comparison of kriging and inverse distance weighted

J. SE Asian Appl. Geol., Jan–Jun 2013, Vol. 5(1), pp. 21–29

COMPARISON OF KRIGING AND INVERSEDISTANCE WEIGHTED (IDW) INTERPOLATIONMETHODS IN LINEAMENT EXTRACTION ANDANALYSIS

Agung Setianto∗1 and Tamia Triandini2

1Geological Engineering Department, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta, Indonesia2Civil and Environmental Engineering, Ehime University, Matsuyama, Japan

Abstract

Analysis that is based on geostatistics eliminatesmany corresponding defects and limitations com-pared to classical statistics which have been devel-oped by random distribution theory of processes andvariables. Interpolation is important for local analy-sis by GIS, because many maps used for GIS opera-tion are made by interpolation. In this research, twodifferent methods which is Kriging method and In-verse Distance Weighted (IDW) method was exam-ined for developing Digital Elevation Model image.Each method’s advantages and disadvantages wereconsidered.

The study are, Kepil, is within Kulon Progo phys-iographic and stratigraphic area, located in the west-ern part of Yogyakarta city. This area is located closeto the Java Island Subduction Zone, hence influ-ence of tectonic plate movement is relatively dom-inant. Geological structures become a main factorthat shapes the recent morphology. This study areaalso has many settlements and has high weatheringand erosion rate.

Lineaments are extracted based on Digital Eleva-tion Model to provide assistance in delineating ge-ological structures. The structural geology analy-sis and an understanding of tectonic phase of thearea provide useful information for geological map-

∗Corresponding author: A. SETIANTO, GeologicalEngineering Department, Faculty of Engineering, Uni-versitas Gadjah Mada. Jl. Grafika No 2, Bulak-sumur, Yogyakarta 55281, Yogyakarta, Indonesia. E-mail:[email protected]

ping. Accuracy of lineament depends on extractionand imagery parameters used. In this study, the ex-traction was conducted by two different raster meth-ods, namely Kriging and Inverse Distance Weighted(IDW) with the same resolution of 30 meters. Lin-eament extracted automatically (digitally) with cer-tain parameter settings.Keywords: Kriging, inverse distance weighted, in-terpolation, lineament, random distribution, digitalelevation model.

1 Introduction

Lineament analysis is performed by using Dig-ital Elevation Model (DEM) data. DEM con-tains elevation and slope information that madeinterpretation easier. In Indonesia, the rate ofweathering and erosion rate makes field map-ping of geological structures becomes difficultwithout the aid of satellite imagery mapping.DEM is basically a numerical representation oftopography that is usually stored in equalizedgrid cells, each with a value of elevation. Itssimple data structure and widespread availabil-ity has made it a popular tool for land character-ization. Because topography is a key parame-ter in controlling the function of natural ecosys-tems, DEMs are highly useful to deal with ever-increasing environmental issues.

The topographic modeler must be particu-larly careful when selecting the technique forinterpolation between the initial sampling data

21

SETIANTO and TRIANDINI

points of altitude, as this may have a great ef-fect on the quality of DEMs. The main objectiveof this study is to evaluate the effects of land-form types, the density of original data, and in-terpolation techniques on the accuracy of DEMgeneration to be used for digital lineament ex-traction.

Prior to the structural lineament analysis,there are three aspects to consider: the type oflineament, the establishment of lineament, andmanifestations that led to form lineament. Fur-thermore, this lineament analysis is intendedto be able to analyze geological structures insome area which contains many eroded or mod-ified structures. Geological structures may havelarge dimensions that is not apparent in thefield. In addition, the civil settlement obscuresome parts of the strucures in the field. Simpleidentifications can be performed by using satel-lite imagery, and there are more than one rasteravailable to use. Comparing two or more rasterwill make identification easier.

Study area

The study area (Figure 1) is within Kulon ProgoHills physiographic and stratigraphic zone.This area is located close to Java Island subduc-tion zone, hence the influence of tectonic platemovement is relatively dominant. Geologicalstructures become a main factor that shapes therecent morphology. The study to analyze theforces that comprise them becomes important.Hills in the study area are formed due to the in-fluence of deformation force. This deformationtakes place in several stages; its manifestationthat can be observed in present circumstancesis a mixture of all phases that has ever beenhappened.

