Spatial distribution analysis of seismic activity based on GMI, LMI, and LISA in China

1 Introduction

Nowadays, human activities which affect the nature are becoming more frequent [1,2,3,4,5,6,7], and more and more natural disasters appear in human life, such as mudslide, earthquake, and so on [8,9,10,11,12,13]. The occurrence of earthquakes is a very complicated process that causes significant harm to humans and usually causes incalculable losses [14,15,16]. Earthquake management and seismogenic mechanisms determine the temporal and spatial propagation of seismic activity. Due to the complexity of seismic activities, the research on the temporal and spatial propagation characteristics of earthquakes is not perfect [17,18]. Earthquake is not an overnight outbreak, it is an extremely long and complex process, which determines the difficulty of its research [19,20]. Therefore, the study of earthquakes is of great significance, and seismology has become a hot topic.

Located in the Ring of Fire, China has been a quake-prone country, some scientists and researchers consistently study earthquakes in China [21,22,23]. In the 1960s, using the optimal segmentation method, they discovered that earthquakes act in groups and introduced three periods (the frequent period, average period, and less frequent period) in relation to seismic activity in China. Zhang [24] and Li et al. [25] used wavelet analysis to analyze seismic activity trends for the future. Wang et al. [26] analyzed three major Chinese natural disasters, and concluded that the reviewed earthquakes concentrated in the southwest of China and Taiwan area. Pei and Zhou [27], proposed a simple statistical analysis called the tablets method to investigate the distribution of epicenters, which detects earthquake line structures. According to emergency investigations and remote sensing, Zhao et al. [28] found that different influencing factors, such as the seismic fault, river, slope aspect, slope angle, rocks, and elevation, have different influences on landslide occurrences, and the coseismic landslides in the hanging wall area and footwall area present obviously different characteristics. Additionally, the post-earthquake effect impacted the recent Sedongpu landslide. Based on the analysis of the earthquake catalog from January 2000 to April 2008, Shi et al. [29] have investigated seismicity change and b-value variation prior to the Ms8.0 Wenchuan earthquake. The results show clear drop in both monthly and quarterly frequency of earthquakes during 2005–2006. Based on the network catalogue, the temporal and spatial distribution of the aftershocks were analyzed by Li et al. [30]. The frequency-magnitude relationship of the aftershocks shows that the activity of aftershocks turned to be weak in 4 months after the main shock. The spatial distribution of the energy released by aftershocks shows that even within 6–24 h after the main shock, the tendency of development of aftershocks in a long time could be captured.

Not only in China, earthquakes happen all over the world from time to time, endangering the safety of human life and property. Grecu and Mateciuc [31] pointed out that the law of seismic evolution is realized by a characteristic function. Conversely, Telesca et al. [32] developed the b-value spatial–temporal scan method, and concluded that earthquakes exhibit long-range correlation features in spatio–temporal seismic fluctuations, which is based on the self-organized criticality theory. In a study by Ogata [33], geostatistics is more intensely applied in seismology. Wang et al. [34] present an inventory of 7,837 coseismic landslides based on the interpretation of the PlanetScope images. And they analyzed the local and global area-volume relationships and their spatial distribution. The observed density of the landslides is jointly controlled by the ground motion, slope gradient, topographic wetness index, and, to a lesser degree, tectonic features, e.g., anticlines and faults. Zohar et al. [35] used Geographic Information System (GIS) to map and evaluate the distribution of the damage and to search for recurring patterns. The temporal appearance of the northern earthquakes is clustered; the central earthquakes are more regular in time, whereas no damage from the north-central and the central quakes, with the exception of the 363 earthquake, seems to have occurred south of the Dead Sea region. Vasylkivska and Huerta [36] utilized the nearest neighbor approach to represent a practical first step toward identifying statistically correlated clusters of recorded earthquake events. They studied the Oklahoma earthquake catalog’s inherent errors, empirical model parameters, and model assumptions in detail.

