicentral distributions of completeness earthquakes with m b  ≥ 4.0 reported during the period 1974 to 2010 (green circles), earthquakes with m b  ≥ 7.0 (blue circles), and significant earthquakes mentioned in the text (red circles). Red lines depict the fault lines compiled by Pailoplee et al. (2009). Grey polygons indicate the geometry of the individual seismic source zones proposed by Pailoplee and Choowong (2013).


Seismic sources

Present-day activities detected at the Indo-Australian and Eurasian plate collision zone have revealed that various styles of tectonic regimes contribute in various ways to the overall seismic activities occurring within MLSEA's territory. Interplate regimes dominate along the Sumatra-Andaman subduction zone, including central Myanmar, central Sumatra Island, and off the coast of the Andaman Sea, whereas an intraplate regime spreads eastward in the vicinity of eastern Myanmar, Thailand, Laos, and southern China (Pailoplee et al. 2013). To analyze seismic hazards, previous research has defined several seismic source zones in the MLSEA. For example, Nutalaya et al. (1985) and Charusiri et al. (2005) proposed 12 and 21 zones, respectively, according to the various available tectonic, geological, and seismicity information. However, based on the most recent data, Pailoplee and Choowong (2013) modified the seismic source zones of both Nutalaya et al. (1985) and Charusiri et al. (2005) and proposed 13 new zones (A to M), which are used in this study (Figure 1; Table 1). The details of each zone are described briefly as follows.

Table 1 FMD coefficients ( a and b values) and fractal dimensions ( D C ) of 13 earthquake sources recognized in MLSEA

The Sumatra-Andaman interplate and intraslab, zones A and B, respectively, relate to the plate boundary of the Indo-Australian and Eurasian plate collision zone. The M w -9.0 earthquake of December 26, 2004 (number 1 in Figure 1) nucleated in zone A. In addition, the Sagaing fault zone striking north-south in central Myanmar, zone C, and the Sumatra fault zone striking northwest-southeast in Sumatra Island, zone E, are the major inland strike-slip faults in this region. According to Brown and Leicester (1933), an M w -8.0 earthquake (number 2 in Figure 1) in zone C was created by the Sagaing fault zone on May 23, 1912, as were a number of other major earthquakes (Kundu and Gahalaut 2012). Zone D, the Andaman Basin off the coast of Andaman Sea, is occupied by transform fault systems consisting of the Andaman transform zone and Central Andaman rift in addition to the West Andaman and Seuliman faults (Cattin et al. 2009). Tectonically, zones C, D, and E include the plate boundary between the Burma and Sunda plates (Kundu and Gahalaut 2012).

Along the Thailand-Laos-Myanmar border, two strike-slip fault systems were detected. The northwest-southeast striking faults included in the Moei-Tongyi (Pailoplee et al. 2009) and Sri Sawat (Nuttee et al. 2005) fault zones are grouped into zone G. An earthquake of M w -5.9 (number 3 in Figure 1) occurred in the Moei-Tongyi fault zone on February 17, 1975, whereas an M w -5.6 earthquake (number 4 in Figure 1) occurred at the Sri Sawat fault zone on April 22, 1983 (Klaipongphan et al. 1991). In contrast, the northeast-southeast striking faults, the Ranong and Klong Marui fault zones, respectively, are delineated in the border between southernmost Myanmar and southern Thailand, which form zone H. An M w -5.0 earthquake (number 5 in Figure 1) originated in this zone on October 8, 2006 (Yadav et al. 2012), at the northern end of the Ranong fault zone.

In northern Thailand, approximately north-south-trending grabens and their basin-bounding normal faults, such as the Lampang-Thoen (Charusiri et al. 2004), Phrae (Udchachon et al. 2005), and Mae Tha (Rhodes et al. 2004) fault zones, are classified as zone J in northern Thailand-Dein Bein Phu (Pailoplee and Choowong 2013). Most earthquakes nucleated in this area have been high-frequency, small-to-medium-sized earthquakes.

