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1 Jour. Korean Earth Science Society, v. 31, no. 2, p , April 2010 (w ) w x 1, *Á 2 1w Ÿ, , Ÿ w 92 2 w w œw, , Ÿ û x 253 A Comparative Analysis of Linearity and Range of Gravity and Magnetic Data Using Variogram Gyesoon Park 1, * and No-Wook Park 2 1 Korea Institute of Geoscience and Mineral Resources (KIGAM), Daejeon , Korea 2 Department of Geoinformatic Engineering, Inha University, Incheon , Korea Abstract: To make reliable interpretations on the sparse spatial data, the spatial distribution characteristics that are inevitable for spatial estimation should be properly analyzed. Variograms have been widely used for obtaining the spatial characteristics inherent to data in spatial estimation problems. But their applications were limited as the basic information for further data estimation. Therefore, the additional analysis of the meaning of variograms is required for more reliable data processing and interpretations. In this paper, we investigated the proper meaning of variogram values and the specific features of distributions which can be obtained through variogram analysis. Variograms can provide the information on both linearity and the strength changes of interrelationships between the data sets according to the direction and lag distance. First, sill and range values, which are main parameters of variograms, were analyzed. Then a similarity range using spatial auto-correlation values was introduced to verify the applicability of linearity analysis through the comparative study of spatial distribution features of gravity and magnetic data collected in Hwasan caldera. Through these analyses, we were able to identify the dissimilar patterns of gravity and magnetic data that became apparent according to the distribution and variation ranges of the data sets. It is inferred that the gravity and magnetic anomalous bodies are extended to the ground because linearity direction of gravity and magnetic data appear similarly with linearity derection of topography in Hwasan caldera.,fzxpset variogram, range, similar range : ƒ w k œ w w» œ s p w w w. œ w ü œ p ƒ w œ w»» w w. w w v w. œ s w š wš, mw œ s p w w. w œw, y w p. w l wš,» w w x ƒ w, y e z œ s p w., s s s ùkù w p ql y w, y e x w x x w w ùkùš t ùkû.,, *Corresponding author: [email protected] *Tel: *Fax:

2 120 Á k w w e w z w» w ƒ š. z w w w k w ww» w w. w w m w œ s p, œ» m œw (Goovaerts, 1997) l k m w ƒ y w (Oh, 2000; Park, 2008). k œ w ƒ w wù œ s p w w. w œ s p ü œ y œw. w œ s ùkü œ w,,, (, 2007; Goovaerts, 1997).» œ ü sw w œw. œ s p txw ƒ r š. m w œ s p w» w, ³e z w w w ƒ j ½»» š (Journel and Huijbregts, 1978; Armstrong, 1984; Cressie, 1993; Olea, 1995; Goovaerts, 1997). w k s w w txw ù» y w eš mw w x. ù w j» p w. w w w q l w ùkù x w w œ s p w. ùkü œ p w w š x k œ s j» x w w š w. w y e w k, wœ k x w ƒ w w x wš ƒ x w w. š x w w z, x ƒ œ s p y w ww. w, w, x, œ w w x (, 2008) w k ƒ w ww. w ùkü tx (Goovaerts, 1997; Deutsch and Journel, 1998). γ( h) 1 = z u 2N( h) N( h) [ ( ) z( u+ h) ] 2 (1)» z(u) e u, z(u+h) z(u) h j e ùkü, N(h) h j ùkü. (1) œ w, ùkü w w œwš. Fig. 1 x xk š. ƒ ƒw ƒw ql. ƒ ƒw ƒ ql š w w. ƒƒ (range) l (sill) w, l w. ƒ 0 0 ùkù w, ƒ 0 0 ùkú ½(nugget) š w. ½ s w ù d w w.

