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/GraphInit{GDIHMatrix null eq{/SavedCTM matrix d : ADO_mxRot concat 0 0 snap +
: 0.48 @ GDIHPatternDict ` YStep mul ~ XStep mul ~ nonzero_dsnap YStep V ~
XStep V ~ E +S/GDIHMatrix matrix currentmatrix readonly d ; : 0.24 -0.24 +S
GDIBWPatternDict ` Width Height E nonzero_dsnap +S/GDIBWPatternMx matrix
currentmatrix readonly d ; ;}if}b
%%EndResource
%%BeginResource: file Pscript_Win_GdiObject_L3 5.0 0
/GDIBWPatternDict 25 dict @ `/PatternType 1 d/PaintType 1 d/RepsV 1 d/RepsH 1 d
/BBox[0 0 RepsH 1]d/TilingType 1 d/XStep 1 d/YStep 1 d/Height 8 RepsV mul d
/Width 8 d/mx[Width 0 0 Height neg 0 Height]d/FGnd null d/BGnd null d
/SetBGndFGnd{BGnd null ne{BGnd aload ! scol BBox aload ! 2 ^ sub ~ 3 ^ sub ~
rf}if FGnd null ne{FGnd aload ! scol}if}b/PaintProc{` SetBGndFGnd RepsH{Width
Height F mx PaintData imagemask Width 0 +}repeat E}b E d/mp/makepattern , d
/build_pattern{CTMsave GDIBWPatternMx setmatrix/nupangle where{! nupangle -90
eq{nupangle R}if}if GDIBWPatternDict @ ` Width Height ne{Width Height gt{Width
Height V 1}{1 Height Width V}? +S}if xOrg yOrg E matrix + mp CTMrestore}b/hbf
{setpattern}b/hf{:/fEOFill ~ d ~ ! setpattern fEOFill{O}{L}? ;}b/pbf{: !
/fEOFill ~ d GDIBWPatternDict `/yOrg ~ d/xOrg ~ d/PaintData ~ d/OutputBPP ~ d
/Height ~ d/Width ~ d/PaintType 1 d/PatternType 1 d/TilingType 1 d/BBox[0 0
Width Height]d/XStep Width d/YStep Height d/mx xOrg yOrg matrix + d 20 dict @ `
/ImageType 1 d/Width Width d/Height Height d/ImageMatrix[1 0 0 1 0 0]d
/BitsPerComponent 8 d OutputBPP 24 eq{/Decode[0 1 0 1 0 1]d}{OutputBPP 8 eq{
/Decode[0 1]d}{/Decode[0 1 0 1 0 1 0 1]d}?}?/DataSource{PaintData}d E/ImageDict
~ d/PaintProc{` ImageDict image E}b & mx makepattern setpattern E fEOFill{O}{L}
? ;}b/mask_pbf{:/fEOFill ~ d 20 dict `/yOrg ~ d/xOrg ~ d/PaintData ~ d/Height ~
d/Width ~ d/PatternType 1 d/PaintType 2 d/TilingType 1 d/BBox[0 0 Width Height]
d/XStep Width d/YStep Height d/mx xOrg yOrg matrix + d/PaintProc{` Width Height
T[1 0 0 1 0 0]{PaintData}imagemask E}b & mx makepattern setpattern E fEOFill{O}
{L}? ;}b/grf4{4 dict `/ShadingType 4 d/DataSource ~ d/ColorSpace ~ d & E
shfill}b
%%EndResource
end reinitialize
: N 167 1617 957 50 rp C 
1 1 1 1 scol  L ; 
%%IncludeResource: font Times-Bold
F /F4 0 /256 T /Times-Bold mF 
/F4S2A F4 [42 0 0 -42 0 0 ] mFS
F4S2A Ji 
478 1658 M (INTRODUCTION)[16 30 28 30 33 30 30 30 28 16 33  0]xS 
812 1658 M ( )S 
: N 167 1667 957 45 rp C 
1 1 1 1 scol  L ; F1S26 Ji 
173 1703 M ( )S 
183 1703 M ( )S 
: N 167 1712 957 45 rp C 
1 1 1 1 scol  L ; 173 1748 M (The geophysical literature is rich in algorithms that attempt )
[23 19 17 15 18 17 18 19 19 17 15 11 16 17 11 15 11 11 11 17 13 17 11 19 13 17 15 11 15 15 13 11
16 19 15 11 19 15 17 11 18 18 13 11 11 19 29 15 14 11 19 17 11 14 17 11 11 17 29 19 11  0]xS 
: N 167 1757 957 45 rp C 
1 1 1 1 scol  L ; 173 1793 M (to recover the approximate position and shape of sources )[11 18 20 13 17 16 18 18 17 13 20 11 19 17 20 17 19 19 13 18 19 11 29 17 11 17 20 19 18 15 11 11
11 18 19 20 17 19 19 20 15 19 17 19 17 20 18 12 20 15 18 19 13 16 17 15  0]xS 
: N 167 1802 957 45 rp C 
1 1 1 1 scol  L ; 173 1838 M (from gravity measurements. Blakely \(1995\) offers a )[12 13 18 29 37 18 13 17 18 11 11 17 36 29 17 17 15 19 13 17 29 17 19 11 15 10 36 25 11 17 19 17
11 17 36 13 19 19 19 19 13 36 18 12 12 17 13 15 36 17  0]xS 
: N 167 1847 957 45 rp C 
1 1 1 1 scol  L ; 173 1883 M (comprehensive overview of the topic. In this paper, we )[16 18 29 19 13 17 19 17 19 15 11 18 17 24 18 18 17 13 18 11 17 27 24 18 12 24 11 19 17 24 11 18
19 11 16 10 24 11 19 24 11 19 11 15 24 19 17 19 17 13 10 23 27 17  0]xS 
: N 167 1892 957 45 rp C 
1 1 1 1 scol  L ; 173 1928 M (propose a new technique to reconstruct the position and shape )
[19 13 18 19 18 15 17 10 17 10 19 17 27 10 11 17 16 19 19 11 19 19 17 10 11 18 10 13 17 16 18 19
15 11 13 19 16 11 10 11 19 17 10 19 18 15 11 11 11 18 19 10 17 19 19 10 15 19 17 19 17  0]xS 
: N 167 1937 957 45 rp C 
1 1 1 1 scol  L ; 173 1973 M (of a block)[18 12 30 17 30 19 11 18 16  0]xS 
363 1973 M (-)S 
375 1973 M (like source from a gravity profile. Unlike )[11 11 19 17 30 15 18 19 13 16 17 30 12 13 18 29 30 17 30 18 13 17 18 11 11 17 29 19 13 18 12 11
11 17 10 29 27 19 11 11 19 17  0]xS 
: N 167 1982 957 45 rp C 
1 1 1 1 scol  L ; 173 2018 M (previously published work, the technique employs simple, )[19 13 17 18 11 18 19 15 11 17 20 19 19 19 11 11 15 19 17 19 20 27 18 13 19 10 20 11 19 17 20 11
17 16 19 19 11 19 19 17 19 17 29 19 11 18 17 15 19 15 11 29 19 11 17 10  0]xS 
: N 167 2027 957 45 rp C 
1 1 1 1 scol  L ; 173 2063 M (direct formulae and does not r)[19 11 13 17 16 11 17 12 18 13 29 19 11 17 17 17 17 19 19 17 19 18 17 15 17 19 18 11 17  0]xS 
666 2063 M (equire a search, resulting in )[17 19 19 11 13 17 17 17 17 15 17 17 13 16 19 10 17 13 17 15 19 11 11 11 19 18 17 11 19  0]xS 
: N 167 2072 957 45 rp C 
1 1 1 1 scol  L ; 173 2108 M (very fast computation.)[18 17 13 17 10 12 17 15 11 10 16 18 29 19 19 11 17 11 11 18 19  0]xS 
511 2108 M ( )S 
: N 167 2117 957 45 rp C 
1 1 1 1 scol  L ; 173 2153 M ( )S 
: N 167 2162 957 45 rp C 
1 1 1 1 scol  L ; 173 2198 M (The rationale behind such simplified approach lies in the fact )
[23 19 17 11 13 17 11 11 18 19 17 11 17 11 19 17 19 11 19 19 11 15 19 16 19 11 15 11 29 19 11 11
12 11 17 19 11 17 19 19 13 18 17 16 19 11 11 11 17 15 11 11 19 11 11 19 17 11 12 17 16 11  0]xS 
: N 167 2207 957 45 rp C 
1 1 1 1 scol  L ; 173 2243 M (that, in the absence of \221a priori\222 information, the limitation )
[11 19 17 11 10 16 11 19 16 11 19 17 16 17 19 15 17 19 16 17 15 18 12 15 13 17 15 19 13 11 18 13
11 13 15 11 19 12 18 13 29 17 11 11 18 19 10 15 11 19 17 15 11 11 29 11 11 17 11 11 18 19  0]xS 
: N 167 2252 957 45 rp C 
1 1 1 1 scol  L ; 173 2288 M (imposed by non)[11 29 19 18 15 17 19 14 19 17 14 19 18  0]xS 
421 2288 M (-)S 
433 2288 M (uniqueness of potential field inversion \(see, )[19 19 11 19 19 17 19 17 15 15 14 18 12 14 19 18 11 17 19 11 11 17 11 14 12 11 17 11 19 13 11 19
18 17 13 15 11 18 19 13 13 15 17 17 10  0]xS 
: N 167 2297 957 45 rp C 
1 1 1 1 scol  L ; 173 2333 M (for example, Hornby et al, 2000\) prevents precise depth and )[12 18 13 14 17 19 17 29 19 11 17 10 13 27 18 13 19 19 17 13 17 11 13 17 11 10 13 19 19 19 19 13
13 19 13 17 18 17 19 11 15 13 19 13 17 16 11 15 17 13 19 17 19 11 19 13 17 19 19  0]xS 
: N 167 2342 957 45 rp C 
1 1 1 1 scol  L ; 173 2378 M (shape information of the source. In such cases, we can argue )
[15 19 17 19 17 13 11 19 12 18 13 29 17 11 11 18 19 13 18 12 13 11 19 17 13 15 18 19 13 16 17 10
13 11 19 13 15 19 16 19 12 16 17 15 17 15 10 12 27 17 12 16 17 19 12 17 13 18 19 17  0]xS 
: N 167 2387 957 45 rp C 
1 1 1 1 scol  L ; 173 2423 M (that all we can hope to recover, under restrictive )[11 19 17 11 36 17 11 11 36 27 17 36 16 17 19 36 19 18 19 17 36 11 18 36 13 17 16 18 18 17 13 10
36 19 19 19 17 13 36 13 17 15 11 13 11 16 11 11 18 17  0]xS 
: N 167 2432 957 45 rp C 
1 1 1 1 scol  L ; 173 2468 M (mathematical assumptions, is approximate information about )[29 17 11 19 17 29 17 11 11 16 17 11 13 17 15 15 19 29 19 11 11 18 19 15 10 13 11 15 13 17 19 19
13 18 19 11 29 17 11 17 13 11 19 12 18 13 29 17 11 11 18 19 12 17 19 18 19 11  0]xS 
: N 167 2477 957 45 rp C 
1 1 1 1 scol  L ; 173 2513 M (the sources. Accordingly, the use of sim)[11 19 17 27 15 18 19 13 16 17 15 10 27 26 16 16 18 13 19 11 19 18 11 17 10 27 11 19 17 27 19 15
17 27 18 12 27 15 11  0]xS 
882 2513 M (ple techniques )[19 11 17 26 11 17 16 19 19 11 19 19 17 15  0]xS 
: N 167 2522 957 45 rp C 
1 1 1 1 scol  L ; 173 2558 M (reconstructing the location and shape of simple bodies may )[13 17 16 18 19 15 11 13 19 16 11 11 19 18 16 11 19 17 16 11 18 16 17 11 11 18 19 16 17 19 19 16
15 19 17 19 17 16 18 12 15 15 11 29 19 11 17 15 19 18 19 11 17 15 15 29 17 17  0]xS 
: N 167 2567 957 45 rp C 
1 1 1 1 scol  L ; 173 2603 M (provide a reasonable working answer.)[19 13 18 18 11 19 17 10 17 10 13 17 17 15 18 19 17 19 11 17 10 27 18 13 19 11 19 18 10 17 19 15
27 17 13  0]xS 
751 2603 M ( )S 
: N 167 2612 957 45 rp C 
1 1 1 1 scol  L ; 173 2648 M ( )S 
: N 167 2657 957 45 rp C 
1 1 1 1 scol  L ; 173 2693 M (The fast, simplified calculation involved in the method allows )
[23 19 17 10 12 17 15 11 10 10 15 11 29 19 11 11 12 11 17 19 10 16 17 11 16 19 11 17 11 11 18 19
10 11 19 18 18 11 18 17 19 10 11 19 10 11 19 17 10 29 17 11 19 18 19 10 17 11 11 18 27 15  0]xS 
: N 167 2702 957 45 rp C 
1 1 1 1 scol  L ; 173 2738 M (the algorithm to be used in an interactive fashion. We )[11 19 17 24 17 11 18 18 13 11 11 19 29 24 11 18 24 19 17 24 19 15 17 19 24 11 19 24 17 19 24 11
