SPATIAL ANALYSIS OF THE DISTRIBUTION OF SINKHOLES ON AN ISLAND

CRES, CROATIA

Tanja Kremenić

(jukeboxe.hero@gmail.com)

SUMMARYThis work is tending to use statistical analysis in order to explain some geomorphological issues that

will be mentioned in the text below. Purpose of this work is to analyse the distribution of the sinkholes on one island and to bring them into correlation with the main kind of relieve in that area and possibly to identify a pattern for their existence (grouped, dispersed or random distribution).

1. INTRODUCTIONThe main objective of this paper is to present an approach to identify active faults in karstic

environments. This is achieved by releasing a relationship between sinkholes or dolines formation, array and active faults mechanism.

To make a proper statistical observation and correlation, there had to be made some different analysis. In analyzing points of the same kind, our interest lies in the detection of spatial patterns in the point distribution.

In the real world, the most important pattern is the similarity between two distributions. If two distributions show similar patterns, it suggests that they are related with each other, either directly or indirectly. Precisely for this paper, I use the pre-knowledge of a proved relationship between sinkholes array and active faults. These results may be applied for the all the similar cases of world’s karstic belt not only the region that has been explored in this work.

In geomorphology of the karst1 relieve, sinkholes2 have a lot of different meaning and purposes. For example, grouped distribution of sinkholes may show us the where the faults are, and therefore, potential for developing earthquakes. Sinkholes also provide us information about microclimate regions. In other hand, on basis of above experiences, determination of active faults and their locations is possible, which is important in seismology so these information apply for buildings, urban area and other structures damage protection. It is known that the areas with larger number of registered sinkholes have higher number of unstable cavities in the underground, and probably a well developed system of caverns.

Parameters used next are the georeferenced events of sinkholes and the chosen area is an island Cres in the Republic of Croatia, where karst relief covers more than 50% of its surface and therefore is very important for researching.

1 A karst landscape has sinkholes, sinking streams, caves, and springs. The term "karst" is derived from a Slavic word that means barren, stony ground usually made of limestone. Geologists have adopted karst as the term for all such terrain.2 One of the terms we may use for this geological relief form. Sometimes, in english literatures, it may appear as “dolinas”, “snake hole”, “swallow hole” or “swallet”.

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Picture 1. Distribution of sinkholes on an island Cres

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2. METHODOLOGY

In digitalization of the points representing sinkholes, projection that has been used is Universal Transverse Mercator’s and WGS 1984 Geographic coordinate system.

Procedure in determining characteristics of spatial distribution is following these steps:1. First task is to see if it's Spatially Random; if not the next step are the 2. First Order Spatial Analysis which tell us Spatial gradient in intensity3. Next are the Second Order Spatial Analysis from which we can define if they're clusteredor regular (dispersed).

To analyze the spatial distribution of sinkholes a variety of spatial analysis tools available in ArcGIS 10 (ESRI) were utilized: Mean Center, Standard Distance, and Standard Deviational Ellipse. Kernel Density Estimation (KDE), Average Nearest Neighbor (NNI), K-function. Kernel density estimates were used to create surfaces for sinkholes to easily identify areas where a large number of events were concentrated in the study area. The NNI method was used to identify clustering of sinkholes by examining conformance with the Independent Random Pattern (IRP) by calculating a ratio (R) of the observed mean nearest neighbor distance to the expected mean nearest neighbor distance of sinkholes. This method calculates a nearest neighbor index based on the average distance from each point feature to its nearest neighboring point feature.

3. THE POINT PATTERN VISUALIZATION OF DATA

To answer the question as: Where's the center? What's the shape and orientation of the data? How dispersed are the features?, the Measuring Geographic Distributions toolset was used (Figure 2).

Standard deviational ellipse summarizes that geographic features's directional trend is NNW – SSE, obviously following the shape of an island and available data. The drawback here is that we don't have data from about the underwater sinkholes (formed when sea levels were lower under the same processes as those on land) which would probably change the main ellipse direction. The same thing applies to mean center.

Using standard distance here also cannot give us much of an information because it give only one geometric mean center and features are concentrated or dispersed around more than one center, as it can be observed also without applying any of the methods.