Along the southern China-Vietnam border, the northeast-southwest and northwest-southeast complex shear zones (Polachan et al. 1991) were grouped into the five zones of F, I, and K to M for the Hsenwi-Nanting, Jinghong-Mengxing, Song Da-Song Ma, Xianshuihe, and Red River fault zones, respectively. Instrumental earthquake records reveal that seismic activities in these zones are not quiescent.


The datasets used for this study are of the instrumentally recorded earthquakes and were provided by (i) the Incorporated Research Institutions for Seismology (IRIS) and (ii) the US National Earthquake Information Center (NEIC) earthquake catalogs. The combined data from these two sources yielded approximately 29,990 recorded earthquake events during the 50-year period of 1962 to 2013. These earthquake magnitudes ranged from 1.0 to 9.0 and were reported mostly in the body-wave magnitude scale (m b ). To homogenize the magnitude scale, earthquake events recorded in moment magnitude (M w ) and surface-wave magnitude (M S ) scales were converted to m b , following the relationships proposed by Pailoplee et al. (2009). Both foreshocks and aftershocks, which are meaningless in seismotectonic investigations, were identified and removed by using the assumption reported by Gardner and Knopoff (1974). As a result, approximately 3,730 unique mainshock events remained in the database.

Thereafter, the Genetic Network Analysis System (GENAS) algorithm (Habermann 1987), implemented in the Z-MAP program (Wiemer 2001), was used to screen for any significant levels of bias from man-made seismicity variations in reporting and seismotectonic activities (Wyss 1991; Zuniga and Wiemer 1999). On the basis of the GENAS algorithm, 2,150 unique mainshock events with magnitudes of ≥4.0 m b reported during the period 1974 to 2010 exhibited a smooth cumulative rate of change and thus formed the completeness catalog used here for the statistical seismicity investigation. The distribution of the completeness earthquakes is shown in Figure 1.

Results and discussions

Frequency-magnitude distribution

According to Gutenberg and Richter (1944), the FMD power law can be expressed as

log N = a - bM

where N is the cumulative number of earthquakes with a magnitude ≥ M. The a and b coefficient values vary in any specific time and space window. Seismotectonically, the a value indicates the entire seismicity level, and the b value relates to tectonic stress (Mogi 1967; Scholz 1968). Lower b values relate to higher levels of accumulated stress (Manakou and Tsapanos 2000).

Although Pailoplee and Choowong (2013) have previously plotted the FMDs and determined the coefficients for all seismic source zones in the MLSEA, the dataset used was not screened to exclude man-made seismicity artifacts. Therefore, to theoretically achieve more accurate results, the FMD a and b values were redetermined (Figure 2) along with the D C values for these 13 zones of the MLSEA (Table 1).

Figure 2
figure 2

Frequency-magnitude distribution (FMD) plots of the 13 seismic source zones (A to M). Triangles and squares represent the number and cumulative number of each individual magnitude level of earthquake, respectively. The lines represent the FMD linear regression fitted with the observed data. M C is defined as the magnitude of completeness (Woessner and Wiemer 2005).

Due to the lack of available earthquake data, the FMD plots of zones Hand K are unavailable. However, the calculated b values for the other zones were within the range of 0.61 to 1.03. The lowest b value was observed in zone E, whereas the highest b value was detected in zone M.

According to Bayrak and Bayrak (2012), the obtained b values can be categorized into four groups of b < 0.7, 0.7 ≤ b < 0.8, 0.8 ≤ b < 0.9, and b ≥ 0.9. The variation in the b values in this study region, expressed as the four aforementioned category groups, is represented in Figure 3 by various colors. The highest b value group was observed at zones F, L, and M. With regard to the corresponding high a values of 5.99 to 6.14 (Table 1), this group is interpreted as a low-stress region due to frequent tension release through small earthquakes. The second group of b values (0.8 to 0.9) was detected at zones B and C, whereas b values of 0.7 to 0.8 were observed in zones A, I, and J. The b values of less than 0.7 were detected at zones D, E, and G. Regardless of the a value, these comparatively low b value regions may accumulate high tectonic stress levels.