19 11 17 13 17 16 11 11 18 17 24 12 17 15 19 11 18 19 10 24 35 17  0]xS 
: N 167 2747 957 45 rp C 
1 1 1 1 scol  L ; 173 2783 M (envisage its use in connection with a visualisation package, in )
[17 19 18 11 15 17 18 17 10 11 11 15 10 19 15 17 10 11 19 10 16 18 19 19 17 16 11 11 18 19 10 27
11 11 19 10 17 10 18 11 15 19 17 11 11 15 17 11 11 18 19 10 19 17 16 19 17 18 17 10 10 11 19  0]xS 
: N 167 2792 957 45 rp C 
1 1 1 1 scol  L ; 173 2828 M (which a gravity profile is extracted by mouse)[27 19 11 16 19 16 17 16 18 13 17 18 11 11 17 16 19 13 18 12 11 11 17 16 11 15 16 17 19 11 13 17
16 11 17 19 16 19 17 16 29 18 19 15  0]xS 
900 2828 M (-)S 
912 2828 M (clicking on a )[16 11 11 16 19 11 19 18 16 18 19 15 17  0]xS 
: N 167 2837 957 45 rp C 
1 1 1 1 scol  L ; 173 2873 M (properly shaped anomaly, and an approximate estimation of )[19 13 18 19 17 13 11 17 15 15 19 17 19 17 19 15 17 19 18 29 17 11 17 10 15 17 19 19 15 17 19 15
17 19 19 13 18 19 11 29 17 11 17 15 17 15 11 11 29 17 11 11 18 19 14 18 12  0]xS 
: N 167 2882 957 45 rp C 
1 1 1 1 scol  L ; 173 2918 M (shape and depth of the source is obtained.  This, in turn, will )
[15 19 17 19 17 12 17 19 19 12 19 17 19 11 19 12 18 12 12 11 19 17 11 15 18 19 13 16 17 11 11 15
11 18 19 11 17 11 19 17 19 10 11 11 23 19 11 15 10 11 11 19 11 11 19 13 19 10 11 27 11 11 11  0]xS 
: N 167 2927 957 45 rp C 
1 1 1 1 scol  L ; 173 2963 M (be accepted or rejected by an expert)[19 17 12 17 16 16 17 19 11 17 19 12 18 13 11 13 17 11 17 16 11 17 19 11 19 17 11 17 19 11 17 19
19 17 13  0]xS 
729 2963 M ( user according to his/her )[11 19 15 17 13 11 17 16 16 18 13 19 11 19 18 11 11 18 11 19 11 15 11 19 17 13  0]xS 
: N 167 2972 957 45 rp C 
1 1 1 1 scol  L ; 173 3008 M (geological knowledge of the area and its complexity. )[18 17 18 11 18 18 11 16 17 11 10 19 19 18 27 11 17 19 18 17 10 18 12 10 11 19 17 10 17 13 17 17
10 17 19 19 10 11 11 15 10 16 18 29 19 11 17 19 11 11 17 10  0]xS 
984 3008 M ( )S 
: N 167 3017 957 45 rp C 
1 1 1 1 scol  L ; 173 3053 M ( )S 
: N 1230 928 957 45 rp C 
1 1 1 1 scol  L ; 1236 964 M (Under certain assumptions about the source magnetic )[27 19 19 17 13 32 16 17 13 11 17 11 19 32 17 15 15 19 29 19 11 11 18 19 15 32 17 19 18 19 11 32
11 19 17 32 15 18 19 13 16 17 31 29 17 18 19 17 11 11 16  0]xS 
: N 1230 973 957 45 rp C 
1 1 1 1 scol  L ; 1236 1009 M (properties, the same technique can also be extended to )[19 13 18 19 17 13 11 11 17 15 10 25 11 19 17 24 15 17 29 17 24 11 17 16 19 19 11 19 19 17 24 16
17 19 24 17 11 15 18 24 19 17 24 17 19 11 17 19 19 17 19 24 11 18  0]xS 
: N 1230 1018 957 45 rp C 
1 1 1 1 scol  L ; 1236 1054 M (magnetic data by pseudogravity transformation. Further work )[29 17 18 19 17 11 11 16 12 19 17 11 17 12 19 17 12 19 15 17 19 19 18 18 13 17 18 11 11 17 12 11
13 17 19 15 12 18 13 29 17 11 11 18 19 10 12 21 19 13 11 19 17 13 12 27 18 13 19  0]xS 
: N 1230 1063 957 45 rp C 
1 1 1 1 scol  L ; 1236 1099 M (on real magnetic data is under way.)[18 19 10 13 17 17 11 10 29 17 18 19 17 11 11 16 10 19 17 11 17 10 11 15 10 19 19 19 17 13 10 27
17 17  0]xS 
1777 1099 M ( )S 
: N 1230 1108 957 45 rp C 
1 1 1 1 scol  L ; 1236 1144 M ( )S 
: N 1230 1153 957 50 rp C 
1 1 1 1 scol  L ; F4S2A Ji 
1523 1194 M (THE ALGORITHM)[28 33 28 11 30 28 33 33 30 16 28 33  0]xS 
1894 1194 M ( )S 
: N 1230 1203 957 50 rp C 
1 1 1 1 scol  L ; F1S2A Ji 
1236 1243 M ( )S 
F1S26 Ji 
1236 1289 M (The algorithm attempts to reconstruct the position and shape )
[23 19 17 13 17 11 18 18 13 11 11 19 29 13 17 11 11 17 29 19 11 15 13 11 18 13 13 17 16 18 19 15
11 13 19 16 11 13 11 19 17 12 19 18 15 11 11 11 18 19 12 17 19 19 12 15 19 17 19 17  0]xS 
1236 1334 M (of a block)[18 12 14 17 14 19 11 18 16  0]xS 
1394 1334 M (-)S 
1406 1334 M (like source by direct calculation. It is well known )[11 11 19 17 13 15 18 19 13 16 17 13 19 17 13 19 11 13 17 16 11 13 16 17 11 16 19 11 17 11 11 18
19 10 13 11 11 13 11 15 13 27 17 11 11 13 19 19 18 27 19  0]xS 
1236 1379 M (that potential field inverse problems are non)[11 19 17 11 12 19 18 11 17 19 11 11 17 11 12 12 11 17 11 19 12 11 19 18 17 13 15 17 12 19 13 18
19 11 17 29 15 12 17 13 17 12 19 18  0]xS 
1924 1379 M (-)S 
1936 1379 M (unique, and can )[19 19 11 19 19 17 10 12 17 19 19 12 16 17 19  0]xS 
1236 1424 M (be made unique only by th)[19 17 11 29 17 19 17 11 19 19 11 19 19 17 11 18 19 11 17 10 19 17 10 11  0]xS 
1642 1424 M (e use of a priori information and by )[17 10 19 15 17 10 18 12 10 17 10 19 13 11 18 13 11 10 11 19 12 18 13 29 17 11 11 18 19 10 17 19
19 10 19 17  0]xS 
1236 1469 M (limiting the search to predetermined shaped bodies. In this )[11 11 29 11 11 11 19 18 17 11 19 17 16 15 17 17 13 16 19 16 11 18 16 19 13 17 19 17 11 17 13 29
11 19 17 19 16 15 19 17 19 17 19 16 19 18 19 11 17 15 10 16 11 19 16 11 19 11 15  0]xS 
1236 1514 M (paper the following a priori assumptions are employed:)[19 17 19 17 13 10 11 19 17 10 12 18 11 11 18 27 11 19 18 10 17 10 19 13 11 18 13 11 10 17 15 15
19 29 19 11 11 18 19 15 10 17 13 17 10 17 29 19 11 18 17 17 19  0]xS 
2076 1514 M ( )S 
1236 1559 M (1\) the body has constant density/susceptibility contrast and is )
[19 13 12 11 19 17 12 19 18 19 17 12 19 17 15 12 16 18 19 15 11 17 19 11 11 19 17 19 15 11 11 17
11 15 19 15 16 17 19 11 11 19 11 11 11 11 17 11 16 18 19 11 13 17 15 11 11 17 19 19 11 11 15  0]xS 
1236 1604 M (characterised by sharp boundaries \(no smooth transition of )[16 19 17 13 17 16 11 17 13 11 15 17 19 18 19 17 18 15 19 17 13 19 18 19 18 19 19 19 17 13 11 17
15 18 13 19 18 17 15 29 18 18 11 19 17 11 13 17 19 15 11 11 11 18 19 17 18 12  0]xS 
1236 1649 M (density or susceptibility is allowed\);)[19 17 19 15 11 11 17 10 18 13 10 15 19 15 16 17 19 11 11 19 11 11 11 11 17 10 11 15 10 17 11 11
18 27 17 19 13  0]xS 
1788 1649 M ( )S 
1236 1694 M (2\) the background material has constant )[19 13 78 11 19 17 77 19 17 16 19 18 13 18 19 19 19 77 29 17 11 17 13 11 17 11 77 19 17 15 77 16
18 19 15 11 17 19 11  0]xS 
1236 1739 M (density/susceptibility;)[19 17 19 15 11 11 17 11 15 19 15 16 17 19 11 11 19 11 11 11 11 17  0]xS 
1569 1739 M ( )S 
1236 1784 M (3\) the source has a rectangular shape.)[19 13 10 11 19 17 10 15 18 19 13 16 17 10 19 17 15 10 17 10 13 17 16 11 17 19 18 19 11 17 13 10
15 19 17 19 17  0]xS 
1809 1784 M ( )S 
1236 1829 M ( )S 
1236 1874 M (The algorithm is based on a number of successive steps:)[23 19 17 10 17 11 18 18 13 11 11 19 29 10 11 15 10 19 17 15 17 19 10 18 19 10 17 10 19 19 29 19
17 13 10 18 12 10 15 19 16 16 17 15 15 11 18 17 10 15 11 17 19 15  0]xS 
2090 1874 M ( )S 
1236 1919 M (1\) it determines the location of the c)[19 13 16 11 11 16 19 17 11 17 13 29 11 19 17 15 16 11 19 17 16 11 18 16 17 11 11 18 19 16 18 12
16 11 19 17 16  0]xS 
1831 1919 M (entre of gravity of the )[17 19 11 13 17 16 18 12 15 18 13 17 18 11 11 17 15 18 12 15 11 19 17  0]xS 
1236 1964 M (block;  )[19 11 18 16 19 10 10  0]xS 
1349 1964 M ( )S 
1236 2009 M (2\) it determines the amount of mass responsible for the )[19 13 22 11 11 22 19 17 11 17 13 29 11 19 17 15 22 11 19 17 22 17 29 18 19 19 11 21 18 12 21 29
17 15 15 21 13 17 15 19 18 19 15 11 19 11 17 21 12 18 13 21 11 19 17  0]xS 
1236 2054 M (gravity anomaly;)[18 13 17 18 11 11 17 10 17 19 18 29 17 11 17  0]xS 
1489 2054 M ( )S 
1236 2099 M (3\) given an \221a priori\222 estimation of density contrast, it )[19 13 24 18 11 18 17 19 24 17 19 24 13 17 24 19 13 11 18 13 11 13 24 17 15 11 11 29 17 11 11 18
19 24 18 12 24 19 17 19 15 11 11 17 24 16 18 19 11 13 17 15 11 10 24 11 11  0]xS 
1236 2144 M (determines the width and thickness of the block.)[19 17 11 17 13 29 11 19 17 15 10 11 19 17 10 27 11 19 11 19 10 17 19 19 10 11 19 11 16 19 19 17
15 15 10 18 12 10 11 19 17 10 19 11 18 16 19  0]xS 
1975 2144 M ( )S 
1236 2189 M ( )S 
1236 2234 M (The different steps are described in the following.)[23 19 17 10 19 11 12 12 17 13 17 19 11 10 15 11 17 19 15 10 17 13 17 10 19 17 15 16 13 11 19 17
19 10 11 19 10 11 19 17 10 12 18 11 11 18 27 11 19 18  0]xS 
1998 2234 M ( )S 
1236 2279 M ( )S 
/F4S26 F4 [38 0 0 -38 0 0 ] mFS
F4S26 Ji 
1236 2325 M (Determination of the centre of gravity)[27 17 13 17 17 31 11 21 19 13 11 18 21 30 18 13 30 13 21 17 30 17 17 21 13 17 17 30 18 13 30 19
17 19 18 11 13  0]xS 
F1S26 Ji 
1952 2325 M (. The largest )[10 29 23 19 17 29 11 17 13 18 17 15 11  0]xS 
1236 2370 M (uncertainty in the analysis of potential field data lies in the )
[19 19 16 17 13 11 17 11 19 11 17 15 11 19 15 11 19 17 15 17 19 17 11 17 15 11 15 15 18 12 15 19
18 11 17 19 11 11 17 11 15 12 11 17 11 19 15 19 17 11 17 14 11 11 17 15 14 11 19 14 11 19 17  0]xS 
