Fuzzy Logic Approach for Earthquake Risk Around Menanga Fault, Lampung

Earthquake mitigation was one of the most complex and challenging parts in disaster risk management due to its complex aspects because there will be surprises of magnitude and uncertain points of shocks. Hence, comprehensive and detailed analysis and modeling is needed to solve this kind of complexity. Fuzzy logic considers the promising approach for risk mitigation modeling with its algorithm that could help to model the uncertainties and ambiguities. Menanga Fault was the active fault that is now believed as the source of the earthquake that happened earlier in the Pesawaran area, Lampung. This paper aims to determine the earthquake risk level around Menanga Fault with fuzzy logic approach. The result of this research shows three levels of risk around the Menanga Fault and the highest was in the south and west area, especially in the coastal area.


Introduction
Indonesia has a complex tectonic setting due to its location at the meeting point of three tectonic plates, named Indo-Australian, Pacific, and Eurasian plates, thus Indonesia has a significant to disasters prone to many other nations [1] [2], especially earthquake and tsunami for the coastal area.Geology hazards are event caused by natural geologic process which cause a damage and loss to human life, natural environment, and economic [3].Hazards pose a potential damage damage and loss for the environment and society.
Earthquake prone area are commonly close to subduction zones and nearby active fault [2].Lampung, in the south-tip of Sumatera island, is one of the area in Indonesia which has a high earthquake risk [4].Recently, Pesawaran area was one of the area that often hit by earthquake.There are some previous research about the earthquake and the recent finding revealed that the earthquake in Pesawaran area was related to Menanga Fault Activity [5].
Earthquake is one of the most deadliest (Figure 1) and complex hazards due to its uncertainty in many aspects such as the surprises of magnitude and uncertain points of shocks [6].Moreover, the earthquake process usually associates with physical characteristic and behaviour of material when the shock happened [7].Hence, comprehensive and detailed analysis and modeling is needed to solve this kind of complexity.Researcher already develop several methods to determine the earthquake risk, such as probabilistic and scoring method [8,9], formulative method [10], zoning method [2], and fuzzy logic approach [11].Fuzzy logic considers the promising approach for disaster risk modeling with its algorithm that could help to model the uncertainties and ambiguities.Previous research have applied the fuzzy logic model in different kind of hazards [12][13][14][15].This research aims to applied Geographic Information System (GIS) with fuzzy logic overlay and Analytical Hierarchy Process (AHP) method to assess the disaster risk related to earthquake near Menanga Fault, Pesawaran area.

Figure 2. Administrative and Geological Map of Pesawaran Regency
Based on the Regional Geology Map of Tanjungkarang [16][17], the Pesawaran Area is composed various of lithologies and structural geology (Figure 2).Geological structures that formed in this area are subject to the subduction and the northern block was the moving up part of the fault.Lithology composition in the vicinity of Menanga fault consists of Undifferentiated Gunung Kasih Complex (Pzg) as metamorphic rocks, Menanga Formation (Km) as pre-tertiary sedimentary, Sabu Formation composed of fluvial sedimentary rocks, Tarahan Formation (Tpot) and Hulusimpang formation (Tomh) as pyroclastic rocks.From Holocene, this area includes Young Volcanic Deposits (Qhvp) and Alluvium (Qa) in the western and southern area.
Menanga Fault became one of the large structures in the Pesawaran Area.Menanga Fault occurred as a reverse fault that showed metamorphic rocks on the northern part of the fault as the basement lifted and exposed to the surface.The existence of Menanga Fault indicated the compressional regime of tectonic that possible to generate an earthquakes.Later, Menanga Fault is indicated as an active fault which triggers the occurrence of swarm earthquakes [5].

Method
Fuzzy logic was used to determine the class of risk by assessing the degree of membership of each parameter [12].The fuzzy logic provides the opportunity to flexibly combine parameters in weighted maps and regard spatial objects on a map as members of a set [14].The application of fuzzy logic in earthquake risk analysis involves these steps: 1) Defining the input and output variables.Input variables include the exposure and vulnerability index, lithology, and distance from the epicenter, while the output variable is the probability rank of damage in the event of an earthquake, 2) Linguistic variable definition and fuzzy set creatio to represent the rank of variables.All of the input data for fuzzy overlay should in Raster, thus for the lithology aspect, we provide the raster by AHP method, 3) The fuzzy rule construction that define how the input variables affect the output variable.The fuzzy membership function and the fuzzy operator of the earthquake were done using ArcGIS Software.We used four operators for assessing the fuzzy logic approach, namely Fuzzy OR, Fuzzy Algebraic SUM, Fuzzy Algebraic PRODUCT, and fuzzy GAMMA operator, and the final step 4) Fuzzy inference and validation.
The main logic used in this research are: 1) The region with high occurrence of earthquake and near the main shock location tend to have a higher risk level, 2) Area with loose sediment or rocks can significantly influence the type of ground shaking and tend to experience more damage compared to the compacted body, 3) The population and the total number of buildings that reflected by vulnerability index consider the economic and physical assets to suffer loss and damage.

