# Earthquake Vulnerability Mapping Using Different Hybrid Models

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## Abstract

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## 1. Introduction

## 2. Overview of the Study Area

#### Data Used

**Distance from the fault;**the faults are one of the objective forms of tectonic factors whose presence or absence can be examined in relation to the seismic hazard of different areas. Fault distance plays a key role in resilience to earthquake hazards, as proximity to it causes high seismic risk and damage, and distance from it will reduce the risk and consequently higher resilience [42].

**Population density;**increasing population growth, population density, and poor distribution of services and infrastructure pose risks to society [43]. In recent earthquakes around the world, it can be said that most of the damage is to humans and with the increase in population it is predicted that in the future the mortality rate will be higher. The earthquake hazard coefficient in urban centers is also more complex and riskier due to urbanization without planning and development [44].

**Distance from the hospital;**access to health services such as hospitals play a key role in controlling post-emergency complications and providing earthquake rescue and hospitalization services. Proper and quick access to medical facilities will increase earthquake resilience [45].

**The number of floors;**the number of floors in a building is directly related to the earthquake vulnerability. The higher the number of floors of a building despite its quality, the greater the vulnerability. The number of floors in the building, if not in accordance with safety principles, will definitely increase the damage [46]. Even if the elevation is met with due diligence and calculations, it is difficult for the evacuation of buildings, search and rescue people. In addition, due to the large population of multi-floor buildings, it is slower to do at the time of the accident and due to the high volume of rescue operations; it is very difficult to save the lives of the occupants of high-rise buildings.

**Building materials;**the type of building materials is one of the most important criteria in determining the vulnerability of cities to earthquakes. Obviously, structures made of high strength and standard materials have good earthquake safety [47].

**Area of each piece;**from factors affecting the earthquake vulnerability in the area of buildings. The greater the area of the building, the less waste it will cause to the buildings and the surrounding passages [48].

**Land use;**proper deployment of land uses on the basis of urban planning principles such as proper accessibility, proper distance from the hotspots biological, safety, comfort, and utility can substantially reduce the amount of vulnerability, injury and economic damage [49]. For this reason, the type of urban land use has a significant impact on earthquake vulnerability.

**Distance from the street**; generally, communication networks are set. up for motor, bicycle and pedestrian traffic. In addition, escaping dangerous situations and facilitating the relief and assistance of the injured require roads and streets to pass vehicles. In most earthquake-affected areas, the number of casualties is not always due to the earthquake itself, but often due to the blockage of communications networks. Therefore, communication networks play a key role in reducing earthquake vulnerability [50].

**Slope;**the slope is another factor affecting the vulnerability of earthquakes to urban environments. Degradation in terrain with steep topography, especially at the top of hills and peaks, is greatly enhanced. According to construction standards, a slope of 5 to 9 percent is suitable for urbanization [42].

**Lithology;**lithological conditions are one of the most important environmental parameters in earthquake events. So that the more geological formation of harder minerals, the lower the earthquake wave transmission power, and the weaker the destructive power of the earthquake. Also, the gaps and cracks in the geological formations are one of the most important areas for earthquake power transfer from earthquake focal point to ground level [50]. The geological units are represented in Figure 3, and detailed corresponding descriptions are shown in Table 2.

**Percentage of population under 4 years old and over 70 years old;**in events such as earthquakes, everyone in the community is vulnerable, but older people and children are the most vulnerable groups in a community and more attention is needed to minimize pain and injury [51]. Children do not tolerate disruption well and older people are psychologically fragile because of their disrupted life rhythms. Elderly, in addition to the specific problems of old age, are exposed to social traits such as social incompatibility, social isolation, rejection, and lack of social support [42].

**Distance from the fire station;**access to the fire stations through the communication networks will speed up rescue operations and service the injured. As such, the greater the distance from the fire stations, the more likely it is to be vulnerable [52].

**Distance from the stream;**the presence of rivers will create post-glacial alluvial sands, making the surface vulnerable to vibration and lubrication [53]. As a result, buildings in the vicinity of the waterway network are subject to slip.

**Altitude;**is one of the effective parameters in earthquake vulnerability [54]. The highs and lows available in each area are highly correlated with landslide susceptibility in each area [55]. So, because of the amount of erosion and its relation to human activity, the higher the altitude of an area, the greater the seismic vulnerability.