1236 2415 M (determination of the source depth. However, under the )[19 17 11 17 13 29 11 19 17 11 11 18 19 26 18 12 26 11 19 17 26 15 18 19 13 16 17 26 19 17 19 11
19 10 26 27 18 27 17 18 17 13 10 26 19 19 19 17 13 26 11 19 17  0]xS 
1236 2460 M (restrictive a priori assumptions listed above, it is possible to )
[13 17 15 11 13 11 16 11 11 18 17 13 17 13 19 13 11 18 13 11 13 17 15 15 19 29 19 11 11 18 19 15
13 11 11 15 11 17 19 13 17 19 18 18 17 10 13 11 11 13 11 15 13 19 18 15 15 11 19 11 17 13 11 18
 0]xS 
1236 2505 M (determine )[19 17 11 17 13 29 11 19 17  0]xS 
1403 2505 M (the location of the centre of gravity of the source. )[11 19 17 14 11 18 16 17 11 11 18 19 14 18 12 14 11 19 17 13 16 17 19 11 13 17 13 18 12 13 18 13
17 18 11 11 17 13 18 12 13 11 19 17 13 15 18 19 13 16 17 10  0]xS 
1236 2550 M (Several papers dealing with this subject have been published )
[21 17 18 17 13 17 11 12 19 17 19 17 13 15 12 19 17 17 11 11 19 18 12 27 11 11 19 12 11 19 11 15
12 15 19 19 11 17 16 11 12 19 17 18 17 12 19 17 17 19 11 19 19 19 11 11 15 19 17 19  0]xS 
1236 2595 M (in the Russian literature in the 60s and 70s and, to our )[11 19 21 11 19 17 21 25 19 15 15 11 17 19 21 11 11 11 17 13 17 11 19 13 17 21 11 19 21 11 19 17
20 19 19 15 20 17 19 19 20 19 19 15 20 17 19 19 10 20 11 18 20 18 19 13  0]xS 
1236 2640 M (knowledge, were never published in English \(Tsaregradskiy )[19 19 18 27 11 17 19 18 17 10 15 27 17 13 17 15 19 17 18 17 13 15 19 19 19 11 11 15 19 17 19 15
11 19 15 23 19 18 11 11 15 19 15 13 23 15 17 13 17 18 13 17 19 15 19 11 17  0]xS 
1236 2685 M (1965, Sokolovskii 1978, Mendelutsa 1967, Managadze, )[19 19 19 19 10 29 21 18 19 18 11 18 18 15 19 11 11 29 19 19 19 19 10 29 34 17 19 19 17 11 19 11
15 17 29 19 19 19 19 10 29 34 17 19 17 18 17 19 16 17 10  0]xS 
1236 2730 M (Glonti and Rusadze 1976, Lyubimov and Lyubimov 1970\). )[27 11 18 19 11 11 17 17 19 19 17 25 19 15 17 19 16 17 17 19 19 19 19 10 17 22 17 19 19 11 29 18
18 17 17 19 19 17 22 17 19 19 11 29 18 18 17 19 19 19 19 13 10  0]xS 
1236 2775 M (Here we propose an alternative, simpler method.)[27 17 13 17 10 27 17 10 19 13 18 19 18 15 17 10 17 19 10 17 11 11 17 13 19 17 11 11 18 17 10 10
15 11 29 19 11 17 13 10 29 17 11 19 18 19  0]xS 
1979 2775 M ( )S 
1236 2820 M ( )S 
: N 176 965 941 79 rp C 
1 1 1 1 scol  L ; F4S2A Ji 
534 1035 M (SUMMARY)[23 30 40 40 30 30  0]xS 
758 1035 M ( )S 
: N 173 962 3 3 rp C 
 L ; : N 173 962 3 3 rp C 
 L ; : N 176 962 941 3 rp C 
 L ; : N 1117 962 3 3 rp C 
 L ; : N 1117 962 3 3 rp C 
 L ; : N 173 965 3 79 rp C 
 L ; : N 1117 965 3 79 rp C 
 L ; : N 176 1044 941 45 rp C 
1 1 1 1 scol  L ; F1S26 Ji 
211 1080 M ( )S 
: N 173 1044 3 45 rp C 
 L ; : N 1117 1044 3 45 rp C 
 L ; : N 176 1089 941 45 rp C 
1 1 1 1 scol  L ; 211 1125 M (Given a gravity profile, the location and size of a block)[27 11 18 17 19 13 17 13 18 13 17 18 11 11 17 12 19 13 18 12 11 11 17 10 12 11 19 17 12 11 18 16
17 11 11 18 19 12 17 19 19 12 15 11 16 17 12 18 12 12 17 12 19 11 18 16  0]xS 
1070 1125 M (-)S 
: N 173 1089 3 45 rp C 
 L ; : N 1117 1089 3 45 rp C 
 L ; : N 176 1134 941 45 rp C 
1 1 1 1 scol  L ; 211 1170 M (like approximation to the source can be found with the )[11 11 19 17 15 17 19 19 13 18 19 11 29 17 11 11 18 19 15 11 18 14 11 19 17 14 15 18 19 13 16 17
14 16 17 19 14 19 17 14 12 18 19 19 19 14 27 11 11 19 14 11 19 17  0]xS 
: N 173 1134 3 45 rp C 
 L ; : N 1117 1134 3 45 rp C 
 L ; : N 176 1179 941 45 rp C 
1 1 1 1 scol  L ; 211 1215 M (use of simple formulas that do not involve any searching. )[19 15 17 11 18 12 10 15 11 29 19 11 17 10 12 18 13 29 19 11 17 15 10 11 19 17 11 10 19 18 10 19
18 11 10 11 19 18 18 11 18 17 10 17 19 17 10 15 17 17 13 16 19 11 19 18 10  0]xS 
: N 173 1179 3 45 rp C 
 L ; : N 1117 1179 3 45 rp C 
 L ; : N 176 1224 941 45 rp C 
1 1 1 1 scol  L ; 211 1260 M (This allows for a very fast algorithm and real)[23 19 11 15 23 17 11 11 18 27 15 23 12 18 13 23 17 23 18 17 13 17 23 12 17 15 11 23 17 11 18 18
13 11 11 19 29 23 17 19 19 23 13 17 17  0]xS 
1002 1260 M (-)S 
1014 1260 M (time )[11 11 29 17  0]xS 
: N 173 1224 3 45 rp C 
 L ; : N 1117 1224 3 45 rp C 
 L ; : N 176 1269 941 45 rp C 
1 1 1 1 scol  L ; 211 1305 M (results. The approach has proven robust when tested )[13 17 15 19 11 11 15 10 21 23 19 17 20 17 19 19 13 18 17 16 19 20 19 17 15 20 19 13 18 18 17 19
20 13 18 19 19 15 11 20 27 19 17 19 20 11 17 15 11 17 19  0]xS 
: N 173 1269 3 45 rp C 
 L ; : N 1117 1269 3 45 rp C 
 L ; : N 176 1314 941 45 rp C 
1 1 1 1 scol  L ; 211 1350 M (against different irregular sources and under noisy )[17 18 17 11 19 15 11 28 19 11 12 12 17 13 17 19 11 28 11 13 13 17 18 19 11 17 13 28 15 18 19 13
16 17 15 27 17 19 19 27 19 19 19 17 13 27 19 18 11 15 17  0]xS 
: N 173 1314 3 45 rp C 
 L ; : N 1117 1314 3 45 rp C 
 L ; : N 176 1359 941 45 rp C 
1 1 1 1 scol  L ; 211 1395 M (conditions. An applicati on to real data is also prese)[16 18 19 19 11 11 11 18 19 15 10 10 26 19 10 17 19 19 11 11 16 17 11 11 10 18 19 10 11 18 10 13
17 17 11 10 19 17 11 17 10 11 15 10 17 11 15 18 10 19 13 17 15  0]xS 
1001 1395 M (nted.)[19 11 17 19  0]xS 
1077 1395 M ( )S 
: N 173 1359 3 45 rp C 
 L ; : N 1117 1359 3 45 rp C 
 L ; : N 176 1404 941 45 rp C 
1 1 1 1 scol  L ; 211 1440 M ( )S 
: N 173 1404 3 45 rp C 
 L ; : N 1117 1404 3 45 rp C 
 L ; : N 176 1449 941 46 rp C 
1 1 1 1 scol  L ; F4S26 Ji 
211 1486 M (Key words:)[30 17 18 15 27 18 17 21 15  0]xS 
F1S26 Ji 
402 1486 M ( Gravity, Magnetics, Inversions, Multiscale )[15 27 13 17 18 11 11 17 10 15 34 17 18 19 17 11 11 16 15 10 15 11 19 18 17 13 15 11 18 19 15 10
15 34 19 11 11 11 15 16 17 11 17  0]xS 
: N 173 1449 3 46 rp C 
 L ; : N 1117 1449 3 46 rp C 
 L ; : N 176 1495 941 74 rp C 
1 1 1 1 scol  L ; 211 1531 M (edges.)[17 19 18 17 15  0]xS 
307 1531 M ( )S 
: N 173 1569 3 3 rp C 
 L ; : N 173 1569 3 3 rp C 
 L ; : N 176 1569 941 3 rp C 
 L ; : N 1117 1569 3 3 rp C 
 L ; : N 1117 1569 3 3 rp C 
 L ; : N 173 1495 3 74 rp C 
 L ; : N 1117 1495 3 74 rp C 
 L ; LH
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%%Page: 2 2
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%%BeginPageSetup
/DeviceRGB dup setcolorspace /colspABC exch def
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0 0 0 1 scol /F2S26 F2 [38 0 0 -38 0 0 ] mFS
F2S26 Ji 
173 122 M ( )S 
F1S2A Ji 
173 3285 M ( )S 
2162 127 M ( )S 
Pscript_WinNT_Incr begin
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; 1068 561 M (\(b\))[13 19  0]xS 
1113 561 M ( )S 
: N 167 570 957 45 rp C 
1 1 1 1 scol  L ; F4S26 Ji 
173 607 M (Figure 1.  Multiscale edges for a block)[24 11 19 21 17 17 12 19 10 12 12 36 21 11 13 11 15 17 19 11 17 12 17 21 19 17 15 12 13 18 17 12
19 12 21 11 18 17  0]xS 
809 607 M (-)S 
822 607 M (shaped source \(a\).  )[15 21 19 21 17 21 11 15 18 21 17 17 17 11 13 19 13 10 10  0]xS 
: N 167 615 957 45 rp C 
1 1 1 1 scol  L ; 173 652 M (\(b\) Multiscale edges for a block \(solid line)[13 21 13 19 36 21 11 13 11 15 17 19 11 17 19 17 21 19 17 15 19 13 18 17 19 19 19 21 11 18 17 20
18 13 15 18 11 11 21 18 11 11 21  0]xS 
914 652 M (s\) and their )[15 13 18 19 21 21 18 13 21 17 11 17  0]xS 
: N 167 660 957 45 rp C 
1 1 1 1 scol  L ; 173 697 M (point source approximation \(dashed lines\).)[21 18 11 21 13 10 15 18 21 17 17 17 10 19 21 21 17 18 19 11 31 19 13 11 18 21 10 13 21 19 15 21
17 21 10 11 11 21 17 15 13  0]xS 
866 697 M ( )S 
: N 167 705 957 45 rp C 
1 1 1 1 scol  L ; 173 742 M ( )S 
F1S26 Ji 
173 786 M (In Figure 1a we show a block)[11 19 27 21 11 18 19 13 17 27 19 17 27 27 17 27 15 19 18 27 27 17 26 19 11 18 16  0]xS 
722 786 M (-)S 
734 786 M (shaped source and the )[15 19 17 19 17 19 26 15 18 19 13 16 17 26 17 19 19 26 11 19 17  0]xS 
173 831 M (multiscale edges obtained from its gravity response. The )[29 19 11 11 11 15 16 17 11 17 23 17 19 18 17 15 22 18 19 11 17 11 19 17 19 22 12 13 18 29 22 11
11 15 22 18 13 17 18 11 11 17 22 13 17 15 19 18 19 15 17 10 22 23 19 17  0]xS 
173 876 M (multiscale edges represent the location of the local extrema of )
[29 19 11 11 11 15 16 17 11 17 10 17 19 18 17 15 10 13 17 19 13 17 15 17 19 11 10 11 19 17 10 11
18 16 17 11 11 18 19 10 18 12 10 11 19 17 10 11 18 16 17 11 10 17 19 11 13 17 29 17 10 18 12  0]xS 
173 921 M (the horizontal gradient of the gravity response, at different )
[11 19 17 17 19 18 13 11 16 18 19 11 17 11 17 18 13 17 19 11 17 19 11 17 18 12 17 11 19 17 17 18
13 17 18 11 11 17 17 13 17 15 19 18 19 15 17 10 17 17 11 17 19 11 12 12 17 13 17 19 11  0]xS 
173 966 M (heights, i.e. at different level of upward continuation. The )
[19 17 11 18 19 11 15 10 18 11 10 17 10 18 17 11 18 19 11 12 12 17 13 17 19 11 18 11 17 18 17 11