3 w x 121 Fig. 1. A typical variogram model.» (E) (σ ) œ 2 (Cov) w x ƒ w. γ(h)=var[z(u) z(u+h)]=e{[z(u) z(u+h)] 2 }=σ 2 Cov(h) (2) m w» (stationarity) s p p w e yw w. š w s³ e w š, (3) (ρ(h)) (2) w (4) w (Goovaerts, 1997; Deutsch, 2002). ρ( h) Cov( h) σ 2 = (3) ρ(h)=1 γ(h)/σ 2 (4) l ƒ 0 ùkü š, ùký, j ùkù. x mw Fig. 1 x xk ƒ w ù, p w x k. ùkú w ql w (Gringarten and Deutsch, 2001). 1) xk ql ùkù œ û w. w xk w w w ù ù v j» e w w. 2) yw ql w, ùkü. 3) l w ùkü, j ³ ùkü w w ùkú k ww» w w Ÿ w w. 4) l w û x, ƒ ƒw ƒ w ùk ù, yƒ w ù d xk ùkú ql. 5) w xkƒ ùkú ƒ ùkù x ƒ w ³ ùkú. k k x œ s p mw ƒ w w» w y e z k ww. y e Fig. 2 š y d swš. y d s ³ w 16 km û w 13 km. z(1988) w y e x» 3». y e ü n w š yr y, y w w d, y w ü e y w, ƒ ü w y e d x w ( z, 1988;»y, 1997). y e d w l ù -w - d d -zs - š- š- -y - d

4 122 Á Fig. 2. Geological map of the survey area. Fig. 3. Gravity measurement points on the terrain map. A, B, C and D indicate locations of Palgongsan, Hwasan, Seunamsan and Geumseungsan, respectively. w d ewš. y w y ƒ z x. y e û qœ y ƒ û w swš, û y ƒ š. Fig. 3 x t e wœ w. y e e z w (, 2008), wœ w 1980 z l 1997 ¾ d 150 m wœ d e v w z w.,,»,, z,, x ww w z w w w. wœ wd r w e, base station w z w»» y, w d û w d ƒ s³ w tie line, 300 m š IGRF w, RTP

5 w x 123 Fig. 4. (a) Bouguer anomaly map(a), (b) magnetic anomaly map (RTP). A, B, C and D indicate locations of Palgongsan, Hwasan, Seunamsan and Geumseungsan, respectively. ww z d w w w. s Fig. 4 ƒƒ ùkü. x mw ƒ k s p, ³ x w» w w,, š w x w. x w w w k w(angle direction) 15 o w ƒƒ w, ƒ x w (tolerance) 15 o ww. 25 ù w x w 50% w. ƒ k y w» w wù v ƒ k y ew w. Fig. 5 w 0 o w 15 o. z w» w Table 1 ù kü l w z l x mw w. l,, x y ƒ w w» w» ùkù ƒ ql e w. mw x k s p w» w w ü. ƒ f ƒw q l ùkü. p w ƒ» w, x p w ql w ùkú» ùk ù ƒ ql e w. w, ƒ w w» w 22,000 m 1 y w ùkü w. Table 2 ùkü. (4)» w w.

6 124 Á Fig. 5. Experimental variograms with respect the changes of direction. w ƒ w ƒ h z i z i+h ƒ 0.3 w r š ew.» 0.3 w ƒ w ùkù l œ š w w. ƒ w s p š w yƒ j x w j» w ùkü. Fig. 6 x v w w. w

7 w x 125 Table 1. Variogram analysis results of the whole survey area Angle Sill values (Gravity) Sill values (Magnetic) Sill values (Elevation) yw š, (a) l, (b), (c) š. l r w w txw. (a) š l ùkùš ù, 15-60o w w x š. x w ql w ewš. p š w û w Ÿ ql ùkùš w. (b)ƒ ùkü ql r, ƒ j ùkùš 30-75o w 15o w j š. w w x w û w ùkùš ù, x ql x w û w ùkùš. (c) w w ùkù w x z,, š o w w x š. ww, x mw x o w w x š ù ql w ùkû. x w ƒ¾ š, š w x š. w p s p w w., w sw w., s š w, š -û w w ¼ sw x š, ƒ š ƒ w š. ƒ ù š w y ƒ š w ql» x w w Table. 2. Variogram analysis results of the whole survey area Angle Range (Gravity) Range (Magnetic) Range (Elevation) Distance (p>0.3) (Gravity) Distance (p>0.3) (Magnetic) Distance (p>0.3) (Elevation)

