Earthquake statistical performance due to increasing of the seismic network around Opak Fault, Yogyakarta

. The seismic event in May 2006 underscored the critical necessity of continuous earthquake monitoring. Observational enhancement through adding more stations is very crucial to obtain a more refined data quality. From January 2009 to September 2019, BMKG PGR ( Pusat Gempa Regional /Regional Earthquake Centre) VII documented approximately 1847 seismic events with magnitudes from 0.9 to 4.9. With the integration of additional seismic station into the array by December 2022, there was a notable increase of 1418 recorded events in the same magnitude interval. The earthquake observation average is increasing as well, from 15.4 events in a month to 20.5 events in a month. This study leverages this data to assess the impact of augmenting seismic stations proximal to the Opak Fault on seismicity parameters within that region. Employing ZMAP 6.0, a comparative analysis of seismicity parameters was conducted between the earthquake catalog from January 2009 to September 2019 and the expanded catalog from January 2009 to December 2022. Declustering process result 1790 and 3141 main earthquake events in each catalog. This research indicate that the inclusion of more stations significantly influences the M c value and earthquake density, however, it does not have a significant effect on the b and a-value .


Introduction
BMKG (Badan Meteorologi Klimatologi dan Geofisika/ Meteorology Climatology and Geophysics Agency) is the only official institution responsible for continuously observing earthquakes in Indonesia [1].The responsibility to perform continuous earthquake observation requires a high density sensor network.Prior to 2019 BMKG only had 3 stations around the Opak Fault, e.g.WOJI, YOGI, and UGM.Additional stations were installed since October 1, 2019 (MKJM, SBJM, GKJM, PGJM, PRJI, and BOJI) [2].The SYJI station was installed in December 2021, while the TAGJI and SAKJI stations were installed in 2023.Until now, BMKG has 12 stations tasked with monitoring earthquakes around the Opak Fault. Figure 1 shows the location of seismic stations around the Opak Fault.Red triangles indicate stations installed before 2019, while blue ones were installed after 2019.Further information about station locations is in the Table 1 [2].The color on the left corresponds to the color in Figure 1._____________________________ * Corresponding author: ws@ugm.ac.idThe Opak Fault, which is located to the East of Yogyakarta City, close to the Opak River, is an active fault.In May 2006, this fault was considered to be the cause of a destructive earthquake in Yogyakarta and its surroundings [3,4,5].This earthquake caused many victims in Yogyakarta and Jawa Tengah provinces [6,7].Figure 2 provides an overview of the earthquake's aftershocks [8].In this study we will compare seismicity parameters before and after the addition of seismic stations around the Opak Fault.

Theory
This research uses the Gutenberg-Richter relationship method to determine seismic parameters [9,10], which are written as: where () is the cumulative number of earthquakes with a magnitude greater than or equal to magnitude M, while the a-value and b-value are constants called seismicity parameters.The b-value describes the comparison between small earthquakes to large earthquakes proportionally in a scale-free population [9].This value is related to distribution of stress and strain in the certain area [11,12].The b-value is the slope or gradient of the frequency magnitude distribution (Figure 3) [9].The low b-value indicate a high seismic moment release and high stress accumulation [13].The a-value is seismicity level of the particular area, that depends on the extent of the area, a number of occurance earthquakes in the region, the largest seismic magnitude and time interval [9]. Figure 3 refers that from frequency magnitude distribution, avalue is the cross point of gradient line with the y axis.
The high a-value represent high seismicity level in the related region.In this research, the b-value is determined using the maximum likelihood method [14], which is formulated as: where  � is the average magnitude,  � is the Magnitude of Completeness, and ∆ ��� is a bin magnitude width.Standard deviation is described as: where n is the number of earthquakes in the calculation sampling.The a-value is determined from the equation: where  � is Magnitude of Completeness, define as the lowest magnitude can be detected completely in the a space-time volume [15,16,17].The Magnitude of Completeness is a statistical way to determine the quality of an earthquake catalog [18].A better catalog would have a low magnitude of completeness.Equation (4) shows that estimating the b-value and determining  � is very important in governing the accuracy of the avalue [15,19].

Methodology
This research was carried out using secondary data, i.e.BMKG's earthquake data catalogue, specially from the PGR VII region.It is covering the boundaries of 5⁰-12⁰ N and 108.0⁰-111.7⁰E in the period January 2009 to December 2022.The data processing and analysis process is as shown in Figure 4.The first step in data processing is to select the data and uniformize the differnent magnitude into moment magnitude (Mw), throughout the complete catalog.We consider a notice that no magnitude other than Mw is capable to express the "size" of earthquakes, even for weak eartquakes (Mw<4) [20].From the complete catalog, we have two different types of magnitude in this catalog, i.e.MLv (2400 events) and mb (856 events).MLv is defined as the local magnitude derived from the vertical component of the instrument, and mb is describe as the short-period body-wave magnitude [21].Both magnitudes are converted to moment magnitude (Mw) with the conversion formula as follows [22]: (5) (6) Then the catalog was rearranged into two parts with September 2019 as a point of separation, so that we get two earthquake catalogs, i.e.(a) earthquakes of January 2009 to September 2019 (named as Catalog I); and (b) earthquakes of January 2009 to December 2022 (named as Catalog II).Then we do declustering process on both earthquake catalogs with the purpose of eliminating the influence of foreshock and aftershock, so we will have independent earthquake events.From the previous results, a frequency-magnitude distribution can be plotted to see the data completeness so that the completeness of the magnitude (Mc) can be determined.The next stage is to calculate the a-value, b-value and seismic density in the research area.The final step is to compare the data from the last result of the two catalogs.
We use ZMAP ver.6.0 as a software to analyze seismicity parameters on this research [23].The method that we use to estimate the b-value is maximum likelihood as shown in equation ( 2).The a-values and bvalues are mapped spatially by dividing the research area into grids, then the two seismicity parameters are calculated for each grid point at a fixed distance.In this research, the distance used was 70 km and the data processing grid was 0.2⁰ x 0.2⁰.By selecting the fixed distance and determined Mc, spatial mapping of seismicity parameters can be done.Next we calculate avalue and b-value based on the selected grid area.As additional analysis, an earthquake density map was created to see seismicity spatially in the study area.
The next stage is to calculate the b-value temporally using the sliding time-window method.This process is calculating the b-value at each shift in the time window on the map obtained from spatial analysis.By using the number of N events and a shift of N/10 events, the bvalue can be calculated with a number of events of 100 and a shift of 10 events.

