Analysis of Changes in Seismicity Pattern for Probabilistic Seismic Hazard Analysis (PSHA) and Mitigation: Mapping Probability Difference before the Large Earthquake and Its Implementation in PSHA & Mitigation around Northern Sumatra

The probability difference before the occurrence of a large earthquake is mapped in the northern part of Sumatra, taking the range of Region Time Length (RTL) before a major earthquake (December 26, 2004) around 15 years. By normalizing the absolute value of probability difference between two periods of RTL and before RTL, the Seismic Quiescence Index (SQI) is then defined. Probability difference analysis is done by dividing observations of shallow earthquake periods into two periods based on the similarity gradient of the annual earthquake production, namely 1963-1990 and 1991-November 2004. The results showed that areas with relatively high SQI were consistent with the presence of major earthquake events after November 2004 to 2016 that are sorted by a radius of 300 km with the center point being the epicenter position of the December 2004 earthquake. The implementation of the SQI was then used for probabilistic seismic hazards study and analysis based on an integrated model that is derived based on the estimated of seismicity rate of around the subduction zone and active fault of Sumatra Fault Zone (SFZ) sources. The map of Probabilistic Seismic Hazard Analysis (PSHA) is then constructed based on Peak Ground Acceleration (PGA) estimated for a 10% Probability Exceedance (PE) level in 50 years. The results of this study may be very useful for earthquake mitigation and modeling efforts for PSHA going forward. area of the quiescence as a function of the spatial probability difference that is defined as the SQI. The results are consistent with the places of the sorted of major earthquakes that occurred from December 2004 to 2016 with the radius around 300km. The implementation of SQI into the PSHA analysis and mitigation is done by weighting the model with the SQI that is based on a longer observation period to get a more stable and representative mean long-term seismicity rate model. The existence of a quiescence zone that may have the potential to be filled with large or relatively large earthquake events is located around the western zone of the island of Nias, northern Sumatra Island where some have already filled by inland earthquake events around Pidie in 2016 and the mainland zone around Lake Toba. The result of this study might be very beneficial for the sake of earthquake mitigation and modeling efforts for PSHA going forward.


INTRODUCTION
Based on the results of previous studies it can be concluded that the presence of earthquake precursors is shown by changing the pattern of seismicity (gradient seismicity rate) in space-time in certain seismotectonic areas that correlate strongly with the phenomenon of the existence of zones and periods of seismic quiescence before major earthquake events (Wyss & Habermann, 1988).
Identification and interpretation of patterns of change in the presence of zones and periods of gradient seismicity rate before a major earthquake in seismic hazard studies and mitigation efforts require careful analysis and modeling based on selected of the appropriate reference model to express the natural sensitivity of evolution or changes in seismicity patterns evolution, both in space and time. To go forward analysis or forecasting efforts that can be linked to the possibility of future seismic hazard analysis or future mitigation, the pattern that may express is a clustering model that can be observed or extracted from earthquake data (Michael 1997). One method that is often applied to extract clustering models is by applying seismicity smoothing using a Gaussian function to earthquake catalog data (Frankel, 1995). Some previous studies have implemented the above algorithm for example, (Frankel 1995 obtained support the existence of a quiescence zone and period phenomenon where it is concluded that the presence of a quiescence zone and period is highly correlated with the seismotectonic process which could be associated with stress perturbation phenomenon before a major earthquake event. The results of a more detailed analysis based on the earthquake catalog dataset indicate the presence of 4 temporal and spatial variations which can be concluded to reveal or express characteristics that are consistent with changes in seismicity patterns.
Referring to the definition of Seismic Quiescence by Wyss and Habermann (1988), in this study the identification of quiescence zones in the RTL period is quantified using probabilities so that it can be quantified and mapped two difference, probability models. They are before the quiescence period and during the quiescence period. Furthermore, the probability difference between the two models can be calculated. By normalizing the probability difference, the scale or index quantification of the quiescence period is obtained as a function of probability difference. This index is proposed as the Seismic Quiescence Index or SQI. The implementation of SQI in the preparation of the PSHA map to be used to characterize or estimate the level of seismic hazard in the future can be done by building a seismicity rate model resulting from the merging of subduction zones and active fault data, then weighted by the SQI for the same study area. Furthermore, a Probabilistic Seismic Hazard Analysis (PSHA) map of Peak Ground Acceleration (PGA) was constructed for a 10% Probability of Exceedance (PE) level in 50 years. Estimates of the long-term geology of large earthquake slip rates are based on Billham et al. (2005). Active fault data is based on Natawidjaja (2017). For earthquake catalog data the PUSGEN 2017 catalog (PUSGEN 2017) is used, by applying a correlation distance in the implementation of the seismicity smoothing algorithm of 75 km (Frankel, 1995). The RTL period selected before major earthquake events is based on the gradient analysis of cumulative shallow earthquake production after the declustering process of the 2017 PUSGEN catalog data. The relatively long RTL period is indicated by the presence of a quiescence period before the major earthquake event of 26 December 2004 (Katsumata, 2015) wherein this study it was taken about 15 years, namely the period 1991 to November 2004. While the period 1963 to 1990 could be categorized as a period with 5 background seismicity with the gradient rate is greater than the quiescence period in RTL. The data used for the SQI implementation in the PSHA analysis and mitigation is based on the integration data and method of the previous study (Triyoso et al., 2020a(Triyoso et al., , 2020b, to obtain a more stable of the long-term seismicity rate model.

