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Aftershock analysis of the 2015 Gorkha-Dolakha (Central Nepal) earthquake doublet

On 25 April 2015, a large earthquake with moment-magnitude (Mw) 7.8 occurred at Gorkha (latitude 28.23° N and longitude 84.73° E) in Central Nepal. Just 17 days later, another large earthquake of Mw 7.3 occurred at Dolakha (latitude 27.80° N and longitude 86.06° E), about 140 km away from the previous epicenter. In this study, we deal with the aftershocks of these two earthquakes that occurred in the region (27°–28.5°N, 84°–87°E) spanning the period from 25 April 2015 to 28 May 2016 to find the spatiotemporal distribution patterns, the size distribution (b-value), and the aftershock decay rate (p-value) of this sequence. Aftershock epicenters of the 2015 Gorkha-Dolakha earthquake doublet are distributed over an area approximately 170 km in length and 70 km in width and largely confined in a depth range from 5 to 25 km. The spatial distribution of epicenters and known geological structures in this study reveals that aftershocks are limited on the east by the surface trace of the Everest lineament and on the south side by the surface trace of the segment of the Main Boundary Thrust (MBT). The estimated b-and p-values of this seismic sequence are 0.93 ± 0.03 and 0.79 ± 0.24, respectively. This b-value is higher than the b-value estimated by the previous studies, while the p-value corresponds in general with the p-value obtained by recent study in the region.


Introduction
On 25 April 2015, a large earthquake with moment-magnitude (M w ) 7.8 occurred in Gorkha district (latitude 28.23 N and longitude 84.73 E) of central Nepal (hereafter referred to as the Gorkha earthquake) at about 32-km east of Lamjung district and about 80-km northwest of Kathmandu. Just 17 days later, another large earthquake of M w 7.3 occurred on 12 May 2015 in Dolakha district (latitude 27.80 N and longitude 86.06 E) farther eastward (hereafter referred to as the Dolakha earthquake) at about 140-km east of the Gorkha earthquake, as shown in Fig. 1. These two large events and associated aftershocks caused many casualties (>8500 deaths), injuries (>22,000), damage (>5 million houses) and economic losses (w7 billion US dollars) in the country (Government of Nepal, 2015). Both earthquakes are occurred in the central segment of a Himalaya collided zone between the Eurasia Plate and the Indian Plate (Bilham, 2015). The ongoing collision of Eurasia-Indian plates governing the present day seismotectonics of the region that is expressed by the existence of active faults and lineaments (Nakata, 1972(Nakata, , 1982(Nakata, , 1989Armijo et al., 1986;Dasgupta et al., 1987;Nakata and Kumahara, 2002;Taylor and Yin, 2009) and the occurrence of large earthquakes in the past (Thapa and Wang, 2013;Thapa et al., 2017).
Both these earthquakes are the two large well-recorded events occurred in Nepal since the 1934 Nepal-Bihar catastrophic earthquake (M w ¼ 8.4). Seismicity history of Nepal (Thapa and Wang, 2013;Thapa et al., 2017) shows that earthquakes of such large magnitudes are common in the country and one slightly smaller magnitude MBT; MFT and active normal faults (Red discontinuous lines) modified from Thapa et al. (2017), STDS modified from Hodges (2000). Epicenter locations of earthquakes (black circles) from 1255 to 24 April 2015 are taken from Thapa et al. (2017). Stars are the epicenters of the 2015 Gorkha and Dolakha earthquakes. event (M w ¼ 7.7, 1833) than the Gorkha earthquake had occurred in an area between the 2015 Gorkha and the Dolakha main shocks. The recent 2015 two earthquakes were followed by a large number of aftershocks, including three events with moment-magnitudes equal to and greater than 6.3 (M w ¼ 6.6, 25 April 2015; M w ¼ 6.7, 26 April 2015; M w ¼ 6.3, 12 May 2015).
As known, aftershocks associated with strong earthquakes give information related to the earth's crust, hence the analysis of aftershocks has become a more common research topic in recent years. Statistical approaches (i.e., the Gutenberg-Richter frequency-magnitude relationship and the modified Omori law/Omori-Utsu law) are often employed for the study of aftershocks. Over the last four decades, several studies have primarily attempted to analyze the aftershocks of individual earthquakes worldwide (e.g., Stephens et al., 1980;Hauksson et al., 1995;Utsu et al., 1995;Guo and Ogata, 1997;Ogata, 1999;Hamburger et al., 2011). These investigations have provided the space-time as well as depth characteristics of the aftershocks. In the context of Nepal, several studies (Adhikari et al., 2015;Ogata and Tsuruoka, 2016;Ichiyanagi et al., 2016) have attempted to provide the account of aftershocks of the 2015 Gorkha earthquake. These studies considered the Dolakha earthquake as the largest aftershock of the Gorkha earthquake, no matter a theoretically conflicting that the magnitude of the Dolakha earthquake was not in accordance with the B ath's law, which stated that the size difference between the main shock and largest aftershock typically lies within a range of 1.1e1.2 magnitude units (B ath, 1965).
Although the longitudinal and transverse faults as well as lineaments have been identified in Central Nepal and the surrounding region (Nakata, 1972(Nakata, , 1982(Nakata, , 1989Nakata and Kumahara, 2002;Dasgupta et al., 1987;Taylor and Yin, 2009) and some aftershocks studies of the 2015 earthquakes have been carried out (e.g., Adhikari et al., 2015;Ichiyanagi et al., 2016;Ogata and Tsuruoka, 2016), no studies have attempted to investigate the spatial relationship between the surface trace of known faults as well as lineaments and epicenter distribution of aftershocks and to analyze aftershocks considering two earthquakes as an earthquake doublet.
Here, we consider these two earthquakes as an earthquake doublet (hereafter referred to as the Gorkha-Dolakha doublet) and analyze their aftershocks and the above mentioned spatial relationship.
The aim of this study is to investigate the aftershocks of the Gorkha-Dolakha earthquake doublet occurring in the region (27 e28.5 N, 84 e87 E) from 25 April 2015 to 28 May 2016. For this purpose, we analyze and present the spatiotemporal distribution patterns, the size distribution (b-value), and the aftershock decay rate (p-value). The analysis result enables us to improve our understanding of the aftershock evolution of this part of Nepal.