18 18 12 18 19 19 27 17 13 19 17 16 18 19 11 11 19 19 17 11 11 18 19 10 17 23 19 17  0]xS 
173 1011 M (multiscale edges behave differently depending on the shape )[29 19 11 11 11 15 16 17 11 17 16 17 19 18 17 15 16 19 17 19 17 18 17 15 19 11 12 12 17 13 17 19
11 11 17 15 19 17 19 17 19 19 11 19 18 15 18 19 15 11 19 17 15 15 19 17 19 17  0]xS 
173 1056 M (of the source. For more details about the theory underlying )[18 12 16 11 19 17 16 15 18 19 13 16 17 10 16 21 18 13 16 29 18 13 17 16 19 17 11 17 11 11 15 16
17 19 18 19 11 15 11 19 17 15 11 19 17 18 13 17 15 19 19 19 17 13 11 17 11 19 18  0]xS 
173 1101 M (multiscale edge analysis of potential fie)[29 19 11 11 11 15 16 17 11 17 15 17 19 18 17 15 17 19 17 11 17 15 11 15 15 18 12 15 19 18 11 17
19 11 11 17 11 15 12 11  0]xS 
802 1101 M (ld data we refer the )[11 19 15 19 17 11 17 15 27 17 15 13 17 12 17 13 14 11 19 17  0]xS 
173 1146 M (reader to Hornby et al \(1999\) and Moreau, et al. \(1997\). )[13 17 17 19 17 13 10 11 18 10 27 18 13 19 19 17 10 17 11 10 17 11 10 13 19 19 19 19 13 10 17 19
19 10 34 18 13 17 17 19 10 10 17 11 10 17 11 10 10 13 19 19 19 19 13 10  0]xS 
1040 1146 M ( )S 
173 1191 M (For the purposes of this paper we note that the multiscale )[21 18 13 17 11 19 17 17 19 19 13 19 18 15 17 15 17 18 12 17 11 19 11 15 17 19 17 19 17 13 17 27
17 17 19 18 11 17 17 11 19 17 11 17 11 19 17 16 29 19 11 11 11 15 16 17 11 17  0]xS 
173 1236 M (edges due to the block)[17 19 18 17 15 11 19 19 17 11 11 18 11 11 19 17 11 19 11 18 16  0]xS 
517 1236 M (-)S 
529 1236 M (like source tend to bend outward close )[11 11 19 17 11 15 18 19 13 16 17 11 11 17 19 19 11 11 18 10 19 17 19 19 10 18 19 11 27 17 13 19
10 16 11 18 15 17  0]xS 
173 1281 M (to the source. The multiscale edges due to a point source )[11 18 19 11 19 17 19 15 18 19 13 16 17 10 18 23 19 17 18 29 19 11 11 11 15 16 17 11 17 18 17 19
18 17 15 18 19 19 17 18 11 18 18 17 18 19 18 11 19 11 18 15 18 19 13 16 17  0]xS 
173 1326 M (however, distribute along 2 lines \(in 2D approximation\) \(see )
[19 18 27 17 18 17 13 10 13 19 11 15 11 13 11 19 19 11 17 13 17 11 18 19 18 13 19 13 11 11 19 17
15 12 13 11 19 12 19 27 12 17 19 19 13 18 19 11 29 17 11 11 18 19 13 12 13 15 17 17  0]xS 
173 1371 M (Figure 1b, dashed lines\). Whether a source can be )[21 11 18 19 13 17 33 19 19 10 33 19 17 15 19 17 19 33 11 11 19 17 15 13 10 33 35 19 17 11 19 17
13 33 17 33 15 18 19 13 16 17 32 16 17 19 32 19 17  0]xS 
173 1416 M (approximated by a block or a point source depends primarily )[17 19 19 13 18 19 11 29 17 11 17 19 13 19 17 13 17 12 19 11 18 16 19 12 18 13 12 17 12 19 18 11
19 11 12 15 18 19 13 16 17 12 19 17 19 17 19 19 15 12 19 13 11 29 17 13 11 11 17  0]xS 
173 1461 M (on its shape, but also on the scale of resolution of the )[18 19 23 11 11 15 23 15 19 17 19 17 10 23 19 19 11 22 17 11 15 18 22 18 19 22 11 19 17 22 15 16
17 11 17 22 18 12 22 13 17 15 18 11 19 11 11 18 19 22 18 12 22 11 19 17  0]xS 
173 1506 M (analysis. Very far from a )[17 19 17 11 17 15 11 15 10 17 27 17 13 17 17 12 17 13 17 12 13 18 29 17 17  0]xS 
595 1506 M (source \(i.e. at very high level of )[15 18 19 13 16 17 17 13 11 10 17 10 17 17 11 17 18 17 13 17 17 19 11 18 19 16 11 17 18 17 11 16
18 12  0]xS 
173 1551 M (upward continuation\), different shaped sources tend to give )[19 19 27 17 13 19 16 16 18 19 11 11 19 19 17 11 11 18 19 13 10 16 19 11 12 12 17 13 17 19 11 16
15 19 17 19 17 19 16 15 18 19 13 16 17 15 16 11 17 19 19 15 11 18 15 18 11 18 17  0]xS 
173 1596 M (similar gravity response. In the limit of infinite upward )[15 11 29 11 11 17 13 24 18 13 17 18 11 11 17 23 13 17 15 19 18 19 15 17 10 23 11 19 23 11 19 17
23 11 11 29 11 11 23 18 12 23 11 19 12 11 19 11 11 17 23 19 19 27 17 13 19  0]xS 
173 1641 M (continuation, all sources of limited spatial extent look like a )
[16 18 19 11 11 19 19 17 11 11 18 19 10 14 17 11 11 14 15 18 19 13 16 17 15 13 18 12 13 11 11 29
11 11 17 19 13 15 19 17 11 11 17 11 13 17 19 11 17 19 11 13 11 18 18 19 13 11 11 19 17 13 17  0]xS 
173 1686 M (point source. This can be seen in Figure 1b \(solid lines\). Very )
[19 18 11 19 11 11 15 18 19 13 16 17 10 10 23 19 11 15 10 16 17 19 10 19 17 10 15 17 17 19 10 11
19 10 21 11 18 19 13 17 10 19 19 10 13 15 18 11 11 19 10 11 11 19 17 15 13 10 10 27 17 13 17  0]xS 
173 1731 M (far from the block the multiscale asymptote to lines with the )
[12 17 13 13 12 13 18 29 13 11 19 17 13 19 11 18 16 19 13 11 19 17 13 29 19 11 11 11 15 16 17 11
17 13 17 15 17 29 19 11 18 11 17 12 11 18 12 11 11 19 17 15 12 27 11 11 19 12 11 19 17  0]xS 
173 1776 M (same inclination as in the point source case. It is important to )
[15 17 29 17 11 11 19 16 11 11 19 17 11 11 18 19 11 17 15 11 11 19 11 11 19 17 11 19 18 11 19 11
11 15 18 19 13 16 17 11 16 17 15 17 10 11 11 11 11 11 15 10 11 29 19 18 13 11 17 19 11 10 11 18
 0]xS 
173 1821 M (notice that the lines intersect at the centre of gravity of the )
[19 18 11 11 16 17 15 11 19 17 11 15 11 19 17 15 11 11 19 17 15 15 11 19 11 17 13 15 17 16 11 15
17 11 15 11 19 17 15 16 17 19 11 13 17 15 18 12 15 18 13 17 18 11 11 17 15 18 12 15 11 19 17  0]xS 
173 1866 M (source, i.e., at the location of the clo)[15 18 19 13 16 17 10 26 11 10 17 10 10 26 17 11 25 11 19 17 25 11 18 16 17 11 11 18 19 25 18 12
25 11 19 17 25 16 11  0]xS 
834 1866 M (sest point source )[15 17 15 11 25 19 18 11 19 11 25 15 18 19 13 16 17  0]xS 
173 1911 M (approximation to the source.  )[17 19 19 13 18 19 11 29 17 11 11 18 19 10 11 18 10 11 19 17 10 15 18 19 13 16 17 10 10  0]xS 
628 1911 M ( )S 
173 1956 M ( )S 
F4S26 Ji 
173 2002 M (Determination of the amount of mass)[27 17 13 17 17 31 11 21 19 13 11 18 21 19 18 13 19 13 21 17 19 19 31 18 21 21 13 19 18 13 18 31
19 15  0]xS 
F1S26 Ji 
819 2002 M (. As can be easily )[10 18 26 15 18 16 17 19 18 19 17 18 17 17 15 11 11 17  0]xS 
173 2047 M (verified, the integral over the plane of the Green\222s function )
[18 17 13 11 12 11 17 19 10 15 11 19 17 15 11 19 11 17 18 13 17 11 15 18 18 17 13 15 11 19 17 15
19 11 17 19 17 15 18 12 15 11 19 17 15 27 13 17 17 19 13 15 14 12 19 19 16 11 11 18 19  0]xS 
173 2092 M (for vertical gravity acceleration is constant, i.e., does not )
[12 18 13 21 18 17 13 11 11 16 17 11 21 18 13 17 18 11 11 17 21 17 16 16 17 11 17 13 17 11 11 18
19 20 11 15 20 16 18 19 15 11 17 19 11 10 20 11 10 17 10 10 20 19 18 17 15 20 19 18 11  0]xS 
173 2137 M (depend on the height from the source \(see Hornby et al., )[19 17 19 17 19 19 19 18 19 19 11 19 17 19 19 17 11 18 19 11 19 12 13 18 29 19 11 19 17 19 15 18
19 13 16 17 19 13 15 17 17 19 27 18 13 19 19 17 18 17 11 18 17 11 10 10  0]xS 
173 2182 M (1999\). Apart from multiplicative constants, this integral )[19 19 19 19 13 10 26 26 19 17 13 11 26 12 13 18 29 25 29 19 11 11 11 19 11 11 16 17 11 11 18 17
25 16 18 19 15 11 17 19 11 15 10 25 11 19 11 15 25 11 19 11 17 18 13 17 11  0]xS 
173 2227 M (equals the amount of mass in the source. Consequently, if we )
[17 19 19 17 11 15 12 11 19 17 12 17 29 18 19 19 11 11 18 12 11 29 17 15 15 11 11 19 11 11 19 17
11 15 18 19 13 16 17 10 11 25 18 19 15 17 19 19 17 19 11 11 17 10 11 11 12 11 27 17  0]xS 
173 2272 M (have a reasonable a priori knowledge of the density of the )[19 17 18 17 17 17 17 13 17 17 15 18 19 17 19 11 17 17 17 17 19 13 11 18 13 11 16 19 19 18 27 11
17 19 18 17 16 18 12 16 11 19 17 16 19 17 19 15 11 11 17 16 18 12 16 11 19 17  0]xS 
173 2317 M (unknown source, it is possible to determine its c)[19 19 19 19 18 27 19 11 15 18 19 13 16 17 10 10 11 11 10 11 15 10 19 18 15 15 11 19 11 17 10 11
18 10 19 17 11 17 13 29 11 19 17 10 11 11 15 10  0]xS 
910 2317 M (ross)[13 18 15  0]xS 
971 2317 M (-)S 
983 2317 M (sectional )[15 17 16 11 11 18 19 17 11  0]xS 
173 2362 M (area in a 2D approximation, or its volume in 3D. )[17 13 17 17 10 11 19 10 17 10 19 27 10 17 19 19 13 18 19 11 29 17 11 11 18 19 10 10 18 13 10 11
11 15 10 18 18 11 19 29 17 10 11 19 10 19 27 10  0]xS 
927 2362 M ( )S 
173 2407 M ( )S 
F4S26 Ji 
173 2453 M (Determination of the shape of the block)[27 17 13 17 17 31 11 21 19 13 11 18 21 10 18 13 10 13 21 17 10 15 21 19 21 17 10 18 13 10 13 21
17 10 21 11 18 17  0]xS 
F1S26 Ji 
813 2453 M (. )[10  0]xS 
833 2453 M ( )S 
173 2498 M (Referring to Figure 1a, the equation of the location of the )[25 17 12 17 13 13 11 19 18 10 11 18 10 21 11 18 19 13 17 10 19 17 10 10 11 19 17 10 17 19 19 17
11 11 18 19 10 18 12 10 11 19 17 10 11 18 16 17 11 11 18 19 10 18 12 10 11 19 17  0]xS 
173 2543 M (multiscale edges for a block)[29 19 11 11 11 15 16 17 11 17 10 17 19 18 17 15 10 12 18 13 10 17 10 19 11 18 16  0]xS 
599 2543 M (-)S 
611 2543 M (shaped source is :)[15 19 17 19 17 19 10 15 18 19 13 16 17 10 11 15 10  0]xS 