Result
This research data uses the BMKG PGR VII earthquake catalog, from January 2009 to December 2022.The catalog contains of 3256 earthquake events, with magnitudes from 0.9 to 4.9.After uniformization process according to equation ( 5) and ( 6), the catalog was divided into Catalog I and Catalog II.BMKG recorded 1847 earthquake events before October 2019.After new seismic installation, 3256 earthquake events were recorded.It means the earthquake observation average is increasing from 15.4 events per month to 20.5 events per month.Figure 5 shows the map of both catalogs.
Declustering process of both catalogs gives us new two catalogs which contain 1790 eartquake events in Catalog I and 3141 earthquake events in Catalog II. Figure 6 describes that number on both catalog in the certain of earthquake magnitude intervals.Blue color represents Catalog I and orange color represents Catalog II.After obtaining the declustered data, the next stage is to create a frequency-magnitude distribution from the previous data.This result gives us the relationship between magnitude and number of earthquake events, as shown in Figure 7a as Catalog I and Figure 7b as Catalog II.The general values of both catalog are written in the Table 2.   Table 2 indicates that there is a decreasing Mc value from 3.2 in Catalog I to 2.9 in Catalog II.This difference, which is 0.3, is a significant difference between them.We conclude that installation of new seismic sensor in around Opak Fault can decrease the Mc value.This result is consistent with previous research, which states that the decrease of Mc is directly related to to the seismic network improvements to monitor seismicity in the region [24,25].The frequency magnitude distribution of both catalogs yields general b-value and a-value as well .The b-value from Catalog I is 0.694 and in Catalog II it is 0.651, which means that the new installation of seismic sensors does not affect changes in the b-value.However, both of b-value is approaching value 1, consistent with previous research [26].The same result we have in general a-value of two catalogs.They have no significant differences, i.e. 5.30 (Catalog I) and 5.22 (Catalog II), which indicates that in general the seismicity level of the two catalogs has not changed significantly.
The spatial variations in the Mc values from both catalogs show that there are quite significant differences (circle 1).In Figure 10a and Figure 10b shows the spatial variations of a-value in both catalog.In the circle 3, there is no significant difference between Catalog I and Catalog II.Since the differences are insignificant, we conclude that adding stations in array has no effect on changes in the a-value.Installation of additional stations on the seismic network affects the earthquake density through spatial variations.It can be seen in Figure 11 where the spatial variation on earthquake density in Catalog II is much higher than Catalog I (see circle 4).This result is in convenient with the increasing of earthquakes occurrence average, from 15.4 events in a month to 20.5 events in a month.

Conclusion
The addition of several seismic stations around the Opak Fault aims to record weak earthquakes in the particular area.This goal has been achieved with the increasing number of average recorded earthquakes, from 15.4 events in a month become 20.5 events in a month.This research shows that the installation has enlarge the earthquake density with spatial variations.The extending number of small earthquakes also made a great effect on the Mc value.After installation seismic stations, the Mc value becomes more smaller.This means that the newest catalog has increasingly complete magnitudes.And then, b-value and a-value can be determined after we estimate Mc value.However, the new installation of seismic sensors has no significant effect on changes in the b-value and a-value.The number of seismic stations do not influence the b-value and a-value, because b-value is related to stress regime and a-value is measured by seismisity level or the number of earthquake in the certain time and space.

Fig. 2 .
Fig. 2. Aftershocks distribution of May 2006 earthquake, it was located to the east of the fault plane of Opak Fault (Walter, 2008).

Fig. 3 .
Fig.3.Frequency magnitude distribution shows the linear relationship between frequency of earthquake occurance to the magnitude(Gutenberg and Richter, 1944)

Fig. 6 .
Fig.6.Number of earthquake events on both catalog after declustering process.

Fig. 9 .
Fig. 9.The spatial variation on b-value: Catalog I (a) and Catalog II (b).

Fig. 10 .
Fig. 10.The spatial variation on a-value: Catalog I (a) and Catalog II (b).

Fig. 11 .
Fig. 11.The spatial variation on earthquake density: Catalog I (a) and Catalog II (b).

Table 2 .
General value from both catalog..