Methodology
The primary problem of seismicity analysis, especially for the aftershock analysis is to choose an appropriate spatial and temporal range for statistics. In this study, we compiled the aftershocks occurred in the geographic window between 27 e28.5 N and 84 e87 E for the period between 25 April 2015 and 28 May 2016 from the United States National Earthquake Information Centre (NEIC), since the occurrence rate and magnitudes of the aftershocks outside the area in the same time period and in the same area outside the time period are both obviously much less and smaller than those selected. This aftershock dataset contains 298 aftershocks with body wave magnitudes equal to or greater than 4.0. It consists of 266 aftershocks between magnitude 4.0 and 4.9, 28 aftershocks between magnitude 5.0 and 5.9, and four between magnitude 6.0 and 6.9.
To analyse this aftershock sequence quantitatively, we adopted two most commonly and widely well-known scaling laws, namely, the Gutenberg-Richter frequencymagnitude relation (Gutenberg and Richter, 1944) and the Modified Omori's Law/Omori-Utsu law (Utsu, 1961). The Gutenberg-Richter law that best characterizes the power-law size distribution of earthquakes can be expressed here below in Equation (1): in which N is the cumulative number of earthquakes with magnitude equal to or greater than magnitude M, and a and b represent the empirical constants of the law. The a and b values in this study are estimated using the least squares regression method considering that the USGS earthquake catalogue is complete with body wave magnitudes equal to or greater than 4.0.
Scaling law that is adopted to estimate the decay rate of aftershocks associated with a major event was initially described more than two-century ago by Omori (1884). The original Omori law (1884) is given here in the following equation: in which n(t) is the occurrence rate of aftershocks in time period t, and K and c are empirical constants (Omori, 1884). During the early-sixties of the last century, Utsu (1961) extended the original Omori law, which is now called as the modified Omori's Law. The well-established modified Omori's Law commonly used in statistical seismology for characterizing the temporal decay process of the occurrence rate of aftershocks sequence can be expressed as (Utsu, 1961;Utsu et al., 1995): where p is an additional constant and other remaining notations are the same as above in Equation (2). In this study, the modified Omori law parameters are estimated using the exponential fitting from aftershocks datasets described above.  of the earthquake doublet (Fan and Shearer, 2015) and is largely bounded on the west side by the Marsyangdi river, on the east by the surface trace of the Everest lineament and on the south side by the surface trace of the active segment of the Main Boundary Thrust (MBT). Both the Everest lineament and the segment of the MBT lies in this aftershock zone are previously recognized to be active geological structures (Nakata, 1972(Nakata, , 1982(Nakata, , 1989Dasgupta et al., 1987), whereas the transverse features and the related tectonic structures along the Marsyangdi River and its tributaries are still unknown. Further detail research is necessary to clarify the existence/non existence of active tectonic features in the Marsyangdi valley. Kathmandu Time (07:05 UTC). The Dolakha main shock produced its own aftershocks, including the strong event (M w ¼ 6.3) that occurred within 31 minutes after the Dolakha quake on the same day at 13:21 Kathmandu Time (07:36 UTC). It was also followed by a productive number of aftershocks that resulted almost doubling the earthquake sequence. In sum, the significant number of aftershocks occurred within the first 2e3 months after the main shocks then the activity in the sequence gradually decaying over the whole study period.