880 2543 M ( )S 
11585 VM?
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07e5004c04d3005d03f4002f02a200410652006306520063064a002a05b4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>
[15961 14417 14187 ] AllocGlyphStorage
]def 
108 44 
PrepFor2015
AddFontInfoBegin
/OrigFontType /TrueType def 
/OrigFontName <53796D626F6C> def
/OrigFontStyle () def
/FSType 0 def
AddFontInfoEnd
[16#2c 16#85ae213a ] AddXUID
Type42DictEnd
1 2330 11 <00010000fe460228058e000f0040401e480a480e6909690b690d780ab602
c7020800080107110113010000080807b8012cb70c7604bb102128182b10
f4fdf43c103c103c003f3f1139393130015d011524001110003715060602
151412160228fefbfedd0132f67b9e4e4894fe712b8201f7012b013701ff
6e2a44ecfe95c5dffe98ed00>/TTE1EBEAC8t00 AddT42Char 
1 0 0 <0002010000000500050000030007003b401e06076302010005046303000a
0605630303021a09070463010019082938182b4e10f43c4dfd3c4e10f63c
4d10fd3c003f3cfd3c3f3cfd3c3130211121112521112101000400fc2003
c0fc400500fb002004c0>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/parenleft 11 def
/.notdef 0 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 1 /parenleft put
pop
F /F5 0 /0 F /TTE1EBEAC8t00 mF 
/F5S19YFFFFFFD4 F5 [25.355 0 0 -43.457 0 0 ] mFS
F5S19YFFFFFFD4 Ji 
199 2613 M <01>S 
533 VM?
1 2462 12 <0001002dfe460255058e000f0040401b2803280538033805580398039805
07000807130111070808000001b8012cb40c7604bb11ba0139025e00182b
10f6fdf43c103c103c003f3f39393130015d133504001110000735363612
353402262d01050123fecef67c9e4d479505642a81fe09fed5fec9fe006e
2b44ec016ac6de0169ed>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/parenright 12 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 2 /parenright put
pop
219 2613 M <02>S 
N 272 2584 M 275 2582 I K 
1 Lj 1 Lc 32 Lw solid N 275 2583 M 280 2594 I : 0.066 0.086 +S K 
; 1 Lw solid N 280 2594 M 287 2561 I K 
N 287 2561 M 300 2561 I K 
N 269 2605 M 302 2605 I K 
449 2613 M <01>S 
559 2613 M <02>S 
N 680 2605 M 683 2603 I K 
32 Lw solid N 683 2603 M 688 2615 I : 0.066 0.086 +S K 
; 1 Lw solid N 689 2615 M 695 2581 I K 
N 695 2581 M 714 2581 I K 
/F5S19YFFFFFFC5 F5 [25.469 0 0 -58.66 0 0 ] mFS
F5S19YFFFFFFC5 Ji 
396 2613 M <01>S 
716 2613 M <02>S 
N 307 2607 M 310 2605 I K 
32 Lw solid N 310 2606 M 315 2623 I : 0.066 0.086 +S K 
; 1 Lw solid N 316 2623 M 322 2574 I K 
N 322 2574 M 723 2574 I K 

%%IncludeResource: font Times-Italic
F /F6 0 /256 T /Times-Italic mF 
/F6S21 F6 [33.176 0 0 -33.176 0 0 ] mFS
F6S21 Ji 
694 2613 M (V)S 
637 2613 M (z)S 
614 2613 M (z)S 
547 2613 M (s)S 
505 2613 M (z)S 
458 2613 M (z)S 
403 2613 M (s)S 
325 2613 M (x)S 
207 2613 M (s)S 
179 2613 M (X)S 
/F6S13 F6 [19.352 0 0 -19.352 0 0 ] mFS
F6S13 Ji 
648 2621 M (l)S 
625 2621 M (d)S 
516 2621 M (l)S 
468 2621 M (d)S 
337 2621 M (m)S 
533 VM?
1 3250 16 <0001000001dd041a02400003001a400c001d03011a050019042028182b4e
10e410e6002f4dfd313011211521041afbe602406300>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/minus 16 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 3 /minus put
pop
/F5S21 F5 [33.176 0 0 -33.176 0 0 ] mFS
F5S21 Ji 
661 2613 M <03>S 
582 2613 M <03>S 
528 2613 M <03>S 
533 VM?
1 3016 14 <000100000000041a041a000b0033b900010273b4030a1d0409b802734010
070a035801061d00075809190c2028182b4e10f44df43cfd3ce4003ff43c
fd3ce4313001331121152111231121352101dd6201dbfe2562fe2301dd04
1afe2261fe2501db6100>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/plus 14 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 4 /plus put
pop
485 2613 M <04>S 
430 2613 M <04>S 
365 2613 M <03>S 
533 VM?
2 12240 114 <000200000000041a04f6000b000f0044b900010273b4030a1d0409ba0273
0007027640160d0c1d0e0f0a030e5801061d0007580f0919102028182b4e
10f43c4df43cfd3cf43c003f3c4dfd3cf6f43cfd3ce43130013311211521
1123112135210121152101de6101dbfe2561fe2201defe22041afbe604f6
fe2161fe2501db61fd4c6300>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/plusminus 114 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 5 /plusminus put
pop
251 2613 M <05>S 
533 VM?
1 6332 32 <00020000011f041a02f7000300070036401d021d01031d00051d0606014b
004b7f07010706011a09070019082028182b4e10f43c10f63c002f714ded
ed3c10ed10ed10ed31301121152111211521041afbe6041afbe602f761fe
ec63>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/equal 32 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 6 /equal put
pop
231 2613 M <06>S 
/F1S21 F1 [33.176 0 0 -33.176 0 0 ] mFS
F1S21 Ji 
600 2613 M (2)S 
383 2613 M (2)S 
: 280 2610 17 36 rc 280 2639 M (6)S 
; 288 2592 M (3)S 
/F1S13 F1 [19.352 0 0 -19.352 0 0 ] mFS
F1S13 Ji 
567 2596 M (2)S 
415 2598 M (2)S 
350 2596 M (2)S 
F1S26 Ji 
728 2596 M (                              \()[10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  0]xS 
1041 2596 M (1)S 
1060 2596 M (\))S 
1073 2596 M ( )S 
1 0 0 1 scol 1827 2596 M ( )S 
0 0 0 1 scol 173 2706 M (where )[27 19 17 13 17  0]xS 
/F6S26 F6 [38 0 0 -38 0 0 ] mFS
F6S26 Ji 
276 2706 M (X\(s\))[23 12 15  0]xS 
F1S26 Ji 
338 2706 M ( is the location of the multiscale edge relative to the )[10 11 15 10 11 19 17 10 11 18 16 17 11 11 18 19 10 18 12 10 11 19 17 10 29 19 11 11 11 15 16 17
11 17 10 17 19 18 17 10 13 17 11 17 11 11 18 17 10 11 18 10 11 19 17  0]xS 
173 2765 M (centre of the block, )[16 17 19 11 13 17 10 18 12 10 11 19 17 10 19 11 18 16 19 10  0]xS 
/F6S1D F6 [29.164 0 0 -29.164 0 0 ] mFS
F6S1D Ji 
509 2778 M (m)S 
/F6S32 F6 [50 0 0 -50 0 0 ] mFS
F6S32 Ji 
486 2765 M (x)S 
F1S26 Ji 
539 2765 M (is the width of the block, )[11 15 10 11 19 17 10 27 11 19 11 19 10 18 12 10 11 19 17 10 19 11 18 16 19 10  0]xS 
F6S1D Ji 
958 2778 M (l)S 
F6S32 Ji 
939 2765 M (z)S 
F1S26 Ji 
979 2765 M (and )[17 19 19  0]xS 
F6S1D Ji 
203 2853 M (d)S 
F6S32 Ji 
182 2840 M (z)S 
F1S26 Ji 
231 2840 M (are the depth to the top and to the )[17 13 17 10 11 19 17 10 19 17 19 11 19 10 11 18 10 11 19 17 10 11 18 19 10 17 19 19 10 11 18 10
11 19 17  0]xS 
755 2840 M (bottom of the block, )[19 18 11 11 18 29 10 18 12 10 11 19 17 10 19 11 18 16 19 10  0]xS 
173 2902 M (respectively, and )[13 17 15 19 17 16 11 11 18 17 11 17 10 10 17 19 19  0]xS 
F6S26 Ji 
440 2902 M (s)S 
F1S26 Ji 
455 2902 M ( is the scale \(level of upward continuation\) )[10 11 15 10 11 19 17 10 15 16 17 11 17 10 13 11 17 18 17 11 10 18 12 10 19 19 27 17 13 19 10 16
18 19 11 11 19 19 17 11 11 18 19 13  0]xS 
173 2947 M (and          )[17 19 19 10 10 10 10 10 10 10 10 10  0]xS 
328 2947 M ( )S 
: 240 2956 12 70 rc /F5S24YFFFFFFB9 F5 [36.957 0 0 -70.891 0 0 ] mFS
F5S24YFFFFFFB9 Ji 
240 3010 M <01>S 
; : 747 2956 12 70 rc F5S24YFFFFFFB9 Ji 
747 3010 M <02>S 
; /F5S24YFFFFFFCA F5 [36.797 0 0 -53.141 0 0 ] mFS
F5S24YFFFFFFCA Ji 
249 3080 M <01>S 
360 3080 M <02>S 
222 3080 M <01>S 
467 3080 M <02>S 
793 3080 M <01>S 
904 3080 M <02>S 
F5S24YFFFFFFB9 Ji 
213 3080 M <01>S 
915 3080 M <02>S 
/F6S17 F6 [23.664 0 0 -23.664 0 0 ] mFS
F6S17 Ji 
891 3090 M (l)S 
822 3090 M (d)S 
665 3090 M (l)S 
633 3090 M (d)S 
454 3090 M (l)S 
422 3090 M (d)S 
347 3090 M (l)S 
278 3090 M (d)S 
734 3021 M (l)S 
632 3021 M (d)S 
523 3021 M (l)S 
441 3021 M (d)S 
268 3021 M (m)S 
/F6S28 F6 [40.57 0 0 -40.57 0 0 ] mFS
F6S28 Ji 
876 3080 M (z)S 
806 3080 M (z)S 
762 3080 M (s)S 
675 3080 M (s)S 
650 3080 M (z)S 
617 3080 M (z)S 
529 3080 M (s)S 
439 3080 M (z)S 
406 3080 M (z)S 
332 3080 M (z)S 
262 3080 M (z)S 
234 3080 M (s)S 
704 3011 M (sz)[16  0]xS 
603 3011 M (sz)[16  0]xS 
508 3011 M (z)S 
425 3011 M (z)S 
357 3011 M (s)S 
251 3011 M (x)S 
175 3011 M (V)S 
/F5S28 F5 [40.57 0 0 -40.57 0 0 ] mFS
F5S28 Ji 
846 3080 M <04>S 
715 3080 M <03>S 
569 3080 M <04>S 
501 3080 M <04>S 
377 3080 M <03>S 
303 3080 M <04>S 
778 3011 M <04>S 
657 3011 M <03>S 
555 3011 M <03>S 
479 3011 M <04>S 
396 3011 M <04>S 
309 3011 M <04>S 
211 3011 M <06>S 
/F1S17 F1 [23.664 0 0 -23.664 0 0 ] mFS
F1S17 Ji 
779 3062 M (3)S 
692 3062 M (2)S 
546 3062 M (4)S 
479 3059 M (2)S 
756 2981 M (2)S 
533 2990 M (2)S 
457 2990 M (2)S 
374 2992 M (2)S 
287 2990 M (2)S 
/F1S28 F1 [40.57 0 0 -40.57 0 0 ] mFS
F1S28 Ji 
742 3080 M (2)S 
596 3080 M (2)S 
175 3080 M (12)[21  0]xS 
684 3011 M (2)S 
583 3011 M (2)S 
337 3011 M (2)S 
F1S26 Ji 
173 3134 M (\(see Hornby et al. \(1999\)\).)[13 15 17 17 10 27 18 13 19 19 17 10 17 11 10 17 11 10 10 13 19 19 19 19 13 13  0]xS 
579 3134 M ( )S 
1236 273 M ( )S 
1236 341 M (After some transformations we )[26 12 11 17 13 10 15 18 29 17 10 11 13 17 19 15 12 18 13 29 17 11 11 18 19 15 10 27 17  0]xS 
1236 409 M (see that, for)[15 17 17 10 11 19 17 11 10 10 12 18  0]xS 
F4S26 Ji 
1416 409 M ( )S 
: 1433 377 17 45 rc /F6S29 F6 [41.535 0 0 -41.535 0 0 ] mFS
F6S29 Ji 
1433 412 M (s)S 
; : 1511 377 17 45 rc F6S29 Ji 
1511 412 M (s)S 
; : 1447 377 21 45 rc /F1S29 F1 [41.535 0 0 -41.535 0 0 ] mFS
F1S29 Ji 
1447 412 M (1)S 
; : 1527 377 21 45 rc F1S29 Ji 
1527 412 M (2)S 
; : 1475 377 23 44 rc 533 VM?