This area has been studied earlier by Bemme-len (1949) who argued that Kulonprogo experi-enced three tectonic phases: the first phase wasIjo, Gajah, and Menoreh Volcano formation;the second phase was a transgression eventthat formed Jonggrangan and Sentolo Forma-tion; and third phase was lifting that producemorphological Kulonprogo recent time. Pu-lunggono et al. (1994) argued that Java Is-land was formed by three main structural pat-terns: Meratus pattern trending NE-SW (Pale-

Figure 1: Study area.

ocene), Sunda pattern trending N-S (Eocene-Late Oligocene), and Java pattern trending W-E (Late Oligocene-Earlier Miocene). By usingLandsat-7 ETM+ and panchromatic aerial pho-tographs, Sudrajat et al. (2010) argued that Ku-lonprogo Hills and surroundings had trends inthree different phases starting from oldest toyoungest were NE-SW, NNW-SSE, and E-W.

This study of lineament analysis comparestwo interpolation methods to improve the re-sults obtained from lineament extraction usingautomatic (digital) and manual correction. Theinterpolation methods are Kriging and IDW.

2 Methodology

The aim of this study is to investigate the differ-ences in the automation of lineament analysisbetween Kriging and IDW interpolation meth-ods. Analysis is based on DEM data. Themethodology used in this study is shown in Fig-ure 2.

2.1 Interpolation method

DEM is usually produced from sampled data.Ideally, the data sources would be used with-out interpolation. For example, only contourlines themselves may represent a model of ter-rain. They can be acquired directly (e.g. by pho-togrammetry from stereo model) or indirectly(e.g. from analogue cartographic data, satel-lite images, by surveying, etc.). Interpolation isalso not necessary in cases where data sourceis very precise and having high density, and

22 © 2013 Department of Geological Engineering, Gadjah Mada University

COMPARISON OF KRIGING AND INVERSE DISTANCE WEIGHTED INTERPOLATION METHODS

Figure 2: The major methodology of lineament analysis.

especially if the data is acquired directly intoregular grid (DEM). But interpolation of datasources to produce DEM is necessary if the datasources themselves do not predict treated land-scape phenomena.

Interpolation techniques are based on theprinciples of spatial autocorrelation which as-sumes that objects close together are more sim-ilar than objects far apart. On the edges ofthe interpolated area, extrapolation is also rea-sonable. Unfortunately, no interpolation tech-nique is universal for all data sources, geo-morphologic phenomenon, or purposes. Weshould be aware that in the praxis, different in-terpolation methods and interpolation param-eters on the same data sources lead to differ-ent results. The best chosen algorithms onfair data sources should not differentiate muchfrom nominal ground, that is idealization of ourdesired model and which is commonly simi-lar to actual Earth’s surface. Divergences be-tween results of interpolation and from nomi-nal ground are especially consequences of thefollowing circumstances:

1. Available data sources do not approximateterrain (distribution, density, accuracy, etc.of the sources is not appropriate),

2. Selected interpolation algorithm is is notenough robust on the employed datasources,

3. Chosen interpolation algorithms or datastructure are not suitable for selected ter-rain geomorphology or application,

4. Perception or interpretation of Earth’s sur-face (better: nominal ground) is not the

same when more DEM operators work onthe same problem; operator’s own imagi-nation is common and reasonable problemin DEM production.

Application requirements play important roleto expected characteristics of the DEM. For ex-ample, we need high geomorphologic qualityof DEM for regional-small scale analysis andfor calculating average altitudes, although geo-morphologic accuracy is more sensitive for vis-ibility analysis and even more for analysis thatuses algorithms based on derivates like slope,aspect, cost surface, drainage, path simulation,etc.