DATA AND METHODS
The seismic data to develop the probability models used in this study are based on the PUSGEN 2017 earthquake catalog is then carried out by the declustering process to get an earthquake event that is mutually free or independent. The declustering process is carried out using ZMAP software (Wiemer, 2001). The data for the PSHA is based on the merging between two models. They are models around the subduction zone and active fault sources. Data around subduction zone is based on the results of Integration between the two models is done by weighting the A-value model from the earthquake catalog with normalized smoothed seismicity obtained from active fault data.

Seismicity Smoothing
In this study, the application of the seismicity smoothing algorithm with the Gaussian kernel is based on the results of previous studies (Frankel 1995 Triyoso et al. 2020b) which were applied to seismic hazard analysis. In brief, the application and process sequence of this algorithm can be described as follows; the initial stage is to conduct a gridding study area then in each grid the number of earthquakes is calculated that is greater or equal to the reference magnitude (M ref ). This quantity is the number of earthquake events whose maximum likelihood is the value of 10 a or the value of A in the Gutenberg-Richter equation (Gutenberg and Richter, 1944) for earthquake events greater or equal to M ref (Bender, 1983). Data on each grid with this value is then smoothed spatially by using seismicity smoothing algorithm with the kernel in the form of a Gaussian function with a correlation distance c (Frankel, 1995). Referring to Triyoso et al.
(2020a), for each cell or grid i, the value of the smoothed seismicity can be obtained from: where ñi is the normalized value to preserve the total number of earthquake events, ∆ij is the distance between the grid i and grid j, c is the correlation distance. In equation (1), the summation or addition process is carried out on the grid j with a distance of 3c from the grid i.

Probability of occurrence
The probability of an earthquake with a magnitude greater than or equal to the reference magnitude m on the i-th grid during the time interval T below the Poisson distribution is given by, where p (≥m) is the probability of occurrence of the quantity of seismicity smoothed on the grid i for the number of earthquakes with magnitudes greater or equal to the reference magnitude (m).

Probability Difference: Seismic Quiescence Index
Decreased earthquake activity can occur in part from or on all mainshock volumes or from mainshock to the next mainshock. The downward trend in seismic activity trend or decrease in gradient rate of seismicity can continue until a major earthquake or mainshock occurs or a downward trend can occur in a relatively short period before the occurrence of a major earthquake which further increases the trend in earthquake activity. Therefore, the duration of the search for zones and periods of quiescence is very dependent on tectonic activity and structure, loading rate, and stress perturbation which are important parameters related to the likelihood of earthquake precursors that will occur. The application of these terminology zones and quiescence periods as precursors of large earthquakes has been used in many seismic studies in various parts of the world and also the Andaman-Northern Referring to the definition of Seismic Quiescence by Wyss and Habermann (1988), in this study the identification of quiescence zones in the RTL period is quantified with probabilities so that it can be quantified and mapped two probability models before the RTL in the quiescence period and during RTL period. Furthermore, by normalizing the probability difference, the scale or index quantification of the zone and quiescence period as a function of the spatial probability difference for a particular RTL period will be 0 to 1. This index is defined as the Seismic Quiescence Index or SQI. intending to get a more stable and representative mean long-term seismicity rate model.

Probability of Exceedance (PE)
Following the previous study (Triyoso and Shimazaki The above equation gives an annual estimate of the PE level for a given peak ground motion value. For the given T year period, equation (7) can be written as follows, (8) The annual PE level of a given value of the peak of the ground motion is calculated by applying equation (7) for each grid. For a certain duration of time T, the PE level of a specified peak ground ( P motion is calculated using equation (8).

Ground Motion Prediction Equation (GMPE)
In this study, an evaluation of potential hazards, where the source is a megathrust or a subduction  Figure 1A is the result of the annual seismicity rate model of the study area with a radius of 400km with the center being the epicenter of the earthquake of December 26, 2004, with Mw ≥ 5.0, generated by data before the RTL period. It is the period of the year of 1963 to 1990. Figure 1B Figure 2A shows the normalized probability difference in this study is defined as the Seismic Quiescence Index (SQI) which is based on the results of Figure 1 (A and B). Figure 2B  the PGA for the 10% PE level can be calculated for 50 years. Figure 3, is the mean PGA map between of three differences GMPE of 10% PE level of 50 years, where the SQI is included.

CONCLUSIONS
In this study, identification of the quiescence zone in the RTL period is quantified based on the probability difference between the two probability models before the quiescence period and during the RTL period. By normalizing the probability difference, the scale or index quantification of the zone or 13 area of the quiescence as a function of the spatial probability difference that is defined as the SQI. The results are consistent with the places of the sorted of major earthquakes that occurred from December 2004 to 2016 with the radius around 300km. The implementation of SQI into the PSHA analysis and mitigation is done by weighting the model with the SQI that is based on a longer observation period to get a more stable and representative mean long-term seismicity rate model. The existence of a quiescence zone that may have the potential to be filled with large or relatively large earthquake events is located around the western zone of the island of Nias, northern Sumatra Island where some have already filled by inland earthquake events around Pidie in 2016 and the mainland zone around Lake Toba. The result of this study might be very beneficial for the sake of earthquake mitigation and modeling efforts for PSHA going forward.

Availability of data and materials
Earthquake Catalog Data is based on PUSGEN Catalog. It has been public domain data