Jour. Korean Earth Science Society, v. 31, no. 2, p. 119 128, April 2010 (w ) w x 1, *Á 2 1w Ÿ, 305-350, Ÿ w 92 2 w w œw, 402-751, 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 305-350, Korea 2 Department of Geoinformatic Engineering, Inha University, Incheon 402-751, 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: gyesoon@paran.com *Tel: 82-42-868-3922 *Fax: 82-42-868-3922
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). 1990 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.
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
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
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.
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
w x 125 Table 1. Variogram analysis results of the whole survey area Angle Sill values (Gravity) Sill values (Magnetic) Sill values (Elevation) 0 11.3 32000 11700 15 13.2 24000 12500 30 16.8 24000 12000 45 17.2 22500 10500 60 13.2 23000 13000 75 11.0 30500 15000 90 9.2 25000 15500 105 7.5 26000 18000 120 6.7 25000 16000 135 6.1 24500 9500 150 6.7 26000 13500 165 8.5 29800 11700 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 120-150o w w x š. ww, x mw x 120-150o 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) 0 0.38709 0.53360 0.39986 0.33333 0.33333 0.23991 15 0.46707 0.81384 0.41330 0.31989 0.28024 0.23991 30 0.62701 0.46707 0.30645 0.33333 0.26545 0.25336 45 0.80040 0.41330 0.22647 0.39986 0.25336 0.23991 60 0.90658 0.38709 0.23991 0.41330 0.22647 0.20026 75 0.72043 0.30645 0.21371 0.42674 0.21371 0.18682 90 0.69354 0.66666 0.20026 0.49328 0.22647 0.18682 105 0.46707 0.58669 0.23991 0.61357 0.25336 0.21371 120 0.34677 0.50672 0.29368 1.00000 0.29368 0.22647 135 0.30645 0.60013 0.18682 1.00000 0.38709 0.28024 150 0.26680 0.64045 0.57325 1.00000 0.44018 0.31989 165 0.26680 0.68010 0.66666 0.74664 0.44018 0.31989
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 120-130 o w w w. w, DEM š w wù w 0-10 o 120-140 o w. š Landsat l 40-60 o 130-140 w o w. œm 130 w o ƒ ùkùš, mww 0-10 o 130-140 w ƒ w o. x mw x š DEM k
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» (R200811135) w w,
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