2.2 Ordinary Kriging (K)

Ordinary Kriging is one of the most basic ofKriging methods. It provides an estimate atan unobserved location of variable z, based onthe weighted average of adjacent observed siteswithin a given area. The theory is derivedfrom that of regionalized variables (Deutschand Journel, 1998) and can be briefly describedby considering an intrinsic random function de-noted by z(si), where si represents all samplelocations, i = 1, 2, . . . , n. An estimate of theweighted average given by the ordinary Krig-ing predictor at an unsampled site z(s0) is de-fined by:

Z(s0) =n

∑i=1

λi z(si) (1)

where, l are the weights assigned to each ofthe observed samples. These weights sum to

© 2013 Department of Geological Engineering, Gadjah Mada University 23


unity so that the predictor provides an unbiasedestimation:

n

∑i=1

λi = 1 (2)

The weights are calculated from the matrixequation:

C = A−1× b (3)

where:

A = A matrix of semi ariances between the datapoints.

b = A vector of estimated semivariances be-tween the data points and the points atwhich the variable z is to be predicted.

c = The resulting weights.

2.3 Inverse Distance Weighting (IDW)

All interpolation methods have been developedbased on the theory that points closer to eachother have more correlations and similaritiesthan those farther. In IDW method, it is as-sumed substantially that the rate of correlationsand similarities between neighbors is propor-tional to the distance between them that canbe defined as a distance reverse function of ev-ery point from neighboring points. It is neces-sary to remember that the definition of neigh-boring radius and the related power to the dis-tance reverse function are considered as impor-tant problems in this method. This method willbe used by a state in which there are enoughsample points (at least 14 points) with a suitabledispersion in local scale levels. The main factoraffecting the accuracy of inverse distance inter-polator is the value of the power parameter p(Burrough and McDonnell, 1998). In addition,the size of the neighborhood and the numberof neighbors are also relevant to the accuracy ofthe results.

Z0 =

N

∑i=1

zi · d−ni

N

∑i=1

d−ni

(4)

where:

Table 1: Parameter raster interpolation usingArcGIS.

Parameter Kriging IDW

Z value Elevation Elevation

Method universal -

Output cell size 30 meters 30 meters

Search radius 12 12

Z0 = The estimation value of variable z in pointI.

zi = The sample value in point I.

di = The distance of sample point to estimatedpoint.

N = The coefficient that determines weighbased on a distance.

n = The total number of predictions for eachvalidation case.

3 Results

According to ESRI (2004), Kriging is one ofthe most complex interpolators. It applies so-phisticated statistical methods that consider theunique characteristics of dataset. IDW takes theconcept of spatial autocorrelation literally. It as-sumes that the nearer a sample point is to thecell whose value is to be estimated, the moreclosely the cell’s value will resemble the samplepoint’s value. The parameters of both interpo-lation methods are seen in Table 1.

The accuracy of both Inverse DistanceWeighted and Kriging is almost the same. Inthis study, since nominal data was used to getthe result, IDW has more simple procedure andfewer steps in comparison Kriging. The advan-tage of IDW is that it is intuitive and efficienthence recommended for the type of data. How-ever, for more informative data, Kriging is morepreferable. Indeed, Kriging provides a more re-liable interpolation because it examines specificsample points to obtain a value for spatialautocorrelation that is only used for estimat-ing around that particular point, rather thanassigning a universal distance power value.Furthermore, Kriging allows for interpolated



Figure 3: Kriging (left) and IDW (right), black line is profile line.

Figure 4: Profile from DEM of Kriging interpolation.

Figure 5: Profile from DEM of IDW interpolation.



cells to exceed the boundaries of the samplerange.

3.1 Lineament Extraction

Lineament extraction can be conducted in twomain ways, which is manual and automatic(digital). Manual lineament extraction requiresfull interpretation and pure user analysis. Au-tomatic lineament extraction uses 3D image(DEM) or in this study is resulted from tworaster interpolation.

Both raster used for comparison were ana-lyzed with same lineament extraction param-eters (Table 2). There are six parameters areused as RADI (Radius of filter in pixels), GTHR(threshold for edge gradient), LTHR (thresholdfor curve length), FTHR (threshold for line fit-ting error), ATHR (threshold for angular dif-ference), and DTHR (threshold for linking dis-tance). After that, error correction is conductedby erasing the lineament as hills or ridge. Thiscorrection is based on the assumption that thelineaments are structural lineaments that iden-tified as valley, river, or erosion line. Compar-ison between two extraction lineaments can beseen in Figure 6.