## 3. Earthquake Vulnerability Mapping

#### 3.1. Background of the Multi-Criteria Decision and Statistical Models Used

#### 3.1.1. Fuzzy Logic

- i.
- Rules Base: This section covers all the rules and conditions that are specified “if … then” by an expert to be able to control the decisions of a “decision system”.
- ii.
- Fuzzy inference: In this section, the degree of fuzzy inputs′ compliance with the basic rules is determined. Thus, based on the percentage of adaptation, different decisions are produced as a result of fuzzy inference.
- iii.
- Aggregation: Because decisions are made on the basis of testing all the rules in parallel, as a result, all the rules calculated by the above method are brought together and a fuzzy set of output is created.
- iv.
- Defuzzification: In the last step, the results of fuzzy inference, which are fuzzy sets, are converted into quantitative data and information. A variety of methods are used for defuzzification, but the COG (relation 1) method provided by the Center of Gravity (COG) is most used [59].

#### 3.1.2. Analytical Hierarchical Process (AHP)

#### 3.1.3. Analytic Network Process (ANP)

#### 3.1.4. Ordered Weight Average (OWA)

#### 3.1.5. Logistic Regression (LR)

_{0}is the width of the model′s origin.

_{n}(i = 0, 1, …, n) estimation coefficients of the sample data, n number of independent variables, and X

_{n}(i = 0, 1, …, n) independent variables. The positive coefficients indicate the correlation between the effective factors and the dependent variable, and the negative coefficients indicate the effect of the opposite. Because the relationship between the independent variables and the probability of occurrence is nonlinear, the iterative algorithm is necessary for parameter estimation [78].

#### 3.2. Validation and Accuracy Assessment

#### 3.2.1. Relative Operating Characteristic (ROC)

#### 3.2.2. Seismic Relative Index (SRI)

#### 3.2.3. Frequency Ratio (FR)

_{i}is the point of occurrence in each class of the Kji criterion, ∑pix is the total number of pixels in the range, li is the pixel values in each class of the Kji criterion, and ∑L

_{i}is the total number of occurrence points in the studied range.

## 4. Experiment Results and Analysis

#### Selection of Training Sites Used in Modeling

## 5. Results

#### 5.1. Seismic Vulnerability Map

#### 5.2. Validation of the Seismic Susceptibility Maps

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Layers standardized in this study. (

**a**). Area of each piece, (

**b**). Building with inappropriate materials, (

**c**). Land use, (

**d**). Distance from the hospital, (

**e**). Distance from the fire station, (

**f**). The number of floors, (

**g**). Distance from the Street, (

**h**). Altitude, (

**i**). Lithology, (

**j**). Distance from Fault, (

**k**). Slope, (

**l**). Distance from the stream, (

**m**). Population density, (

**n**). Percent of population under 4 years old and over 70 years old, (

**o**). Family density.

**Figure 5.**Training sites map extracted from A-ordered weight averaging (OWA) and A-fuzzy hybrid models.

**Figure 7.**Resulting earthquake vulnerability maps based on hybrid models of (

**a**) A-fuzzy, (

**b**) A-OWA, (

**c**) fuzzy-logistic regression (LR) and (

**d**) OWA-LR.

**Figure 8.**Area under the relative operating characteristic (ROC) curve (area under curve; AUC) for hybrid models.

Row | Fault Name | Fault Type | Fault Length (Km) | Minimum Distance from the Site (km) | Maximum Distance from the Site (km) |
---|---|---|---|---|---|

1 | Morvarid | strike-slip fault | 23 | 29 | 43 |

2 | Sartakht | strike-slip fault | 75 | 39 | 71 |

3 | Piranshahr | strike-slip fault | 149 | 34 | 150 |

4 | Dinoor | strike-slip fault | 52 | 66 | 111 |

5 | Sahneh | strike-slip fault | 47 | 103 | 150 |

6 | Nahavand | strike-slip fault | 16 | 133 | 150 |

7 | Zagros | Rivers fault | 250 | 91 | 150 |

8 | Garun | strike-slip fault | 47 | 133 | 138 |

9 | Takht soleaman | strike-slip fault | 30 | 130 | 150 |

Unit | Description | Percent |
---|---|---|

k2av | Andesite volcano | 1 |

kpef | Limestone and conglomerate | 1 |

kupl | Limestone | 8 |

kussh | Dark gray hose and Sandstone | 68 |

peEf | Sandstone and calcareous ash | 2 |

Qft2 | Quaternary formation | 20 |

Operator | Mathematical Expression |
---|---|

X AND Y | Min (X, Y) |

X OR Y | Max (X, Y) |

not X | 1-X |

**Table 4.**The Fundamental Scale for Making Judgments [66].

Definition | The Intensity of Relative Importance |
---|---|

Extremely Preferred | 9 |

Very strongly Preferred | 7 |

Strongly Preferred | 5 |

Moderately Preferred | 3 |

Equally Preferred | 1 |

Intermediate Values Between | 2, 4, 6, 8 |

**Table 5.**The Normalized Weights for the Classes of the Factors Based on Multi-Criteria Decision Analysis (MCDA) Models.

