Comparing Gardner-Knopoff, Gruenthal, and Uhrhammer Earthquake Declustering Methods in Aceh, Indonesia

The sudden release of energy from inside the earth, which generates seismic waves, causes earthquakes on the earth’s surface. Foreshock, mainshock, and aftershock are terms commonly used in this subject. These phrases refer to the three stages of an earthquake event—before the main event, the primary event, and after the main event. The earthquake data catalogue, however, typically does not distinguish between mainshock data and foreshocks/aftershocks. For seismic-related studies, justifying the mainshock is very crucial. There are several methods for separating the mainshock of earthquake data from the foreshocks/aftershocks. This study employs three declustering techniques, including Gardner-Knopoff (1974), Gruenthal, and Uhrhammer (1986). The present study collected and analyzed 3543 earthquake events from 1971 to 2021 for Aceh region. In order to determine which method provides the highest a-value and b-value outcomes for Aceh’s seismicity conditions, this study compares the aforementioned three approaches. The Uhrhammer method (1986) has an a-value of 5.82, a b-value of 1.05, 1893 main shock events, 305 clusters, and 3.3 percent of the total seismic moment generated at that location are the findings from this study. According to the Gruenthal method, the results had an a-value of 4.53, a b-value of 0.823, 776 mainshock events, 304 clusters, and released 1.3 percent of the total seismic moment at that location. a-value of 5.1, b-value of 0.929, 1097 main shock events, 319 clusters, and a release of 1.08 percent of the total seismic moment at that location were the results of the Gardner-Knopoff method (1974). For seismic hazard evaluation with the highest level of risk, the Uhrhammer (1986) technique is appropriate. The Gruenthal approach is suggested for more conservative cases.


Introduction
The first step in performing a seismic hazard analysis is to justify the mainshock of the earthquakes.Many declustering techniques, including the Gardner-Knopoff [1], Reasenberg [2], Zhuang [3], Uhrhammer method [4], and others, have been proposed by earlier scholars.Each technique for segregating seismic data has benefits and drawbacks.Stiphout [5] used earthquake data from southern California and Japan with a time range of 1932-2010 to compare the declustering methods of Reasenberg [2], Zhuang [3], and Gardner-Knopoff [1].According to this study, using Reasenberg [2] and Zhuang [3], declustering causes a slowdown for long events and a quick drop in time for brief events.Furthermore, Stiphout [5] also suggested that estimations become redundant at close distances; the Gardner-Knopoff technique [1] only eliminates occurrences that are close in space and time and is not possible long-distance estimation.Using earthquake catalogue data from Turkey, Azak [6] attempted to compare the approaches of Gardner-Knopoff [1], Reasenberg [2], and Zaliapin [7].This study indicated that none of the used approaches accurately identified events from the catalogue.The number of clusters found using the Reasenberg [2] and Gardner-Knopoff [1] approaches differs significantly.The Gardner-Knopoff [1] approach and the Zaliapin [7] method both produced results that were pretty close [6]The present study attempted to compare the declustering approach, which has the same principle as the windows method, as this is the simplest method for figuring out mainshock and foreshocks/aftershocks.The largest earthquakes in a specific window of time and space are known as the main earthquakes or main shocks, whereas the earthquakes that precede the main earthquake are known as foreshocks [8]The aftershocks are earthquakes that follow the main earthquake.The Gardner-Knopoff [1], the Gruenthal [9], and the Uhrhammer [4] methods are a few declustering techniques that take advantage of this fundamental idea [10]

Declustering earthquake methods
As aforementioned, the precede shocks will be classified as a foreshock for every earthquake in the catalogue with magnitude M if it takes place within a specific window of time and space.The earthquake with the greatest magnitude in the sequence usually becomes the main shock.Within a specific window of time and space, the subsequent shocks are classified as an aftershock for every earthquake in the catalogue.Based on the abovementioned assertion, each declustering technique offers a mathematical formula for the two determining factors, time and distance.The Gardner-Knopoff technique [1] equations ( 1), (2), and (3) are used to calculate the mainshock and foreshock, whereas equations ( 4), (5), and ( 6) are for the Gruenthal approach [9], which the author developed as an alternative to the Gardner-Knopoff method.The final equations are (7) and ( 8), proposed by Uhrhammer [4] for the relationship between time and distance [10] Gardner-Knopoff method [1]  = 10 0.032+2.7389  ≥ 6.5 = 10 0.5409−0.547  < 6.5 = 10 2.8+0.024  < 6.5 (5) Uhrhammer method [4]  =  −2.87+1.235(7) where M is the earthquake magnitude (Mw), t is the time (days), and d is the distance (km).