3.2 Analysis

That lineament extraction is analyzed by usingstatistical rose diagram. Rose diagram are madeusing digital processes with frequency intervalof 10°. The analysis is based on the Kriging andIDW interpolation methods results (Figure 7).

The major lineament direction trends in NE-SW. A small difference can be seen betweenthe two rose diagrams. The diagram resultedfrom Kriging method shows a random linea-ment and almost same in all directions, whereasIDW method shows a rather random lineamentand less NW-SE trends.

4 Discussion and conclusion

Several important points emerge from this re-search. Because the primary objective is to com-pare different interpolation methods, we firstconsider the effect of interpolation method onaccuracy [as measured by log (MSE)]. The most

striking result along these lines was that theKriging method consistently and substantiallyoutperformed the two inverse distance weight-ing methods over all levels of the other factors.A second point pertaining to the comparison ofinterpolation methods is that although the Krig-ing methods were consistently superior to in-verse squared distance weighting over all lev-els of the other factors, the extent of superioritywas affected by the other factors. More specifi-cally, the disparity in performance between thetwo types of methods tended to be greatest atthose levels of the other factors at which all fourmethods performed best.

Although the primary objective of this inves-tigation was to compare interpolation methods,the effects of the other factors on overall inter-polation performance were also of some inter-est. The significance of the main effects andthe relatively small magnitude of the interac-tions allow us to make several points and tonote some aspects that require further investi-gation. First, our results indicate that overallinterpolation performance deteriorated consis-tently and significantly as the sampling patternvaried from the most regular pattern, hexago-nal, to the next most regular, inhibited, to a ran-dom pattern, and finally to the most irregularpattern, clustered.

Finally, consider the effect of surface type. Wefound that interpolation performance was bestfor the plane, next best for the sombrero, andworst for Morrison’s surface. That the planeyielded the best performance is not surprisingin light of this surface’s extreme smoothness,but it is difficult to characterize the sombrero orMorrison’s surface as smoother than the otherand hence difficult to explain why performancewas better for the former than for the latter. Ad-ditional investigation is required to understandhow surface type affects interpolation perfor-mance at both the overall level [as measured,for example, by log (MSE)] and the micro level.In particular, more work is needed to explicitlyidentify and parameterize those surface char-acteristics (e.g., peaks, troughs, or portions ofthe surface with large gradients) that are re-sponsible for the greatest discrepancies in per-formance. At finer scales, the grid evaluation



Table 2: Parameter of lineament extraction.

Parameter Value for Kriging andIDW raster

Parameter Value for Kriging andIDW raster

RADI 3 FTHR 3

GTHR 5 ATHR 5

LTHR 3 DTHR 3

Figure 6: Comparison of lineament extraction in Kriging and IDW raster.

Figure 7: Rose diagram with bearing parameter (a) Kriging and (b) IDW.



Figure 8: Frequency distribution of lineament resulted from kriging interpolation.

Figure 9: Frequency distribution of lineament resulted from IDW interpolation.

approach used in this paper could serve as thebasis for visualizing and evaluating local per-formance characteristics

This study also evaluated the accuracy of twointerpolation techniques for generating DEMs.Different landform types and density values ofheight measurement were considered. Irrespec-tive of the surface area, landscape morphologyand sampling density, few differences existedbetween the employed interpolation techniquesif the sampling density was high. At lower sam-pling densities, in contrast, the performance ofthe techniques tended to vary. Kriging yieldedbetter estimates if the spatial structure of alti-tude was strong. The spatial structure of heightwas weak as observed at the IDW.

These results may help GIS specialists toselect the best method for the generation ofDEMs. A technique should be chosen not onlyfor its performance on a specific landform typeand data density, but also for its applicability toa wide range of spatial scales. The result of themethodology used in IDW raster is lineament

looks smoother and more firmly drawn thanlineament from kriging raster extraction. Fur-thermore, lineaments analyzed by using Rosediagram show that the lineament in IDW rasteris more accurate than Kriging because the pres-ence of minor lineaments and the less displayof maxima whic are useful as an interpretationof the force that form lineament. The analysisfrom Kriging raster shows that there are manymajor maxima in study area, hence making ge-ological interpretation less accurate.

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comparison of kriging and inverse distance weighted

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