Magnitude-frequency distribution and decay rate of the aftershocks
The earthquake number-size distribution with b-value and the aftershock decay rate (p-value) of the sequence has been estimated by means of the magnitude-frequency relation of Gutenberg and Richter given in Equation (1) and the modified Omori law given in Equation (3)    Gorkha-Dolakha earthquake doublet. One can see from the figure that the occurrence rate decayed very fast in the first 7 days, and then decayed gradually within 60 days afterwards. The data points in the figure also shows that the Dolakha quake occurred 17 days after the first main shock is far away from the curve; but does not disturb the decaying process. The parameters of the Omori's law primarily vary with the tectonic environment (e.g., styles of faulting) of the region (Tahir and Grasso, 2015). The estimated p-value in this study 0.79 AE 0.24, is very close to the value 0.80 AE 0.4 estimated by Adhikari et al. (2015) for the 2015 main cluster and is slightly lower than that of Tahir and Grasso (2015) who obtained p-value 0.82 AE 0.02 for the thrust faulting. The result of the present study shows that p-value of an earthquake doublet seems to be similar with that of a single main shock.
In a nutshell, the Dolakha earthquake must not be considered as an aftershock of the Gorkha shock for the magnitude-frequency analysis, but does not appears to affect the analysis of the decay rate of aftershocks. Doublet seismic events are welldocumented in the recent seismological literature (e.g., Gibowicz and Lasocki, 2005;Vall ee and Di Luccio, 2005;Karakostas et al., 2015). It is thus concluded that these two 2015 earthquakes occurred in Nepal should be considered as an earthquake doublet and aftershocks must be analyzed as those of an earthquake doublet.

Conclusions
Aftershocks

Declarations
Author contribution statement Dilli Ram Thapa: Conceived and designed the analysis; Analyzed and interpreted the data; Contributed analysis tools or data; Wrote the paper.
Xiaxin Tao: Conceived and designed the analysis; Analyzed and interpreted the data.
Feng Fan and Zhengru Tao: Analyzed and interpreted the data.