8 126 Á Fig. 6. Variogram analysis results. (a) sill values, (b) range, and (c) separation distance that has more than 0.3 correlation value. Fig. 7. The extracted lineaments: (a) displays fault lines in the geologic map, (b) and (c) show the lineament extracted from DEM and Landsat image, respectively (Park et al., 2008). ƒ,»»ƒ 0 ùkù». w ù š ƒ š w { w s» x w w w ùküš ƒ ¼ ùkù p. w w ql q. x ƒ x w wš t x r» w k mw x w. k Ÿ q w» w GDPA(Gradient Direction Profile Aogorithm)» (Wang and Zhang, 2000; Lee and Yu, 2002) w, DEM, Landsat l wš» t d wì x w ww (, 2008). ƒ x Fig. 7 ùkü, Fig. 8 x w y w. d y y d ùkù» w û w ¼š w d w o w w w. w, DEM š w wù w 0-10 o o w. š Landsat l o w o w. œm 130 w o ƒ ùkùš, mww 0-10 o w ƒ w o. x mw x š DEM k

9 w x 127 Fig. 8. The rose diagrams of lineaments in study area: (a), (b) and (c) results from each lineament in (d) represents all lineaments (a, b, and c) by one rose diagram (Park et al., 2008). mw x ƒ š» w x k y w. x x w w p š, { w x wš, mw x w ƒ z y w. w, w x ùkü, ƒ t x w w. mw ƒ t q w w. w, l w, š s p ww» œw y w. œ s p w š t. x s p œ w»» w, w w v w. l wì w x s p ww. x k w x w z w, y w s p w w. w yƒ š q p. w» w, ƒ ¼ ùkù w p w s w y w ùkü. s š w w p p w ùk ù p. x w w ƒw p s p., w, p y w. w, y e x w x x w w ùkùš t q.» x œ s p mw ƒ w w w, y e ùkù s p w. w» sƒ» (R ) w w,

10 128 Á. mw» - x m» x (07 m C03) w w. w, z Ì. š x,,,, «,, ½, y, 2008, sl w mw y e w. w wz, 29, z, 1988, y y y w g. w wz, 24, »y,, 1997, y y. y, 30, , 2007, m w. v,, 386 p. Armstrong, M., 1984, Improving the estimation and modeling of the variogram. In Verly, G., David, M., Journel, A.G. and Marechal, A., (eds.), 1984, Geostatistics for Natural Resources Characterization. Reidel, Holland, Cressie, N., 1993, Statistics for spatial data. Wiley, NY, USA, 900 p. Deutsch, C.V., 2002, Geostatistical Reservoir Modeling. Oxford University Press, NY, USA, 376 p. Deutsch, C.V. and Journel, A.G., 1998, GSLIB: Geotatistical Software Library and User s Guide. Oxford University Press, NY, USA, 369 p. Goovarets, P., 1997, Geostatistics for Natural Resources Evaluation. Oxford University Press, NY, USA, 483 p. Gringarten, E. and Deutsch, C.V., 2001, Variogram interpretation and modeling. Mathematical Geology, 33, Journel, A.G. and Huijbregts, Ch.J., 1978, Mining geostatistics: Academic Press, NY, 600 p. Lee, K. and Yu, Y.-C., 2002, Automatic extraction of road network using GDPA (Gradient Direction Profile Algorithm) for transportation geographic analysis. Proceedings of International Symposium on Remote Sensing, Oh, S., 2000, Geostatistical approach to Bayesian inversion of geophysical data. Ph.D. Thesis, Seoul National University, 99 p. Olea, R.A., 1995, Fundamentals of semivariogram estimation, modeling, and usage. In Yarus, J.M. and Chambers, R.L. (eds.), Stochastic modeling and geostatistics: Principles, methods, and case studies. AAPG Computer Applications in Geology, 3, Park, K., 2008, Geostatistical integration of multi-parametric geophysical data to enhance spatial resolution. Ph.D. Thesis, Seoul National University, 120 p. Wang, J. and Zhang, Q., 2000, Applicability of a Gradient profile algorithm for road network extraction-sensor, resolution and background considerations. Canadian Journal of Remote Sensing, 26, š k