The premise of earthquake prediction is that we should understand the temporal and spatial characteristics of earthquake occurrence, the physical mechanism of the earthquake occurrence process, and the earthquake management and seismogenic characteristics of regional and local structures. This can provide a reference information for earthquake prediction. Only by mastering the temporal and spatial propagation characteristics of earthquakes can the accuracy of earthquake prediction be improved. Therefore, the temporal and spatial characteristics of earthquakes studied in this article are of great significance both academically and in ensuring people’s safety [37,38]. At present, scholars have also made some achievements in the study of earthquakes in the application of spatial statistics. However, most analyses ignored the interaction between regions [39]. On the contrary, this article studies the spatial–temporal propagation characteristics of earthquakes, which is very useful for processing spatial attribute data. In this article spatial autocorrelation is used for detailed analysis of the spatial–temporal propagation characteristics of China’s continental earthquakes.

2 Methods

Spatial autocorrelation analysis [39,40] can detect the spatial correlation between the two phenomena. If the survey data are consistently of high (or low) values both at the observation and at the surrounding region, the spatial autocorrelation is positive. Otherwise, the spatial autocorrelation is negative. If the observed values are rendered randomly, it means no spatial correlation occurs [41]. Spatial autocorrelation analysis is divided into global spatial autocorrelation and local spatial autocorrelation [42].

Global spatial autocorrelation analysis is a description of spatial characteristics of properties throughout the region [43]. This article uses Moran’s I index, which is expressed by the following formula [44]:

where I is the index of Moran; x _i is the value of observations in region i; w _ij is the spatial weights matrix; the variance of x _i is S 2 = 1 n ∑ i ( x i − x ¯ ) 2 ; and the mean value of x _i is x ¯ = 1 n ∑ i = 1 n x i .

Then, Z scores from the following formula apply to test the significance of global spatial autocorrelation index I:

where E ( I ) = − 1 ( n − 1 ) ; var ( I ) = E ( I 2 ) − E ( I ) 2 .

The global spatial autocorrelation assumes that the space is homogeneous. However, spatial heterogeneity is more common than spatial homogeneity. Local spatial autocorrelation can grasp the spatial heterogeneity more accurately and calculate the spatial position and range of the aggregate. In this article, Moran’s I index is used to measure the local spatial autocorrelation indexes with the following formula:

where I _i (or I _j ) represents the local Moran’s I value in region i (or j), z _i is the standardized form of observed values in region i, and w _ij is the standardized spatial weights matrix. The Z scores in region i are as follows:

where the local Moran I value’s standard deviation in region i is presented by S ( I i ) = var ( I i ) .

3 Results

Earthquakes are difficult to observe in relatively short time periods and small spatial areas [45]. Therefore, we selected a large-range spatio–temporal scale to study the space and time properties of earthquake activity. The mainland China (33 provinces) was the study region. The study dataset contains earthquakes with a Richter scale magnitude greater than two [35]. Each province is set as a spatial unit. We analyzed 73,484 earthquakes from 1970 to 2013 (Figure 1) from the United States Geological Survey.

Figure 1

The epicenter distribution from 1970 to 2013 in mainland China.

We grouped the data into nine sub-periods [46]. Each sub-period was analyzed with global spatial autocorrelation using the spatial autocorrelation tool in ArcGIS. The frequencies of earthquake activity in each province for each sub-period are used as input fields and the inverse distance works as the conceptualization of spatial relationships. Moran’s I Index and Z-value sequence from 1970 to 2013 are shown in Figures 2 and 3. And the numerical values of Moran’s I index, Z-value, and P-value for each period are shown in Table 1.

Figure 2

Moran’s I index sequence diagram of earthquake frequency.

Figure 3

Z-value sequence diagram of earthquake frequency.

There are two methods for local spatial autocorrelation analysis: The Moran scatter plot and the Moran I local statistics, revealing spatial correlation characteristics from different perspectives [47].

The horizontal coordinate of the Moran scatter plot is a standardized attribute value for each spatial unit (the average number of earthquakes in the region), while the vertical coordinate represents the average of the attribute values with adjacent units, determined by the spatial connection matrix (space-vector hysteresis) [48]. The Moran scatter plot is composed of four quadrants: the first quadrant (HH, “high-high”); the second quadrant (LH, “low-high”); the third quadrant (LL, “low-low”); and the fourth quadrant (HL, “high-low”). The first letter stands for the value of a unit, and the second is the value of the surrounding areas. The values in HH and LL quadrants are heterogeneous and they show a strong positive correlation; however, values in LH and HL quadrants show a strong negative correlation, which also means heterogeneous.

The Moran scatter plots in different sub-periods are shown in Figure 4. Then, we counted the number of regions in the four quadrants, which are shown in Table 2.