Exposure and Vulnerability Index
The exposure data reflects the total population, total area, population density, and number of facilities, while the vulnerability index is the calculation result based on the exposure data.The data of economic vulnerability index (IKE), social vulnerability index (IKS), and facility vulnerable index (IKF) and overall vulnerability index (VI) [18] are shown in table below.Gedong Tataan and Tegineneng District were the most prone area with high value of vulnerability index.The parameter of vulnerability index is processed with a large fuzzy membership due to its character which the increase in its value exerts greater influence in decision making.It is already revealed that distance from epicentre serves as a proxy for shaking intensity [19].Generally, the intensity of ground shaking becomes weak away from the fault,but still affected by the surface condition (lithology, building characteristics).Moreover, epicentral distance is a more precise indicator for small to mid -level earthquakes [20].We prefer to use the distance parameters rather than Peak Ground Acceleration (PGA) prior to scale concern.
Based on the latest USGS data [21], there are five earthquake points near Menanga Fault (Table 2).The distance is divided in to 3 classes based on Euclidean distance measurement results.This parameter is processed with small fuzzy membership because the least distance means the greater influence on risk.

Lithology
Lithology affects the ground-shaking rhythm that furtherly creates damage to the surface.Lithology input are in the form of regional geology formation.The dynamic amplification effects is higher for the soft rock slopes rather than for hard rock slopes [7].We simplify the lithology into crystalline rocks, sedimentary rocks, and unconsolidated rocks.The amplification effect in sedimentary rocks can cause surface ground motions to be stronger than expected based on the magnitude of the earthquake.Furthermore, sedimentary rocks are susceptible to liquefaction, which exacerbates the amplification effect of the ground acceleration, causing various types of surface damage, such as subsidence and landslides.On the other hand, crystalline rocks, which are characterized by their higher rigidity, exhibit a lower amplification effect and less susceptible to liquefaction.Meanwhile, unconsolidated rocks have a lower resistance to ground shaking and are more prone to liquefaction due to their porosity and lack of cementation.The unconsolidated rocks undergo compaction and dilation cycles as the seismic waves propagate through the ground.Scoring with the AHP method was carried out on these three rock types.The value for each class is 0.11 for crystalline rocks, 0.31 for sedimentary rock, and 0.58 for unconsolidated rock.The parameter of lithology is processed with a MSlarge fuzzy membership due to its character which the increase in its value exerts great influence in decision making.The following table provide the input variables of fuzzy logic overlay in this research.

Fuzzy overlay
The output generated from the fuzzy overlay analysis is the degree of fuzzy membership which the value ranging from 0 to 1 [13].The rank number which closer to 1 means the higher degree of risk, on the contrary the number which closer to 0 means the lower risk.The fuzzy analysis were carried in four algorithms, the OR, SUM, PRODUCT, and GAMMA.Each algorithm generates fuzzy interval of different membership.The OR operators provide the output from single evidence, the SUM operator tend to provide increasing value as the effects of aljabar substitution logic, while the PRODUCT operator tend to result the decreasing value as the effect of multiple aljabar logic.In addition, the GAMMA operator is an algebraic of fuzzy product and fuzzy sum, which are both raised the gamma power.
The result of Fuzzy Value through PRODUCT, SUM, and OR operators are relatively the same, while the GAMMA operation resulted different classification area of risk (Figure 3-4).The result of PRODUCT, SUM, and OR operation did not show any significant different risk in coastal and land area or in the different type of lithology and vulnerability characteristic.The distance of the epicentrum plays a huge impact for the risk assessment hence risk seems to be homogeny in the area with certain radius from the main shock point, while for the GAMMA, the operated results was majorly afflicted by lithology characteristic.
Geological approach on assessments of zone stability shows how stable the area is in response to earthquake.In terms of compactness, hardness, and material, the rock's physical properties reveal the state of its strength to withstand load and pressure.The morphology and location of the land can reflect how stable the land is against the possibility of damage, and other secondary hazards, such as landslide and liquefaction.Earthquake character is a measure of how strong an earthquake is based on the acceleration of the ground and earthquake magnitude.
The verification method was performed by comparison of existing earthquake risk map and newly computerized risk map from fuzzy approach.Based on hazard risk index map [18], Pesawaran area categorized as medium risk from central to southern area and low risk for the rest (Figure 5).GAMMA operation take the best role in adjusting geological logic while not only suitable with hazard risk index map from BNPB but also give some additional details information in several area that involve lithological data significantly.Furthermore, red polygon as high rank in eastern area caused by unconsolidated material existing which led more potential damage.The fuzzy logic overlay revealed that Way Lima, Padang Cermin, Marga Punduh, Punduh Pidada, and Teluk Pandan District -especially the coastal area-were in the higher risk than compared to other districts.Based on this analysis, it is necessary to define the earthquake-prone area by using fuzzy logic approach.GAMMA operator was the best choice due to its detail and logical result but still it can not depict the effect of the morphology so we still need to compared it qualitatively with previous risk map in this paper, hence more parameters and detailed characterization were needed in the future to provide more comprehensive results.

Conclusions
Based on the computed fuzzy parameters and operators, the earthquake prone area of Pesawaran Regency were concentrated in the coastal area and west part of the study area, administratively it is belongs to Way Lima, Padang Cermin, Marga Punduh, Punduh Pidada, and Teluk Pandan.The fuzzy logic approach with GAMMA operator represents a potent instrument for combining fuzzy sets, rendering it the optimal selection for identifying earthquake-vulnerable zones.Further research is needed to substantiate the effectiveness of this proposed technique.Nonetheless, we maintain the conviction that the application of fuzzy logic and the GAMMA operator has the potential to enhance disaster management and mitigate the consequences of seismic events.

Figure 3 .
Figure 3. Fuzzy overlay result for OR and PRODUCT operator

Figure 4 . 7 Figure 5 .
Figure 4. Fuzzy overlay result for SUM and GAMMA operator

Table 1 .
Vulnerability Index

Table 3 .
Input variables and classification