Figure 3
figure 3

Map showing distributions of estimated b values for zones A to M proposed in MLSEA.

Fractal dimension (D C )

In this study, the D C value was evaluated according to the correlation integral technique (Grassberger and Procaccia 1983) expressed as

C r = 2 N N - 1 N R < r

where N is the number of earthquakes analyzed, and N(R < r) is the number of event pairs separated by a distance R < r. If the distribution is fractal, the relation obtained will be the same as that in Equation 3 (Kagan and Knopoff 1980), which can be expressed as

C r ~ r D C .

Unlike the b value, the D C value has not been reported previously for the MLSEA. Therefore, the D C graphs of the 13 seismic source zones in the MLSEA were established (Figure 4). The slopes of the linear fit of graphs log(C(r))-log(r) were the estimated D C values (Table 1). Because of the statistical insufficiency of the available earthquake data, the D C values for zones G, H, and K could not be evaluated.

Figure 4
figure 4

Graphs showing relationship between log( C ( r )) and log( r ) of earthquake data for 13 seismic source zones (A to M). The slopes of linear fit (solid black lines) are the fractal dimension (D C ).

The calculated D C values varied between 1.48 and 2.17, with the lowest D C values found at zones F and M. The highest D C value, 2.17, was observed at zone D. From the definition of Tosi (1998), which states that the D C value of seismogenically active sources ranges between 0 and 2, most of the MLSEA zones were interpreted as being seismically active.

The D C values were divided into four groups of D C  < 1.5, 1.5 ≤ D C  < 1.7, 1.7 ≤ D C  < 1.9, and D C  ≥ 1.9 (Bayrak and Bayrak 2012) and are mapped in Figure 5 by various colors. The highest D C values were detected in zones A, B, D, and E. Second-level D C values (1.7 to 1.9) were detected in zones I, J, and L; D C values between 1.5 and 1.7 were observed only in zone C.

Figure 5
figure 5

Map showing distributions of estimated D C values for zones A to M proposed in MLSEA.

Empirically, a D C value close to 1 or 2 signifies that the earthquake epicenters are homogeneously distributed over a line and two-dimensional (2-D) fault plane, respectively (Yadav et al. 2011). Therefore, most zones mentioned exhibit the near-plane characteristics of the seismogenic structures. Moreover, the lowest D C values (<1.5), indicating an active linear fault system, were observed in zones F and M.

D C /b relationship

The D C /b ratio has been suggested as an effective indicator of seismic hazards (Bayrak and Bayrak 2011, 2012). Accordingly, in this study, the correlation between the D C and b values was investigated according to that reported in previous works (Legrand 2002; Wyss et al. 2004; Mandal and Rastogi 2005; Bayrak and Bayrak 2012). On the basis of the obtained D C and b values (Table 1), the empirical D C /b relationship was calibrated as shown in Figure 6a and can be expressed as

D c = 2.80 - 1.22 b
Figure 6
figure 6

Empirical relationships. (a) Between the b and D C values and (b) between the a/b ratios and D C values for the 13 seismic source zones (A to M). The straight lines represent the linear regressions fitted with the observed data.

Empirically, the D C /b correlation can be either a positive or a negative regression. For example, positive regression was reported for the San Andreas fault in the USA, in addition to faults in India (Wyss et al. 2004; Yadav et al. 2012), whereas negative correlation was reported for fault zones in Japan, Turkey, and Iran (Hirata 1989; Öncel et al. 1996; Barton et al.1999; Öncel and Wilson 2002; Poroohan and Teimournegad 2010).