Figure 4

Scatter plot of Moran’s I index for each period. (a) 1970–1974, (b) 1975–1979, (c) 1980–1984, (d) 1985–1989, (e) 1990–1994, (f) 1995–1999, (g) 2000–2004, (h) 2005–2009, and (i) 2010–2012.

Since the Moran scatter plot does not test the level of statistical significance for the spatial pattern of heterogeneity, Local Indicators of Spatial Association (LISA) can be used to qualitatively assess the extent of correlation with neighboring regions for each spatial unit. In order to obtain the LISA clustering analysis, the Anselin Local Moran’s I tool in ArcGIS was applied to the outlier distribution analysis of provincial earthquake activity in each sub-period. It is also necessary to set the inverse distance as the conceptualization of spatial relationships in local spatial autocorrelation analysis.

Three or four classes compose each sub-period (Figure 5) used in LISA agglomeration for time sub-periods. Figure 5(a)–(i) represents the LISA cluster map in the 1970–1974, 1975–1979, 1980–1984, 1985–1989, 1990–1994, 1995–1999, 2000–2004, 2005–2009, and 2010–2013 sub-periods, respectively. Quadrant colors correspond to those in the Moran scatter plot to emphasize the local indicators in spatial agglomeration areas with statistical significance (P < 0.05). Light red represents the HH quadrant and blue represents LL. A positive spatial autocorrelation was observed from the result. Meanwhile, light blue and light purple represent HL and LH, respectively, and a negative spatial autocorrelation was observed.

Figure 5

LISA agglomeration of the year. (a) 1970–1974, (b) 1975–1979, (c) 1980–1984, (d) 1985–1989, (e) 1990–1994, (f) 1995–1999, (g) 2000–2004, (h) 2005–2009, and (i) 2010–2013.

4 Discussion

To ensure that the results are more credible, the Gutenberg-Richter formula is used to analyze the integrity of the data [49]. In order to determine the initial magnitude of the seismic data used in this study, the error of the data points caused by the omission of the base station measurement is determined. Then, we used the processed data to analyze the spatial autocorrelation of earthquakes in mainland China.

First, the seismic data in the study area are discretized by province, and the discretized data are divided into five years as a study area. During the time period, we obtained and analyzed the global autocorrelation coefficient Moran’s I [50], and further obtained the local Moran scatter plot. Then, we drew a cluster map to get the relationship between specific areas and the changing trend of the state. Finally, combined with the geological structure of the study area, the reasons for the formation of the agglomeration pattern are analyzed.

Through the analysis of global spatial autocorrelation and local spatial autocorrelation of earthquakes in mainland China, the following conclusions are drawn:

(1) Earthquakes in Chinese mainland have significant global autocorrelation features. The Global autocorrelation coefficients were positive, and the earthquake pattern showed a spatial agglomeration feature of earthquake activity in China.

(2) The frequency of earthquakes in mainland China presents spatial clustering characteristics. However, there were a few provinces that showed negative spatial autocorrelation features. Earthquakes occurred not only in response to adjacent areas, but were also influenced by regional geological structures. Furthermore, the 1975–1979 agglomeration map changed greatly after the Tangshan earthquake.

(3) Practice proved that spatial autocorrelation could be used to analyze earthquake clustering, exploring the potential correlations between local and neighborhood regions. However, incomplete seismic data and different standards for defining spatial weight matrices may have influenced the accuracy of our results where further research is required.

Due to the limited scope of the author’s consideration, there are still many ill-considered situations in this article [51]. For example, the seismic sample data itself may be incomplete, the analysis focus is different [52], the criteria used to define the spatial weight matrix in spatial autocorrelation are different [53], the selection of clustering indicators will affect the results of the temporal and spatial propagation characteristics of earthquakes to a certain extent [54], and further research is needed in this regard.

5 Conclusion

The results in Table 1 show that the Z scores are greater than 1.96, which means the Global Moran’s I index is significant for all sub-periods (P < 0.05) except the sub-period from 1975 to 1979. Moran’s I indicators are positive in all sub-periods from 1970 to 2013, indicating a positive correlation and spatial agglomeration characteristics.

The changes in Moran’s I indices and Z scores are similar (Figures 2 and 3). The obvious inflection points appeared in three sub-periods: 1975–1979, 1995–1999, and 2005–2009. Important points of increase correspond to 1980–1984, 2000–2004, and an upward trend for the last period.