2 13770 122 <000100000000041b041a001300b840360407080b0c0c030112110e0d030c
0c1d0d02140d0d020d0c03020104120711080e0b0c05081111100b0e0e0f
07121213040101000203b8023440110006131d05004b101d0f091d0a0a0f
0d0cb8023440170f0a05090606050f1013001517171a053e001914202818
2b4e10f44dfd4e456544e6103c3c3c103c103c103c002f4df43c103c10ed
10edfd3cfd3c10f43c103c103c103c103c103c103c103c103c0112173987
2e2b7d10c4103c3c3c3c87103cc43c3c3130112113330321152103211521
0323132135211321025ca46ca20151fe799b0222fda5a36ea5feac018a9d
fdd902f70123fedd5ffee95ffede01225f011700>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/notequal 122 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 7 /notequal put
pop
/F5S29 F5 [41.535 0 0 -41.535 0 0 ] mFS
F5S29 Ji 
1475 412 M <07>S 
; F1S26 Ji 
1554 409 M (:)S 
1563 409 M ( )S 
: 1529 479 11 39 rc /F5S20YFFFFFFD6 F5 [32.52 0 0 -41.289 0 0 ] mFS
F5S20YFFFFFFD6 Ji 
1529 509 M <01>S 
; : 1566 479 11 39 rc F5S20YFFFFFFD6 Ji 
1566 509 M <02>S 
; : 1627 479 11 39 rc F5S20YFFFFFFD6 Ji 
1627 509 M <01>S 
; : 1670 479 11 39 rc F5S20YFFFFFFD6 Ji 
1670 509 M <02>S 
; F5S20YFFFFFFD6 Ji 
1529 553 M <01>S 
1566 553 M <02>S 
1630 553 M <01>S 
1673 553 M <02>S 
N 1502 521 M 1682 521 I K 
1714 528 M <01>S 
1817 528 M <02>S 
/F1S12 F1 [18.242 0 0 -18.242 0 0 ] mFS
F1S12 Ji 
1828 512 M (2)S 
1413 515 M (2)S 
1336 512 M (2)S 
/F1S1F F1 [31.27 0 0 -31.27 0 0 ] mFS
F1S1F Ji 
1655 553 M (2)S 
1551 553 M (1)S 
1652 509 M (2)S 
1551 509 M (1)S 
1481 529 M (4)S 
/F6S12 F6 [18.242 0 0 -18.242 0 0 ] mFS
F6S12 Ji 
1805 536 M (l)S 
1741 536 M (d)S 
1319 536 M (m)S 
/F6S1F F6 [31.27 0 0 -31.27 0 0 ] mFS
F6S1F Ji 
1791 529 M (z)S 
1726 529 M (z)S 
1641 553 M (s)S 
1540 553 M (s)S 
1638 509 M (s)S 
1540 509 M (s)S 
1383 529 M (H)S 
1303 529 M (x)S 
1242 529 M (D)S 
/F5S1F F5 [31.27 0 0 -31.27 0 0 ] mFS
F5S1F Ji 
1764 529 M <04>S 
1690 529 M <03>S 
533 VM?
1 7130 36 <00020000000005a0056b001c001f0120404f2414390a31144901480e5514
641476107c117d177c1a7c1b7a1d971098110f1f1e01011f1e02001d1e1e
1c090e0a1e09161c171e160802071e081511141e15011f1e09001d151078
1e0f10200f0e0eb8016f4026021e1402021e101111271c1e141c1c1e020e
09111c151e1c110e020401161e0f00012d1f1f1db801bc400f1040100f03
16150908082117171a15b80142b71e200fd51053401eb801afb420091920
21b8015db321437d182b2b4ef41a194dfd1a18fde61a1910fd184e456544
e6003f3c3c3c3f3c1a4d10fd3c10fd3c1239111217390111123939123939
870e2e2b057d10c4870e2e182b057d10c42b1112393911123939180010ed
0110c00010ed0110c00010ed0110c00010ed0110c007103c3c073c3c073c
3130015d0121070615141617152135363736370133011616171521353636
3534270b020399fdf35c223a63fe555519333e01dd2301d8385e53fde953
36276ee6ec01c6d64f20262f0725250f183093045cfb978751052525042e
2e245c010b0224fddc00>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/Alpha 36 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 8 /Alpha put
pop
1606 553 M <08>S 
1580 553 M <03>S 
1505 553 M <08>S 
: 1605 479 22 37 rc 533 VM?
1 7530 37 <00030000000004c4054c001e002a003600da403959080f231e0922221023
1e16222332230003252b36322b032d00342a231f03282150343409162850
171716022d500808090825ab1c21307604b8014d40090f2a2b27100f1937
38bc014d00210041016500182b2b4ef43c4dfd3c10fdedf4ed003f3c10ed
3f3c10ed1112392fed111739113912173901111217392b2b313043794041
2e332227181e01070225322623251a1b191b020606263301305703221e25
570327182557012e07305701310334570101241d2157001e00261b285701
2f052d57002b2b103c2b3c2b012b2b2b2b2b2a2b2b2b8181818101161716
151406062321353332373635113427262323352132171616151406251633
32363635342623220711163332363534262623220703908d466180dfe5fd
80335525171d274d33024aa463969e7dfd7c4b6f94944ec2bb6350746eb8
be55c297753502b41e425c8466b95525362372036c7e212c251824b77766
a10f0e3f824d77a816fb6f1ba3784e935409>/TTE1EBEAC8t00 AddT42Char 
/TTE1EBEAC8t00 findfont /CharStrings get begin
/Beta 37 def
end
/TTE1EBEAC8t00 findfont /Encoding get
dup 9 /Beta put
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1605 509 M <09>S 
; : 1580 479 17 37 rc 1580 509 M <03>S 
; : 1507 479 22 37 rc 1507 509 M <09>S 
; 1463 529 M <03>S 
1436 529 M <06>S 
1357 529 M <03>S 
1275 529 M <06>S 
F4S26 Ji 
1844 507 M (= constant      \( )[22 10 17 18 21 15 13 19 21 13 10 10 10 10 10 10 13  0]xS 
2096 507 M (2)S 
2115 507 M (\))S 
1 0 0 1 scol 2128 507 M ( )S 
0 0 0 1 scol F1S26 Ji 
1236 626 M (where:)[27 19 17 13 17  0]xS 
1338 626 M ( )S 
1236 694 M (H is the block thickness)[27 10 11 15 10 11 19 17 10 19 11 18 16 19 10 11 19 11 16 19 19 17 15  0]xS 
1601 694 M ( )S 
/F5S24YFFFFFFD7 F5 [36.68 0 0 -40.223 0 0 ] mFS
F5S24YFFFFFFD7 Ji 
1274 768 M <01>S 
1308 768 M <02>S 
1432 768 M <01>S 
1466 768 M <02>S 
: 1586 726 15 58 rc /F5S2BYFFFFFFC8 F5 [43.746 0 0 -55.633 0 0 ] mFS
F5S2BYFFFFFFC8 Ji 
1586 772 M <01>S 
; : 1721 726 15 58 rc F5S2BYFFFFFFC8 Ji 
1721 772 M <02>S 
; /F5S23 F5 [35.426 0 0 -35.426 0 0 ] mFS
F5S23 Ji 
1243 770 M <08>S 
/F6S23 F6 [35.426 0 0 -35.426 0 0 ] mFS
F6S23 Ji 
1291 770 M (s)S 
1399 770 M (X)S 
1449 770 M (s)S 
1569 770 M (s)S 
1602 770 M (z)S 
1680 770 M (z)S 
1802 770 M (s)S 
/F6S14 F6 [20.664 0 0 -20.664 0 0 ] mFS
F6S14 Ji 
1621 779 M (l)S 
1699 779 M (d)S 
F5S23 Ji 
1334 770 M <06>S 
1512 770 M <03>S 
1645 770 M <04>S 
1744 770 M <04>S 
/F1S23 F1 [35.426 0 0 -35.426 0 0 ] mFS
F1S23 Ji 
1371 770 M (2)S 
1545 770 M (2)S 
1778 770 M (2)S 
/F1S14 F1 [20.664 0 0 -20.664 0 0 ] mFS
F1S14 Ji 
1483 751 M (2)S 
1822 754 M (2)S 
: 1236 790 1122 43 rc F1S26 Ji 
1236 824 M ( )S 
; /F5S23YFFFFFFD3 F5 [35.82 0 0 -44.016 0 0 ] mFS
F5S23YFFFFFFD3 Ji 
1268 908 M <01>S 
1302 908 M <02>S 
1494 908 M <01>S 
1527 908 M <02>S 
: 1361 856 14 71 rc /F5S29YFFFFFFC0 F5 [41.23 0 0 -63.703 0 0 ] mFS
F5S29YFFFFFFC0 Ji 
1361 913 M <01>S 
; : 1562 856 14 71 rc F5S29YFFFFFFC0 Ji 
1562 913 M <02>S 
; : 1589 856 15 70 rc /F5S2AYFFFFFFC3 F5 [42.723 0 0 -60.879 0 0 ] mFS
F5S2AYFFFFFFC3 Ji 
1589 912 M <01>S 
; : 1778 856 15 70 rc F5S2AYFFFFFFC3 Ji 
1779 912 M <02>S 
; 1892 908 M <01>S 
1925 908 M <02>S 
: 1575 856 14 79 rc /F5S29YFFFFFFAF F5 [41.043 0 0 -80.566 0 0 ] mFS
F5S29YFFFFFFAF Ji 
1575 917 M <01>S 
; : 1961 856 14 79 rc F5S29YFFFFFFAF Ji 
1961 917 M <02>S 
; 2075 908 M <01>S 
2108 908 M <02>S 
/F5S26 F5 [38.766 0 0 -38.766 0 0 ] mFS
F5S26 Ji 
1242 911 M <09>S 
/F6S26 F6 [38.766 0 0 -38.766 0 0 ] mFS
F6S26 Ji 
1285 911 M (s)S 
1377 911 M (s)S 
1462 911 M (X)S 
1510 911 M (s)S 
1606 911 M (z)S 
1680 911 M (z)S 
1762 911 M (s)S 
1860 911 M (X)S 
1909 911 M (s)S 
2043 911 M (X)S 
2092 911 M (s)S 
/F6S16 F6 [22.613 0 0 -22.613 0 0 ] mFS
F6S16 Ji 
1624 921 M (l)S 
1698 921 M (d)S 
F5S26 Ji 
1326 911 M <06>S 
1424 911 M <03>S 
1646 911 M <04>S 
1728 911 M <03>S 
1823 911 M <03>S 
1983 911 M <03>S 
/F1S16 F1 [22.613 0 0 -22.613 0 0 ] mFS
F1S16 Ji 
1396 894 M (2)S 
1543 890 M (2)S 
1795 883 M (2)S 
1942 890 M (2)S 
2125 890 M (4)S 
/F1S26 F1 [38.766 0 0 -38.766 0 0 ] mFS
F1S26 Ji 
2016 911 M (4)S 
: 1236 942 1122 43 rc F1S26 Ji 
1236 976 M ( )S 
; F1S26 Ji 
1236 1044 M (From the observations listed in the last three sections we can )
[21 13 18 29 10 11 19 17 10 18 19 15 17 13 18 17 11 11 18 19 15 10 11 11 15 11 17 19 10 11 19 10
11 19 17 10 11 17 15 11 10 11 19 13 17 17 10 15 17 16 11 11 18 19 15 10 27 17 10 16 17 19  0]xS 
1236 1089 M (now uniquely determine the location and shape of the block.)[19 18 27 10 19 19 11 19 19 17 11 17 10 19 17 11 17 13 29 11 19 17 10 11 19 17 10 11 18 16 17 11
11 18 19 10 17 19 19 10 15 19 17 19 17 10 18 12 10 11 19 17 10 19 11 18 16 19  0]xS 
/F1S32 F1 [50 0 0 -50 0 0 ] mFS
F1S32 Ji 
2155 1089 M ( )S 
F1S26 Ji 
1236 1134 M ( )S 
: N 1230 1143 957 50 rp C 
1 1 1 1 scol  L ; F4S2A Ji 
1514 1184 M (SYNTHETIC TESTS)[23 31 30 28 33 28 28 16 30 11 28 28 23 28  0]xS 
1902 1184 M ( )S 
: N 1230 1193 957 50 rp C 
1 1 1 1 scol  L ; F1S2A Ji 
1236 1233 M ( )S 
F1S26 Ji 
1236 1279 M (In the real w)[11 19 28 11 19 17 28 13 17 17 11 28  0]xS 
1482 1279 M (orld, no perfect block)[18 13 11 19 10 28 19 18 28 19 17 13 12 17 16 11 27 19 11 18 16  0]xS 
1861 1279 M (-)S 
1873 1279 M (like sources exist. )[11 11 19 17 27 15 18 19 13 16 17 15 27 17 19 11 15 11 10  0]xS 
1236 1324 M (Accordingly, we tested our algorithm against irregularly )[26 16 16 18 13 19 11 19 18 11 17 10 26 27 17 26 11 17 15 11 17 19 25 18 19 13 25 17 11 18 18 13
11 11 19 29 25 17 18 17 11 19 15 11 25 11 13 13 17 18 19 11 17 13 11 17  0]xS 
1236 1369 M (shaped sources. Obviously, all we can hope for is to )[15 19 17 19 17 19 28 15 18 19 13 16 17 15 10 28 27 19 18 11 18 19 15 11 17 10 27 17 11 11 27 27
17 27 16 17 19 27 19 18 19 17 27 12 18 13 27 11 15 27 11 18  0]xS 
1236 1414 M (reconstruct the closest block)[13 17 16 18 19 15 11 13 19 16 11 17 11 19 17 17 16 11 18 15 17 15 11 17 19 11 18 16  0]xS 
1688 1414 M (-)S 
1700 1414 M (like approximation to the real )[11 11 19 17 17 17 19 19 13 18 19 11 29 17 11 11 18 19 17 11 18 17 11 19 17 17 13 17 17 11  0]xS 
