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Spatial Statistical Technique in relating earthquake epicentres with structural features

A K Saraf
A K Saraf, B Sarma and Chandramani
Department of Earth Sciences 
Indian Institute of Technology, Roorkee, India 
saraffes@iitr.ernet.in
 


The Geographic Information System (GIS) is not only capable of displaying spatial data but also allows spatial data analysis. The ability to manage geographic objects across different scales has made GIS a very valuable tool for many research fields and applications. The characteristic that makes spatial data unique is the location information embedded in it apart from the attributes describing the characteristics of the observations (Lee and Wong, 2000). Observing the importance of spatial data, it has become very essential to combine statistical analysis with GIS so that geographic data can be processed, analysed and mapped in the same working environment.

The state of Himachal Pradesh in India and its neighborhood, which forms an important part of the Western Himalayas, is seismically a very active region. Historical documents show that a large number of earthquakes of moderate to high intensities have occurred in this region in the past. Most of the earthquakes in the Himalayas are associated with thrusts and faults that are a result of movement of Indian Plate towards north direction. We need a close network of seismographs to record all the tremors and their regional implications for a correct understanding of the various processes responsible for extensive seismic activity (Srikantia and Bhargava, 1998). The study of various aspects of the structure and tectonics suggest that major earthquakes in the Himalayas occur as the Indian shield is thrust beneath the Himalayas. The severity of tectonic activity has resulted in the development of a complex geological picture. This area is conspicuous by the presence of numerous thrusts and faults. Himachal Pradesh is a confirmed seismic zone with several NW-SE trending thrusts (Srikantia and Bhargava, 1998). The seismic status of many of these thrusts is not known.

The position of the epicenters and the associated information of the earthquakes that occurred in an area can help to establish a relationship between the geological structural features and the occurrences of earthquakes. Since the locations of earthquake epicenters are represented as points in geographical space, the analysis of those can be done with the help of point pattern analysis in spatial statistics, and the results of epicenter distribution trend is analysed with the orientation of prevailing and prominent faults and thrusts then a relationship between epicenter distribution pattern and structural features can be determined and identified. This paper demonstrates a GIS based spatial statistical analysis technique to analyse a relationship between the distribution patterns of the reported earthquake epicentres and the geological structures mainly thrusts, faults and folds occurring in the area.

Characteristics of point data pattern
Points may be used to indicate spatial occurrences or events and their spatial pattern. Point pattern analysis is concerned with the location of events and with answering questions about the distribution of those locations, whether they are clustered, distributed randomly or regularly. Point pattern analysis is used to identify whether occurrences or events are interrelated or not. The main characteristic of the point data pattern is its central tendency. The central tendency of a set of values gives some indication of the average value as their representation. When dealing with spatial data set, the concept of average in classical statistics can be extended to the concept of center, as a measure of spatial central tendency. This is because geographical features have spatial reference in 2-D space; the measure of spatial central tendency needs to incorporate coordinates that define the locations of the features (Lee and Wong 2000). Central tendency in the spatial context will be the mean center, the weighted mean center or median center of a spatial point distribution.

Mean Center
The mean center, or spatial mean gives the average location of a set of points i.e. if the points in the distribution represent occurrences of earthquakes in different periods of time, then the mean center of the distribution of those locations will represent the location around which the distribution of all the epicentres is having most balanced clustering (Fig. 1). 

Median Center
The concept of median of a set of values as described in classical descriptive statistics can be extended to the median center of a set of points but the median in geographical space cannot be defined precisely. So the concept of median center is the center of minimum travel i.e. the total distance from the median center to each of the points in the region is the minimum.

Standard distance
In spatial statistical analysis, standard deviation is expressed as standard distance. While standard deviation indicates how observations deviate from the mean, standard distance indicates how points in a distribution deviate from the mean center. Standard deviation is expressed in the units of observation values, but standard distance is expressed in distance units. In terms of its application, standard distance is usually used as the radius to draw a circle around the mean center to give the spatial spread of the point distribution it is based on. 

Standard deviation ellipse
When the set of point locations comes from a particular geographic phenomenon that has a directional bias, standard deviation ellipse is used instead of standard distance circles. Similarly, the geological structural features control earthquake epicenters, thereby showing a directional bias in their distribution. Under these circumstances the standard distance circle will not be able to reveal the directional bias of the process (Lee and Wong 2000). The deviation along the major axis will be the direction of maximum spread of the points and the minor axis will be the direction of minimum spread of the points. 