Group | Factors | Class | Pixels in Domain | Percentage of Domain | Weight of AHP-ANP | Eigenvalue AHP-ANP |
---|---|---|---|---|---|---|

Physical | Area | <100 | 2549 | 0.60 | 0.05945 | 0.006 |

100–200 | 341,103 | 80.72 | 0.807 | |||

200–300 | 9554 | 2.26 | 0.023 | |||

300–400 | 27331 | 6.47 | 0.065 | |||

400< | 42051 | 9.95 | 0.100 | |||

Inappropriate materials | <20 | 2549 | 0.60 | 0.05944 | 0.006 | |

20–40 | 390,554 | 92.42 | 0.924 | |||

40–60 | 21947 | 5.19 | 0.052 | |||

60–80 | 6281 | 1.49 | 0.015 | |||

80< | 1257 | 0.30 | 0.003 | |||

Land use | Group 1 | 2698 | 0.64 | 0.07825 | 0.006 | |

Group 2 | 6532 | 1.55 | 0.015 | |||

Group 3 | 4909 | 1.16 | 0.012 | |||

Group 4 | 314,582 | 74.44 | 0.744 | |||

Group 5 | 93867 | 22.21 | 0.222 | |||

Distance from hospital | <1000 | 2613 | 0.62 | 0.06863 | 0.006 | |

1000–2000 | 115,241 | 27.27 | 0.273 | |||

2000–3000 | 154,422 | 36.54 | 0.365 | |||

3000–4000 | 85,553 | 20.25 | 0.202 | |||

4000< | 64759 | 15.32 | 0.153 | |||

Distance from fire station | <1300 | 2613 | 0.62 | 0.06889 | 0.006 | |

1300–2400 | 88,341 | 20.90 | 0.209 | |||

2500–3600 | 89,141 | 21.09 | 0.211 | |||

3700–4800 | 97,463 | 23.06 | 0.231 | |||

4800< | 145,030 | 34.32 | 0.343 | |||

Number of floors | 1 Floor | 320,809 | 75.92 | 0.06866 | 0.759 | |

2 Floor | 32,503 | 7.69 | 0.077 | |||

3 Floor | 46,257 | 10.95 | 0.109 | |||

4 Floor | 16,548 | 3.92 | 0.039 | |||

5 Floor | 6471 | 1.53 | 0.015 | |||

Distance from the Street | <100 | 2578 | 0.61 | 0.06054 | 0.006 | |

100–200 | 27,649 | 6.54 | 0.065 | |||

200–300 | 15,473 | 3.66 | 0.037 | |||

300–400 | 30,891 | 7.31 | 0.073 | |||

400< | 345,997 | 81.88 | 0.819 | |||

Environmental | Altitude | <1400 | 2560 | 0.61 | 0.03929 | 0.006 |

1400–1500 | 13124 | 3.11 | 0.031 | |||

1500–1600 | 175,334 | 41.49 | 0.415 | |||

1600–1700 | 182,582 | 43.21 | 0.432 | |||

1700< | 48,988 | 11.59 | 0.116 | |||

Lithology | K2av | 1484 | 0.35 | 0.07935 | 0.004 | |

Kupl | 4601 | 1.09 | 0.011 | |||

Kussh | 33,517 | 7.93 | 0.079 | |||

PeEf | 288,315 | 68.23 | 0.682 | |||

Qft2 | 94,671 | 22.40 | 0.224 | |||

Distance from Fault | <1300 | 2549 | 0.60 | 0.08766 | 0.006 | |

1300–2400 | 56,655 | 13.41 | 0.134 | |||

2400–3500 | 100,967 | 23.89 | 0.239 | |||

3500–4600 | 113,184 | 26.78 | 0.268 | |||

4600< | 149,233 | 35.31 | 0.353 | |||

Slope | <10 | 2560 | 0.61 | 0.04609 | 0.006 | |

10–15 | 32850 | 7.77 | 0.078 | |||

15–20 | 149,963 | 35.49 | 0.355 | |||

20–25 | 118,412 | 28.02 | 0.280 | |||

25 < | 118,803 | 28.11 | 0.281 | |||

Distance from stream | < 300 | 2558 | 0.61 | 0.06054 | 0.006 | |

300–600 | 322,256 | 76.26 | 0.763 | |||

600–900 | 47,553 | 11.25 | 0.113 | |||

900–1200 | 24,051 | 5.69 | 0.057 | |||

1200< | 26,170 | 6.19 | 0.062 | |||

