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Spatial Statistical Technique in relating earthquake epicentres with structural features


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 Historical documents show that a large number of earthquakes of moderate to high intensities have occurred in this region in the past.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.