For the MLSEA, the D C /b relationship showed a distinct negative linear regression (Figure 6a), which implies increased accumulated stress and decreased earthquake clustering (Barton et al. 1999; Öncel and Wilson 2002). Therefore, in the MLSEA, zones D and E were defined as the highest stress regions, whereas zones F and M exhibited low-stress accumulations. Moreover, zones A, B, C, I, J, and L cluster in the middle of the graph with b values of approximately 0.71 to 0.92 and D C values of approximately 1.61 to 2.03.

In addition, the relation between the D C values and a/b ratios were investigated as per Bayrak and Bayrak (2012). The calibration (Figure 6b) revealed a positive correlation as

D c = 0.27 a / b - 0.01

A comparison of Figure 6a,b reveals that the distributions of both the D C /b and D C -(a/b) correlations were not significantly variant in terms of the data scatter. However, the D C -(a/b) correlation showed a positive regression, whereas the D C -b correlation showed a negative regression. Zones A and B of the interplate regime were moved from the middle group to the first group, which are of high a/b and D C values. According to the entire seismicity rate, the a value for both zones was higher than that in the other zones. Although Bayrak and Bayrak (2012) mentioned that the D C -(a/b) relationship was more reliable and effective than that of the D C -b for indicating seismic hazards, both relationships in this study depicted an identical accuracy based on the R2 values of 0.65 to 0.68. Therefore, both relationships between D C -b and D C -(a/b) could potentially reflect local seismicity and earthquake risk and can thus be useful in hazard studies, particularly in the MLSEA.


In this study, instrumental earthquake data recorded within the MLSEA were analyzed simultaneously in terms of the FMD b and the D C values from 13 seismic source zones. The results revealed that regional variations in both the b and D C values could imply local tectonic stress and hazard levels. According to the obtained D C values, nearly all of the zones in the MLSEA are seismically active, and earthquakes are homogeneously distributed within the aerial fault plane. In addition, among the 13 seismic sources, zones A, B, D, and E showed comparatively low b and high D C values. Conversely, zones F and M exhibited prominently high b and low D C values.

Both the D C -b and D C -(a/b) relationships were calibrated in this study for the MLSEA region. Although the D C /b correlation showed a negative regression, that for the D C -(a/b) correlation was positive. In contrast to that reported by Bayrak and Bayrak (2012), which states that the D C -(a/b) correlation represents seismotectonics more accurately than that of the D C -b, in the present study of the MLSEA, both showed essentially similar correlations with R2 values of 0.65 to 0.68. Therefore, both relationships can be used as an effective indicator of seismic hazards in the MLSEA region.

On the basis of both D C /b and D C -(a/b) relationships, it is interpreted tectonically that zones F and M are the low-stress zones that maybe safer against seismic hazards than other regions. Moreover, the interplate regimes of zones A, B, D, and E accumulated high levels of tectonic stress, which poses risks for generating large earthquakes in the future. Therefore, it is reasonable to suggest the introduction of seismic hazard warnings and the development of mitigation plans for the ASEAN community.


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This research was jointly sponsored by the Ratchadapiseksomphot Endowment Fund of Chulalongkorn University (RES560530028CC) and the Thailand Research Fund (TRF) Grant for New Researchers. Additional thanks are extended to T. Pailoplee for the preparation of the draft manuscript. We thank the Publication Counseling Unit (PCU), Faculty of Science, and Chulalongkorn University for critical reviews and suggestions for improving the English. We also acknowledge the thoughtful comments and suggestions by Y. Ogawa (Editor in Chief), T. Okada, and anonymous reviewers, which significantly enhanced the quality of this manuscript.

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SP carried out the seismicity investigations, performed the statistical analysis, and drafted the manuscript. MC participated in the design of the study and the sequence alignment. Both authors read and approved the final manuscript.

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Pailoplee, S., Choowong, M. Earthquake frequency-magnitude distribution and fractal dimension in mainland Southeast Asia. Earth Planet Sp 66, 8 (2014).

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