Social | Population density | <35 | 2549 | 0.60 | 0.08810 | 0.006 |

35–92 | 193,194 | 45.72 | 0.457 | |||

93–150 | 77,680 | 18.38 | 0.184 | |||

160–230 | 71,061 | 16.82 | 0.168 | |||

240–440 | 78,104 | 18.48 | 0.185 | |||

Percent of population | <390 | 2549 | 0.60 | 0.07809 | 0.006 | |

400–990 | 160,639 | 38.01 | 0.380 | |||

1000–1700 | 107,761 | 25.50 | 0.255 | |||

1800–2700 | 90,444 | 21.40 | 0.214 | |||

2800–43000 | 61,195 | 14.48 | 0.145 | |||

Family density | <10 | 2708 | 0.64 | 0.04879 | 0.006 | |

11–27 | 212,088 | 50.19 | 0.502 | |||

28–45 | 107,093 | 25.34 | 0.253 | |||

46–48 | 63,093 | 14.93 | 0.149 | |||

69–110 | 37,606 | 8.90 | 0.089 |

Hybrid Model | Class | Pixel | pi | SV (Occurrence) | Pi | RI |
---|---|---|---|---|---|---|

A-OWA | Very Low | 2553 | 0.60 | 0 | 0.00 | 0 |

Low | 136,693 | 32.35 | 1 | 10.00 | 4 | |

Moderate | 165,176 | 39.09 | 3 | 30.00 | 10 | |

High | 79,187 | 18.74 | 0 | 0.00 | 0 | |

Very High | 38979 | 9.22 | 6 | 60.00 | 86 | |

A-fuzzy | Very Low | 2551 | 0.60 | 0 | 0.00 | 0 |

Low | 125,175 | 29.62 | 1 | 10.00 | 5 | |

Moderate | 165,388 | 39.14 | 3 | 30.00 | 11 | |

High | 84,126 | 19.91 | 0 | 0.00 | 0 | |

Very High | 45,348 | 10.73 | 6 | 60.00 | 84 |

Hybrid Model | AUC | Std. Error | Confidence Interval (95%) | |
---|---|---|---|---|

Lower | Upper | |||

A-fuzzy | 0.805 | 0.0966 | 0.569 | 0.945 |

A-OWA | 0.855 | 0.0830 | 0.627 | 0.970 |

Fuzzy-LR | 0.850 | 0.0872 | 0.621 | 0.968 |

OWA-LR | 0.9 | 0.0667 | 0.683 | 0.988 |

Hybrid Model | Class | No. Pixels in Domain | Percentage of Domain | No. of SV | Percentage of SV | FR |
---|---|---|---|---|---|---|

Fuzzy-LR | Very Low | 20,068 | 4.75 | 0 | 0 | 0 |

Low | 113,849 | 26.94 | 2 | 10 | 2.20 | |

Moderate | 75,272 | 17.81 | 2 | 10 | 3.32 | |

High | 140,599 | 33.27 | 0 | 0 | 0.00 | |

Very high | 72,800 | 17.23 | 6 | 30 | 10.30 | |

OWA-LR | Very Low | 15,254 | 3.61 | 0 | 0 | 0.00 |

Low | 169,861 | 40.20 | 1 | 5 | 0.74 | |

Moderate | 105,310 | 24.92 | 2 | 10 | 2.37 | |

High | 59,440 | 14.07 | 0 | 0 | 0.00 | |

Very high | 72,723 | 17.21 | 7 | 35 | 12 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yariyan, P.; Avand, M.; Soltani, F.; Ghorbanzadeh, O.; Blaschke, T.
Earthquake Vulnerability Mapping Using Different Hybrid Models. *Symmetry* **2020**, *12*, 405.
https://doi.org/10.3390/sym12030405

**AMA Style**

Yariyan P, Avand M, Soltani F, Ghorbanzadeh O, Blaschke T.
Earthquake Vulnerability Mapping Using Different Hybrid Models. *Symmetry*. 2020; 12(3):405.
https://doi.org/10.3390/sym12030405

**Chicago/Turabian Style**

Yariyan, Peyman, Mohammadtaghi Avand, Fariba Soltani, Omid Ghorbanzadeh, and Thomas Blaschke.
2020. "Earthquake Vulnerability Mapping Using Different Hybrid Models" *Symmetry* 12, no. 3: 405.
https://doi.org/10.3390/sym12030405