1236 1459 M (source. The algorithm performed reasonably well, properly )[15 18 19 13 16 17 10 18 23 19 17 18 17 11 18 18 13 11 11 19 29 18 19 17 13 12 18 13 29 17 19 18
13 17 17 15 18 19 17 19 11 17 18 27 17 11 11 10 18 19 13 18 19 17 13 11 17  0]xS 
1236 1504 M (locating the centre of gravity and reconstructing a close block )
[11 18 16 17 11 11 19 18 12 11 19 17 12 16 17 19 11 13 17 11 18 12 11 18 13 17 18 11 11 17 11 17
19 19 11 13 17 16 18 19 15 11 13 19 16 11 11 19 18 11 17 11 16 11 18 15 17 11 19 11 18 16 19  0]xS 
1236 1549 M (approximation around it \(see Figure 2a\).)[17 19 19 13 18 19 11 29 17 11 11 18 19 10 17 13 18 19 19 19 10 11 11 10 13 15 17 17 10 21 11 18
19 13 17 10 19 17 13  0]xS 
1854 1549 M ( )S 
1236 1594 M ( )S 
1236 1942 M (\(a\) )[13 17 13  0]xS 
: : N 1289 1603 840 339 irp C 
1 1 1 1 scol O ; 642 253 1 81 840 339 1289 1603 F F 3 [ 0 ] F 
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: : N 1580 1951 371 562 irp C 
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!.Y~> Z
; 1951 2513 M ( )S 
: N 1230 2522 957 45 rp C 
1 1 1 1 scol  L ; F4S26 Ji 
1236 2559 M (Figure 2.  Sources \(thin line\) and reconstructed sources )[24 11 19 21 17 17 16 19 10 16 16 21 18 21 17 17 17 15 16 13 13 21 11 21 15 11 11 21 17 13 15 19
21 21 15 17 17 17 18 21 15 13 17 21 17 13 17 21 15 15 18 21 17 17 17 15  0]xS 
: N 1230 2567 957 45 rp C 
1 1 1 1 scol  L ; 1236 2604 M (\(solid line\). The synthetic profiles have )[13 15 18 11 11 21 19 11 11 21 17 13 10 19 25 21 17 19 15 18 21 13 21 17 13 11 17 18 21 17 18 13
11 11 17 15 18 21 19 18 17  0]xS 
1926 2604 M (been generated )[21 17 17 21 18 19 17 21 17 17 19 13 17 21  0]xS 
: N 1230 2612 957 45 rp C 
1 1 1 1 scol  L ; 1236 2649 M (using irregularly shaped sources \(a\) and spherical or )[21 15 11 21 19 23 11 17 17 17 19 21 11 19 17 11 18 23 15 21 19 21 17 21 22 15 18 21 17 17 17 15
22 13 19 13 22 19 21 21 22 15 21 21 17 17 11 17 19 11 22 18 17  0]xS 
: N 1230 2657 957 45 rp C 
1 1 1 1 scol  L ; 1236 2694 M (ellipsoidal sources \(b\).)[17 11 11 11 21 15 18 11 21 19 11 10 15 18 21 17 17 17 15 10 13 21 13  0]xS 
1599 2694 M ( )S 
: N 1230 2702 957 45 rp C 
1 1 1 1 scol  L ; F1S26 Ji 
1236 2738 M ( )S 
: N 1230 2747 957 45 rp C 
1 1 1 1 scol  L ; 1236 2783 M (In another test we tried to recover spherical/ellipsoidical )[11 19 23 17 19 18 11 19 17 13 22 11 17 15 11 22 27 17 22 11 13 11 17 19 22 11 18 22 13 17 16 18
18 17 13 22 15 19 19 17 13 11 16 17 11 11 17 11 11 11 19 15 18 11 19 11 16 17 11  0]xS 
: N 1230 2792 957 45 rp C 
1 1 1 1 scol  L ; 1236 2828 M (shaped sources. This test is particularly interesting. Potential )
[15 19 17 19 17 19 13 15 18 19 13 16 17 15 10 12 23 19 11 15 12 11 17 15 11 12 11 15 12 19 17 13
11 11 16 19 11 17 13 11 17 12 11 19 11 17 13 17 15 11 11 19 18 10 12 21 18 11 17 19 11 11 17 11
 0]xS 
: N 1230 2837 957 45 rp C 
1 1 1 1 scol  L ; 1236 2873 M (field theory says that the response of block like sources and )
[12 11 17 11 19 14 11 19 17 18 13 17 14 15 17 17 15 14 11 19 17 11 14 11 19 17 14 13 17 15 19 18
19 15 17 14 18 12 14 19 11 18 16 19 14 11 11 19 17 14 15 18 19 13 16 17 15 13 17 19 19  0]xS 
: N 1230 2882 957 45 rp C 
1 1 1 1 scol  L ; 1236 2918 M (of spherical sources behave very differently as a function of )
[18 12 15 15 19 19 17 13 11 16 17 11 15 15 18 19 13 16 17 15 15 19 17 19 17 18 17 14 18 17 13 17
14 19 11 12 12 17 13 17 19 11 11 17 14 17 15 14 17 14 12 19 19 16 11 11 18 19 14 18 12  0]xS 
: N 1230 2927 957 45 rp C 
1 1 1 1 scol  L ; 1236 2963 M (distance from the source. This phenomenon is known to the )[19 11 15 11 17 19 16 17 15 12 13 18 29 14 11 19 17 14 15 18 19 13 16 17 10 14 23 19 11 15 14 19
19 17 19 18 29 17 19 18 19 14 11 15 14 19 19 18 27 19 14 11 18 14 11 19 17  0]xS 
: N 1230 2972 957 45 rp C 
1 1 1 1 scol  L ; 1236 3008 M (practitioner via the concept of a structural index, related to )
[19 13 17 16 11 11 11 11 18 19 17 13 16 18 11 17 16 11 19 17 16 16 18 19 16 17 19 11 16 18 12 15
17 15 15 11 13 19 16 11 19 13 17 11 15 11 19 19 17 19 10 15 13 17 11 17 11 17 19 15 11 18  0]xS 
: N 1230 3017 957 45 rp C 
1 1 1 1 scol  L ; 1236 3053 M (Euler deconvolution \(see, for example, Blakely,)[23 19 11 17 13 28 19 17 16 18 19 18 18 11 19 11 11 18 19 28 13 15 17 17 10 28 12 18 13 28 17 19
17 29 19 11 17 10 28 25 11 17 19 17 11 17  0]xS 
2054 3053 M ( 1995\). )[28 19 19 19 19 13 10  0]xS 
: N 1230 3062 957 45 rp C 
1 1 1 1 scol  L ; 1236 3098 M (Further generalisation of the concept, under the framework of )
[21 19 13 11 19 17 13 11 18 17 19 17 13 17 11 11 15 17 11 11 18 19 11 18 12 11 11 19 17 11 16 18
19 16 17 19 11 10 11 19 19 19 17 13 11 11 19 17 10 12 13 17 29 17 27 18 13 19 10 18 12  0]xS 
LH
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0 0 0 1 scol F2S26 Ji 
173 122 M ( )S 
F1S2A Ji 
173 3285 M ( )S 
2162 127 M ( )S 
: N 167 237 957 45 rp C 
1 1 1 1 scol  L ; F1S26 Ji 
173 273 M (wavelet theory can be found in Hornby et al., \(1999\). In a )[27 17 18 17 11 17 11 17 11 19 17 18 13 17 17 16 17 19 17 19 17 16 12 18 19 19 19 16 11 19 16 27
18 13 19 19 17 16 17 11 16 17 11 10 10 16 13 19 19 19 19 13 10 16 11 19 16 17  0]xS 
: N 167 282 957 45 rp C 
1 1 1 1 scol  L ; 173 318 M (typical Euler deconvolution, an inaccurate estimation of the )
[11 17 19 11 16 17 11 16 23 19 11 17 13 16 19 17 16 18 19 18 18 11 19 11 11 18 19 10 16 17 19 15
11 19 17 16 16 19 13 17 11 17 15 17 15 11 11 29 17 11 11 18 19 15 18 12 15 11 19 17  0]xS 
: N 167 327 957 45 rp C 
1 1 1 1 scol  L ; 173 363 M (structural index \(or, in other words, confusing a spherical )[15 11 13 19 16 11 19 13 17 11 19 11 19 19 17 19 19 13 18 13 10 19 11 19 19 18 11 19 17 13 19 27
18 13 19 15 10 18 16 18 19 12 19 15 11 19 18 18 17 18 15 19 19 17 13 11 16 17 11  0]xS 
: N 167 372 957 45 rp C 
1 1 1 1 scol  L ; 173 408 M (source with a block)[15 18 19 13 16 17 18 27 11 11 19 18 17 18 19 11 18 16  0]xS 
493 408 M (-)S 
505 408 M (like or vice versa\) would result in an )[11 11 19 17 18 18 13 18 18 11 16 17 18 18 17 13 15 17 13 18 27 18 19 11 19 17 13 17 15 19 11 11
17 11 19 17 17 19  0]xS 
: N 167 417 957 45 rp C 
1 1 1 1 scol  L ; 173 453 M (erroneous estimation of the source depth. However, as can be )
[17 13 13 18 19 17 18 19 15 12 17 15 11 11 29 17 11 11 18 19 11 18 12 11 11 19 17 11 15 18 19 13
16 17 11 19 17 19 11 19 10 11 27 18 27 17 18 17 13 10 11 17 15 11 16 17 19 11 19 17  0]xS 
: N 167 462 957 45 rp C 
1 1 1 1 scol  L ; 173 498 M (seen Figure 2b our technique estimates the source depth with )
[15 17 17 19 12 21 11 18 19 13 17 12 19 19 11 18 19 13 11 11 17 16 19 19 11 19 19 17 11 17 15 11
11 29 17 11 17 15 11 11 19 17 11 15 18 19 13 16 17 11 19 17 19 11 19 11 27 11 11 19  0]xS 
: N 167 507 957 45 rp C 
1 1 1 1 scol  L ; 173 543 M (very good accuracy.)[18 17 13 17 10 18 18 18 19 10 17 16 16 19 13 17 16 17  0]xS 
472 543 M ( )S 
: N 167 552 957 45 rp C 
1 1 1 1 scol  L ; 173 588 M ( )S 
: N 167 597 957 45 rp C 
1 1 1 1 scol  L ; 173 633 M (The reason for such an apparent contradiction lies in the )[23 19 17 20 13 17 17 15 18 19 20 12 18 13 20 15 19 16 19 20 17 19 20 17 19 19 17 13 17 19 11 20
16 18 19 11 13 17 19 11 16 11 11 18 19 19 11 11 17 15 19 11 19 19 11 19 17  0]xS 
: N 167 642 957 45 rp C 
1 1 1 1 scol  L ; 173 678 M (lo)[11  0]xS 
202 678 M (cation at which the calculation is performed. Standard )[16 17 11 11 18 19 24 17 11 23 27 19 11 16 19 23 11 19 17 23 16 17 11 16 19 11 17 11 11 18 19 23
11 15 23 19 17 13 12 18 13 29 17 19 10 23 21 11 17 19 19 17 13 19  0]xS 
: N 167 687 957 45 rp C 
1 1 1 1 scol  L ; 173 723 M (Euler deconvolution is performed on a grid, usually measured )
[23 19 11 17 13 11 19 17 16 18 19 18 18 11 19 11 11 18 19 11 11 15 11 19 17 13 12 18 13 29 17 19
11 18 19 11 17 10 18 13 11 19 10 10 19 15 19 17 11 11 17 10 29 17 17 15 19 13 17 19  0]xS 
: N 167 732 957 45 rp C 
1 1 1 1 scol  L ; 173 768 M (either on the ground \(gravity maps\) or at small distance from )
[17 11 11 19 17 13 12 18 19 12 11 19 17 12 18 13 18 19 19 19 12 13 18 13 17 18 11 11 17 12 29 17
19 15 13 12 18 13 12 17 11 11 15 29 17 11 11 11 19 11 15 11 17 19 16 17 11 12 13 18 29  0]xS 
: N 167 777 957 45 rp C 
1 1 1 1 scol  L ; 173 813 M (the ground \(airborne magnetic surveys\). At such heights, )[11 19 17 22 18 13 18 19 19 19 22 13 17 11 13 19 18 13 19 17 22 29 17 18 19 17 11 11 16 22 15 19
13 18 17 17 15 13 10 21 26 11 21 15 19 16 19 21 19 17 11 18 19 11 15 10  0]xS 
: N 167 822 957 45 rp C 
1 1 1 1 scol  L ; 173 858 M (signals from sources of different shape differ considerably. In )
[15 11 18 19 17 11 15 12 12 13 18 29 12 15 18 19 13 16 17 15 11 18 12 11 19 11 12 12 17 13 17 19
11 11 15 19 17 19 17 11 19 11 12 12 17 13 11 16 18 19 15 11 19 17 13 17 19 11 17 10 11 11 19  0]xS 
: N 167 867 957 45 rp C 
1 1 1 1 scol  L ; 173 903 M (our algorithm, the estimation of the location of the centre of )