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Figure 2. Applying Measuring Geographic Distributions toolset: Mean Center, Directional Distribution and Standard Distance

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3.1. ANALYSIS OF THE FIRST ORDER

3.1.1. KERNEL DENSITY

This point layer of sinkholes has been made by digitizing their bottoms - each point represents a bottom of a sinkhole. Data was gathered from topographic maps. With the application od Kernel algorithm, space density of point objects was determined, based on a square Kernel function. It calculates the total number of units within a unit area of one square kilometer (Figure 3). Kernel density calculates the number of observed units within defined neighborhood (unit area) around these objects. Density values of the sinkholes are defined as an attribute for each central unit cell area of the new grid.

Figure 3 clearly shows that there are zones with densely arranged sinkholes and those with no developed topographic depressions, which is due to the lithological structure of the area. Red colors on figure 3 represent areas of high density of sinkholes, therefore at least 6 zones can be singled out as the ones that should be put under research, mostly on the high north and occupying a great zone of south of the island.

Only after applying Kernel density, I combined it with the Standard Deviation tool to make a very aproximate distribution tendency of each cluster (Figure 4).

Figure 3. Kernel density estimation. Magnitude per square kilometer.

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Figure 5. Directional tendencies of some sinkhole cluster (direction needed for fault observaton).

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3.2. ANALYSIS OF THE SECOND ORDER

3.2.1. NEAREST NEIGHBOR ANALYSIS

Nearest neighbor analysis (NNA) was extended to include different scales of concentrated zones of sinkholes, and directions to the nearest sinkholes. Average Nearest Neighbor compares the mean distance between observed and expected distributions to determine the extent of dispersion present in the events with the calculation of R statistics. If R = 1 the events are random, if R <1 the events are clustered and if R > 1 the events are evenly dispersed.

From the Figure 4 we can see that the observed mean distance (123,14) is lower than the expected (179,08) which makes the ratio 0,69. Ratio is lower than 1 which means these events are clustered, formed in groups. Also, p-value (Probability) of 0,0 and z-score (Deviation) of -33,62 mean there is less than 1% chance these events could be randomly designed. This way, the null hypothesis for the pattern analysis tools (Complete Spatial Randomness (CSR)) can be rejected.

The statistical results, along with the sinkhole density distribution, indicate that sinkholes tend to form in highly concentrated zones instead of scattered individuals. The pattern changes from clustered to random to regular.

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Figure 6. Results of the Average Nearest Neighbor method

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3.2.2. K-FUNCTION

Figure 7. K function

The K-function here we can also reject a null hypothesis of Complete Spatial Randomness. When the observed K value is larger than the expected K value for a particular distance, the distribution is more clustered than a random distribution at that distance (scale of analysis). When the observed K value is smaller than the expected K value, the distribution is more dispersed than a random distribution at that distance. Blue line shows us that expected K value is higher than the observed. The cluster value is higher where distance is lower which again brings us to the same conclusion – point pattern is clustered and spatially dependent.

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4. DISCUSSION

The sinkholes appear to be a sensitive indicator of the recent tectonic activity. Their spatial distribution allows us the measurement of strain and stress to which the studied area has been submitted during recent periods. The results of this spatial statistics show sinkholes array and their relationship with valley fault imply that fault activities depend upon spatial distribution of sinkholes array, on faults direction. Therefore, it could be concluded that the areas with high number of sinkholes have similar geological and topographic characteristics, and the areas with high density of sinkholes per surface area intensify erosion processes and stimulate further generation of new sinkholes increasing in that way the geological hazard. Generation of new sinkholes is a slow natural process which cannot be stopped, but can be accelerated by in impact of human activities.

From the Nearest Neighbor Methof some hypotheses are drawn that may explain this karst phenomenon: areas in the highly concentrated zones of sinkholes have similar geologic and topographical settings that favor sinkhole formation; existing sinkholes change the hydraulic gradient in the surrounding area and increase the solution and erosional processes that eventually form more new sinkholes.

Further, since the sinkholes are a direct link between the surface and the underground, they are potentially very dangerous points for propagation of accident related contamination directly into the underground causing contamination of the groundwater. The groundwater in karst aquifers generally streams through underground karst conduits, its flow rates are much higher than in other aquifers, thus any ingress of contaminant into the underground water bearing system could result in contaminant transportation to large distances in a very short period of time. This makes them exceptionally vulnerable and endangered systems.

LITERATURE/SOURCESARC GIS http://resources.arcgis.com/en/

Khorsandi, A., Miyata, T.( 2007): Fault determination due to sinkhole array on Lar Valley northeast of

Tehran (Iran), ACTA CARSOLOGICA 36/2, 203-208, POSTOJNA

Catita, C. (2013), Notes from the lectures in subject Spatial Analysis.

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