Maximum likelihood model
In order to obtain the most representative data, the maximum likelihood model can statistically calculate earthquake activity characteristics and can eliminate magnitude gaps at specific intervals.This model's output parameter is called b-value.The fragility of the rock will grow if the b-value is high.The area's shear stress level will also be higher if the b-value is low [11]The equation provided by Utsu [12] can be employed to determine b-values (equation 9) [13]The equation proposed by Wekner [14] can be used to determine a-values (equation 10).The a-value is a parameter that is affected by the volume, time window, and the number of earthquake events.In other words, it can be said that if the a-value is high, the seismic activity is high [15]  = = log ( ≥   ) + log ( ln 10) +    (10) where, variable  ̅ is the average magnitude; variable Mmin or Mo is the minimum magnitude contained in the research data; N is the number of earthquake events that occur; a is the seismicity parameter that depends on the number of earthquake events, volume, and time window; b is the parameter seismicity related to the level of rock fragility or the level of shear stress.

Result and discussion
The study is being conducted in the Indonesian province of Aceh.Geographically, the study area lies between latitudes 0.297 -7.569 N and longitudes 93.208 -97.822E. There were 3543 earthquake events recorded in the earthquake data from 1971 to 2021.This data was obtained from the USGS data catalog [16].The data is earthquake data with a minimum magnitude of 4 Mw.The location of the study and the information used is shown in Figure 1 below.

Result
This study separates earthquake data using three techniques: Gruenthal [9], Uhrhammer [4], and Gardner-Knopoff [1].Table 1 below compares the number of earthquake events falling within a particular scale range.The findings are then modeled with the maximum likelihood model to produce the a-values and b-values, as shown in Table 2.The outcomes of maximum likelihood modeling for the three approaches are shown in Figure 2. The outcomes of the three declustering techniques are shown in Figure 3.The comparison of magnitude-to-time and magnitude-to-distance in each approach is shown in Figure 4.   4. Comparison of magnitude-to-distance and magnitude-to-time (a) Gardner-Knopoff method [1], (b) Gruenthal method [2], (c) Uhrhammer method [3], (d) combined graph of the three methods [1], [4], [9].

Discussion
The outcomes revealed some variations among the three techniques.The first comparison of how many main shocks each method produced (see Table 1).The Uhrhammer technique [4], which included 1892 earthquake events, identified the highest number of main shocks after the declustering process.The Gardner-Knopoff approach [1], which includes 1097 earthquake events, comes in second.Lastly, Gruenthal approach [9] suggested 776 earthquake events.The outcomes of recurrence modeling using the Gutenberg-Richter [1] approach provide the basis for the second comparison (see Table 2).
According to the results of the present study, as shown in Table 2, the Uhrhammer [4] method get the highest a-value 5.82.It is followed by Gardner-Knopoff [1] approach with an a-value of 5.1.The Gruenthal method [9]is the last one with a-value of 4.53.The level of seismic activity in a zone increases with increasing a-value.Additionally, the b-values for each technique are as follows: 0.929 for the Gardner-Knopoff [1], 0.823 for the Gruenthal method [9], and 1.05 for the Uhrhammer [4].However, the more brittle the rocks there are, the greater the b-value in a zone denotes a smaller shear stress experienced.Thus, using the Gruenthal approach [9], it may be concluded that there is significant shear stress in the zone.Utilizing the Uhrhammer method [4], the zone exhibits the highest level of rock fragility.
The Gardner-Knopoff method of declustering [1] produced 319 clusters, of which 2446 events (or 69.04 percent) were eliminated from 3543 earthquake occurrences (Figure 4a).As can be observed in Table 1, the total mainshock contained by this method is 1097 occurrences, distributed throughout each magnitude interval.This technique released 1.08 percent of the total seismic moment in the zone as seismic energy.Gruenthal's approach [9] of declustering produced 304 clusters, of which 2767 events (78.1%) were left out of the total of 3543 earthquake occurrences (Figure 4b).The distribution of the 776 total mainshock occurrences included in this manner for each magnitude interval is shown in table 1.The seismic moment that was released using this technique makes up 1.3% of the total seismic moment in the zone.Following that, the Uhrhammer method [4] of declustering produced 305 clusters, of which 1650 occurrences (or 46.57percent of the total events) were eliminated from the 3543 earthquake events (Figure 4c).This technique contains 1893 mainshock events in total.3.3 percent of the total seismic moment was discharged using this way.

Conclusion
The present study suggests that the Uhrhammer [4] technique produces data with an a-value of 5.82, bvalue of 1.05, 1893 mainshock events, 305 clusters, and 3.3% of the total seismic moment released at that location.With an a-value of 4.53, a b-value of 0.823, a total of 776 mainshock events, 304 clusters, and 1.3 percent of the total seismic moment released at that location, the results of the Gruenthal [9] method are presented.With an a-value of 5.1, a b-value of 0.929, 1097 main shock events, 319 clusters, and a release of 1.08 percent of the total seismic moment at that location, the Gardner-Knopoff [1] method produced findings.The Uhrhammer [4] approach is appropriate for assessing seismic hazards with the highest level of risk.The Gruenthal [9] approach is advised in the meanwhile for outcomes that are more conservative.

Figure 1 .
Figure 1.The research location incorporated 3543 earthquake events recorded from 1971 to 2021

Table 1 .
Number of earthquake events in each declustering method

Table 2 .
Parameters a-value and b-value for each declustering method