The review of data analyzed shows that China’s earthquake trends changed persistently from 1970 to 2013. Furthermore, the correlation between areas and their adjacent areas grew stronger, and the volatility of the correlation index shows an upward trend. The perspective of tectonic movement can explain this phenomenon.

Friction produces great energy and its storing occurs differently across geological locations, resulting in the different frequencies of earthquakes in different regions [55]. In periods of high-frequency high-magnitude earthquake, the correlation among different neighboring regions gradually increased due to interactions in space. Then, seismic activity calmed and tend to be stable, while the differences in the earthquake occurrence frequency between different regions grew larger. Meanwhile, the correlation among different neighboring regions grew weaker (Figures 2 and 3).

Figure 4 shows that most points fall into the LL and HH quadrants, making obvious the spatial cluster feature of epicenter. Table 2 shows that over 80% of points fall into the HH and LL quadrants, indicating that the earthquake frequency of the local area have strong positive spatial autocorrelation and a significant local agglomeration. The remaining points fall in the LH and HL quadrants, showing strong negative spatial autocorrelation, rendering a local discrete distribution pattern.

Figure 5(a) shows that small quakes occurred within the 1970–1974 sub-period in the Hubei Province, Guangdong Province, and two provinces in western China (Tibet and Xinjiang). We concluded that earthquake frequency was a positive spatial autocorrelation in 1970–1974.

Conversely, Figure 5(b) shows higher earthquake frequency in 1975–1979 than that in the previous sub-period (1970–1974), from Tibet, Qinghai, to Sichuan, Inner Mongolia, and to Tianjin, in North China. Although earthquake frequency increased during this stage, southern China was almost unaffected.

On the other hand, Figure 5(c) shows a period of calmness during 1980–1984. Since Beijing was already in LH state, and is almost surrounded by Hebei, the “high” status should refer to Hebei, not Beijing. Guangdong, Jiangxi, and Hubei remained in LL state. Five provinces (Tibet, Qinghai, Sichuan, Yunnan, and Gansu) all stayed in HH state.

Figure 5(d) shows that after the Tangshan earthquake, North China experienced a calm period in 1985–1989. Meanwhile, earthquake location clustered in western China. Four provinces (Xinjiang, Gansu, Qinghai, and Tibet) were in HH state, while Guangdong and Anhui stayed in LL state.

The spatial pattern of HH and LL states in 1990–1994 in Figure 5(e) is similar to Figure 5(d). This means that the local spatial autocorrelation had no obvious difference, and earthquake frequency maintained a relatively stable state in the two sub-periods of 1985–1989 (Figure 5(d)) and 1990–1994 (Figure 5(e)).

Figure 5(f) shows that Qinghai, Tibet, and Gansu were in HH state, while Guangdong, Jiangxi, Anhui, and Jiangsu were in LL state in the 1995–1999 sub-period. Conclusively, the Qinghai-Tibet region remained earthquake-prone.

Figure 5(g) shows a clear aggregation state. The western region, (Qinghai, Tibet, Xinjiang, and Gansu,) were in HH state, while the adjacent southeast region (Guangdong, Jiangxi, Fujian, Zhejiang, and Jiangsu) were in LL state in the 2000–2004 sub-period.

Figure 5(h) shows that Tibet, Qinghai, Gansu, and Yunnan were in HH states, while Guangdong was in LL state in the 2005–2009 sub-period.

Figure 5(i) shows that during the 2010–2013 sub-period, Tibet, Qinghai, Gansu, and Xinjiang had significant HH states, while Guangdong, Jiangxi, and Jiangsu had significant LL states.

LISA analysis [43] showed that southern China has been in calm state since 1970, especially Guangdong and its surrounding areas. Then, due to the impact of large seismic activities, frequency in north China was high between 1975 and 1979. However, the Qinghai-Tibet plateau area experienced frequent earthquakes, which is related to its geography [56]. High-frequency seismic areas gradually increased across the continent, from west to east.

In addition, the HH quadrant state showed strong spatial agglomeration in 1975–1979 period, especially serious in north and northeast China. It is not surprising that the famous Tangshan earthquake occurred during this time. Then, after 1985–1989 period, this area remained calm for following years.