Methodology
The methodology adopted in this study can be described in the following steps. All spatial statistical analysis were performed using Arc View (AV) scripts provided by Lee and Wong (2000). Rose diagram were plotted using Geo Tools (Ver. 1.0) Extension developed by T. Thatcher (available at http://www.dtmgis.com/GeoTools.htm):
  • The map of Himachal Pradesh and its surrounding areas is digitised and the epicenters of the recorded earthquakes of more than 4 magnitudes in the region were plotted (total 253 events). From the geological map of the Himachal Pradesh the faults and thrusts (after Saraf, et. al. 2002) are digitised and taken for analysis. (Source: USGS Earthquake epicenter data with magnitude≥ 4 occurring between 1839-1994).
  • Various spatial statistical operations were performed like the calculation of mean center, weighted mean center, median center, standard distance, standard deviation ellipse etc. on the epicenter data. The horizontal location accuracy of earthquake events has been accepted assuming to be the best made available by USGS.
  • Quadrat analysis and the nearest neighbour analysis were performed on the epicenter dataset to find out the spatial pattern in the point distribution.
  • Finally, the spatial auto correlation coefficients like the Gearyís ratio (C) and Moranís (I) were calculated to measure and test how clustered/ dispersed the positions of epicenters were in space with respect to their attribute values i.e. the magnitude of the earthquakes.
Results and Dissussion
The statistical operations for central tendency of the distribution for the data of earthquake epicenters in and around Himachal Pradesh were done with the help of Arc View 3.2 GIS software. The spatial mean and the median center for the distribution of the epicenters were calculated (Fig. 1). Both spatial mean and the median center when calculated with weightage given to the magnitude of the earthquake for that particular epicenter did not show much variance in their locations, thereby indicating that the epicenters with contrasting magnitude i.e. very low or very high compared to the magnitude of the majority of the earthquake epicenters do not lie scattered at far distant places. It, thereby, shows that the entire area is continuously being struck by earthquakes of varying magnitude that seem to be controlled by the same structural disturbances. Otherwise, the weighted mean center and the median center could have been at significant distance apart.

After performing quadrat analysis and the nearest neighbor analysis, it has been observed that the entire dataset of epicenters shows a distinct statistical clustering. Further spatial autocorrela-tion parameters like Gearyís C and Moranís (I) were calculated to measure the similarity of the characteristics of the locations of the epicenters and the results are compared with the Standard Numeric scales for Gearyís and Moranís Index (Table 1).

Table 1: Standard Numeric scales for Gearyís and Moranís Index.
Spatial Pattern Gearyís C Moranís I
Clustered pattern in which adjacent points show similar characteristics 0 < C < 1 I > E (I)
Random pattern in which points do not show particular pattern of similarity  C ≈ 1 I ≈ E (I)
Dispersed / uniform pattern in which adjacent points show different characteristics 1 < C < 2 I < E (I)

E (I) = (-1) / (n-1), with n denoting the number of points in distribution.
(Source: Lee and Wong, 2001)
The observed values for the above two parameters are: 
Gearyís C = 0.233047 
Moranís (I) = 0.8311, E (I) = - 0.00381679

Both the C and I, when compared to the above-mentioned table suggest that the data show clustered pattern in which the epicenters with similar magnitude lie close to each other.

Moreover, the standard deviation ellipse for the data of epicenters of earthquakes is drawn with the calculated major and minor axes that show the directions of maximum and minimum spread of locations respectively (Chandramani, 2001). It has been observed that the orientation of the major axis of the standard deviation ellipse is more or less parallel with the trend of the major thrusts and faults occurring in that area (Fig. 1). This is a clear indication of the major role the structural features, mainly the thrusts, play in the occurrences of earthquakes in the region. Further, the Rose diagrams plotted for both the faults and the thrusts show that the major thrust (NNW-SSE) and the fault planes (NW-SE) have the trend that is more or less parallel to the major axis of the standard deviation ellipse.


Fig. 1: The state of Himachal Pradesh and its surrounding areas showing the positions of earthquake epicenters, structural features like faults and thrusts, Rose diagrams for the thrusts and the faults and calculated central tendencies like mean and median centers (almost overlapping at this scale) and standard distance ellipse.


Conclusion
The proliferation of GIS has prompted researchers in many fields to reconsider their way of conducting research or solving practical problems. With the facility of statistical analysis within GIS, analysts can now process larger volumes of data within a shorter period of time and with greater precision. For detecting spatial pattern in point distribution, three techniques are commonly used. The first one is the Quadrat analysis, which determines if a point distribution is similar to a random pattern. The second one is the nearest neighbor analysis, which compares the average distance between nearest neighbor in a point distribution to that of a theoretical pattern. The third one is the spatial autocorrelation coefficient, which measures how similar and dissimilar an attribute of neighboring point is. In this study, the spatial dataset containing information of earthquake epicenters provides a very good example of point distribution. The statistical analysis of this dataset reveals a clustered pattern in which adjacent points show similar characteristics.

The structural features mainly thrusts and faults occurring in the area are believed to be instrumental in the occurrence of earthquakes. This is further strengthened by the orientation of the major axis of the standard deviation ellipse, which is parallel to the orientation of the major thrusts present in that area. 

Reference
  • Chandramani, (2001), Point Pattern Analysis with GIS, M.Tech. Seminar Report, Department of Earth Sciences, Indian Institute of Technology, Roorkee. (Unpublished).
  • Lee, J., and D. W. S. Wong, (2001), Staistical Analysis with ArcView GIS, John Wiley & Sons, New York.
  • Saraf, A. K., P. Mishra, S. Mitra, B. Sarma and D. K. Mukhopadhyay, (2002) Remote Sensing and GIS Technologies for improvements in Geological Structures Interpretation and mapping. International Journal of Remote Sensing, (in press).
  • Srikantia, S.V. and O. N. Bhargava, (1998) Geology of Himachal Pradesh, Geological Society of India Publications, Bangalore, India.
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