[18 19 13 14 17 11 18 18 13 11 11 19 29 10 14 11 19 17 14 17 15 11 11 29 17 11 11 18 19 14 18 12
13 11 19 17 13 11 18 16 17 11 11 18 19 13 18 12 13 11 19 17 13 16 17 19 11 13 17 13 18 12  0]xS 
: N 167 912 957 45 rp C 
1 1 1 1 scol  L ; 173 948 M (gravity is performed at very high levels of upward )[18 13 17 18 11 11 17 33 11 15 33 19 17 13 12 18 13 29 17 19 33 17 11 33 18 17 13 17 33 19 11 18
19 33 11 17 18 17 11 15 33 18 12 33 19 19 27 17 13 19  0]xS 
: N 167 957 957 45 rp C 
1 1 1 1 scol  L ; 173 993 M (continuation, where all sources of limited extent tend to look )
[16 18 19 11 11 19 19 17 11 11 18 19 10 12 27 19 17 13 17 12 17 11 11 12 15 18 19 13 16 17 15 12
18 12 12 11 11 29 11 11 17 19 12 17 19 11 17 19 11 12 11 17 19 19 12 11 18 11 11 18 18 19  0]xS 
: N 167 1002 957 45 rp C 
1 1 1 1 scol  L ; 173 1038 M (alike, all behaving like point sourc)[17 11 11 19 17 10 10 17 11 11 10 19 17 19 17 18 11 19 18 10 11 11 19 17 10 19 18 11 19 11 10 15
18 19 13  0]xS 
702 1038 M (es. Once the location of the )[17 15 10 10 27 19 16 17 10 11 19 17 10 11 18 16 17 11 11 18 19 10 18 12 10 11 19 17  0]xS 
: N 167 1047 957 45 rp C 
1 1 1 1 scol  L ; 173 1083 M (centre of gravity is accurately detected, the reconstruction of a )
[16 17 19 11 13 17 10 18 12 10 18 13 17 18 11 11 17 10 11 15 10 17 16 16 19 13 17 11 17 11 17 10
19 17 11 17 16 11 17 19 10 10 11 19 17 10 13 17 16 18 19 15 11 13 19 16 11 11 18 19 10 18 12 10
17  0]xS 
: N 167 1092 957 45 rp C 
1 1 1 1 scol  L ; 173 1128 M (close block)[16 11 18 15 17 28 19 11 18 16  0]xS 
361 1128 M (-)S 
373 1128 M (like approximation is relatively simple and )[11 11 19 17 28 17 19 19 13 18 19 11 29 17 11 11 18 19 28 11 15 28 13 17 11 17 11 11 18 17 11 17
28 15 11 29 19 11 17 28 17 19 19  0]xS 
: N 167 1137 957 45 rp C 
1 1 1 1 scol  L ; 173 1173 M (reliable. This explains the quality of the results presented in )
[13 17 11 11 17 19 11 17 10 13 23 19 11 15 13 17 19 19 11 17 11 19 15 13 11 19 17 13 19 19 17 11
11 11 17 13 18 12 13 11 19 17 13 13 17 15 19 11 11 15 13 19 13 17 15 17 19 11 17 19 12 11 19  0]xS 
: N 167 1182 957 45 rp C 
1 1 1 1 scol  L ; 173 1218 M (Figure 2.)[21 11 18 19 13 17 10 19  0]xS 
311 1218 M ( )S 
: N 167 1227 957 45 rp C 
1 1 1 1 scol  L ; 173 1263 M ( )S 
: N 167 1272 957 50 rp C 
1 1 1 1 scol  L ; F4S2A Ji 
336 1313 M (APPLICATION TO REAL DATA)[30 25 25 28 16 30 30 28 16 33 30 11 28 33 11 30 28 30 28 11 30 30 28  0]xS 
955 1313 M ( )S 
: N 167 1322 957 50 rp C 
1 1 1 1 scol  L ; F1S2A Ji 
173 1362 M ( )S 
F1S26 Ji 
173 1408 M (When an algorithm is applied to real data, certain formulas )[35 19 17 19 15 17 19 15 17 11 18 18 13 11 11 19 29 15 11 15 15 17 19 19 11 11 17 19 15 11 18 15
13 17 17 11 15 19 17 11 17 10 15 16 17 13 11 17 11 19 14 12 18 13 29 19 11 17 15  0]xS 
173 1453 M (may misbehave under the complexity of real geological )[29 17 17 25 29 11 15 19 17 19 17 18 17 25 19 19 19 17 13 25 11 19 17 25 16 18 29 19 11 17 19 11
11 17 25 18 12 25 13 17 17 11 25 18 17 18 11 18 18 11 16 17 11  0]xS 
173 1498 M (scenarios. In our tests on real data we choose some )[15 16 17 19 17 13 11 18 15 10 29 11 19 29 18 19 13 29 11 17 15 11 15 29 18 19 29 13 17 17 11 29
19 17 11 17 29 27 17 29 16 19 18 18 15 17 28 15 18 29 17  0]xS 
173 1543 M (particularly irregular profiles. While the method to determine )
[19 17 13 11 11 16 19 11 17 13 11 17 11 11 13 13 17 18 19 11 17 13 11 19 13 18 12 11 11 17 15 10
11 35 19 11 11 17 11 11 19 17 11 29 17 11 19 18 19 11 11 18 11 19 17 11 17 13 29 11 19 17  0]xS 
173 1588 M (centre of gravity and amount of)[16 17 19 11 13 17 13 18 12 13 18 13 17 18 11 11 17 13 17 19 19 13 17 29 18 19 19 11 13 18  0]xS 
664 1588 M ( mass has proven particularly )[12 29 17 15 15 12 19 17 15 12 19 13 18 18 17 19 12 19 17 13 11 11 16 19 11 17 13 11 17  0]xS 
173 1633 M (robust, equation 2 proved unstable under such hard tests. The )
[13 18 19 19 15 11 10 11 17 19 19 17 11 11 18 19 11 19 11 19 13 18 18 17 19 11 19 19 15 11 17 19
11 17 11 19 19 19 17 13 11 15 19 16 19 10 19 17 13 19 10 11 17 15 11 15 10 10 23 19 17  0]xS 
173 1678 M (quantity D was not constant, showing quite strong )[19 19 17 19 11 11 11 17 37 27 36 27 17 15 36 19 18 11 36 16 18 19 15 11 17 19 11 10 36 15 19 18
27 11 19 18 36 19 19 11 11 17 36 15 11 13 18 19 18  0]xS 
173 1723 M (oscillations.  )[18 15 16 11 11 11 17 11 11 18 19 15 10 10  0]xS 
376 1723 M ( )S 
173 1768 M ( )S 
173 1813 M (Here we want to show that the multiscale edges can offer )[27 17 13 17 18 27 17 18 27 17 19 11 18 11 18 17 15 19 18 27 17 11 19 17 11 17 11 19 17 17 29 19
11 11 11 15 16 17 11 17 17 17 19 18 17 15 17 16 17 19 17 18 12 12 17 13  0]xS 
173 1858 M (further visual information that can constrain the problem to )
[12 19 13 11 19 17 13 16 18 11 15 19 17 11 15 11 19 12 18 13 29 17 11 11 18 19 15 11 19 17 11 15
16 17 19 15 16 18 19 15 11 13 17 11 19 15 11 19 17 15 19 13 18 19 11 17 29 15 11 18  0]xS 
173 1903 M (the point of allowing a reasonable reconstruction even when )[11 19 17 14 19 18 11 19 11 14 18 12 14 17 11 11 18 27 11 19 18 14 17 14 13 17 17 15 18 19 17 19
11 17 13 13 17 16 18 19 15 11 13 19 16 11 11 18 19 13 17 18 17 19 13 27 19 17 19  0]xS 
173 1948 M (equation 2 can not be used. In Figure 3 we see the multiscale )
[17 19 19 17 11 11 18 19 12 19 12 16 17 19 11 19 18 11 11 19 17 11 19 15 17 19 10 11 11 19 11 21
11 18 19 13 17 11 19 11 27 17 11 15 17 17 11 11 19 17 11 29 19 11 11 11 15 16 17 11 17  0]xS 
173 1993 M (edges, as well as the two lines due to a point source )[17 19 18 17 15 10 25 17 15 25 27 17 11 11 24 17 15 24 11 19 17 24 11 27 18 24 11 11 19 17 15 24
19 19 17 24 11 18 24 17 24 19 18 11 19 11 24 15 18 19 13 16 17  0]xS 
173 2038 M (approximation, for 2 different block)[17 19 19 13 18 19 11 29 17 11 11 18 19 10 14 12 18 13 14 19 13 19 11 12 12 17 13 17 19 11 13 19
11 18 16  0]xS 
734 2038 M (-)S 
746 2038 M (like sources. In the f)[11 11 19 17 13 15 18 19 13 16 17 15 10 13 11 19 13 11 19 17 13  0]xS 
1068 2038 M (irst )[11 13 15 11  0]xS 
173 2083 M (case the block section is wide and flat \(a\), in the second case )
[16 17 15 17 12 11 19 17 12 19 11 18 16 19 12 15 17 16 11 11 18 19 12 11 15 12 27 11 19 17 12 17
19 19 11 12 11 17 11 11 13 17 13 10 11 11 19 11 11 19 17 11 15 17 16 18 19 19 11 16 17 15 17  0]xS 
173 2128 M (the block section is narrow and thick \(b\). It can be seen that )
[11 19 17 13 19 11 18 16 19 13 15 17 16 11 11 18 19 13 11 15 13 19 17 13 13 18 27 13 17 19 19 13
11 19 11 16 19 13 13 19 13 10 13 11 11 13 16 17 19 12 19 17 12 15 17 17 19 12 11 19 17 11  0]xS 
173 2173 M (the two lines and the multiscale edges behave differently. In )
[11 19 17 14 11 27 18 13 11 11 19 17 15 13 17 19 19 13 11 19 17 13 29 19 11 11 11 15 16 17 11 17
13 17 19 18 17 15 13 19 17 19 17 18 17 13 19 11 12 12 17 13 17 19 11 11 17 10 13 11 19  0]xS 
173 2218 M (one case the multiscale edges are located \221outside\222 the 2 lines )
[18 19 17 11 16 17 15 17 11 11 19 17 11 29 19 11 11 11 15 16 17 11 17 11 17 19 18 17 15 11 17 13
17 10 11 18 16 17 11 17 19 10 13 18 19 11 15 11 19 17 13 10 11 19 17 10 19 10 11 11 19 17 15  0]xS 
173 2263 M (\(a\) in the other case \221inside\222 \(b\). This simple visualisation )
[13 17 13 17 11 19 17 11 19 17 16 18 11 19 17 13 16 16 17 15 17 16 13 11 19 15 11 19 17 13 16 13
19 13 10 16 23 19 11 15 16 15 11 29 19 11 17 16 18 11 15 19 17 11 11 15 17 11 11 18 19  0]xS 
173 2308 M (gives us some very approximate information on the relative )[18 11 18 17 15 16 19 15 15 15 18 29 17 15 18 17 13 17 15 17 19 19 13 18 19 11 29 17 11 17 15 11
19 12 18 13 29 17 11 11 18 19 15 18 19 15 11 19 17 15 13 17 11 17 11 11 18 17  0]xS 
173 2353 M (size of the block width and thickness. )[15 11 16 17 10 18 12 10 11 19 17 10 19 11 18 16 19 10 27 11 19 11 19 10 17 19 19 10 11 19 11 16
19 19 17 15 15 10  0]xS 
756 2353 M ( )S 
173 2398 M ( )S 
: 536 264 8 536 938 512 173 2407 F F 3 [ 0 ] F 
X
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Jbalml1k~> Z
; 1111 2919 M ( )S 
F4S26 Ji 
173 2956 M (Figure 3. Different behaviour of multiscale edges due to )[24 11 19 21 17 17 15 19 10 15 27 11 13 13 17 17 17 21 13 15 21 17 21 19 18 11 18 21 17 15 18 13
15 31 21 11 13 11 15 17 19 11 17 15 17 21 19 17 15 15 21 21 17 14 13 18  0]xS 
173 3001 M (blocks of different shape, compar)[21 11 18 17 20 15 23 18 13 23 21 11 13 13 17 17 17 21 13 23 15 21 19 21 17 10 22 17 18 31 21 19
 0]xS 
766 3001 M (ed to the multiscale )[17 21 22 13 18 22 13 21 17 22 31 21 11 13 11 15 17 19 11 17  0]xS 
173 3046 M (edges due to a single point source approximation.)[17 21 19 17 15 10 21 21 17 10 13 18 10 19 10 15 11 21 19 11 17 10 21 18 11 21 13 10 15 18 21 17
17 17 10 19 21 21 17 18 19 11 31 19 13 11 18 21  0]xS 
973 3046 M ( )S 
F1S26 Ji 
173 3090 M ( )S 
1236 273 M (Also, we know that the edges tend to spread outward from )[26 11 15 18 10 16 27 17 16 19 19 18 27 16 11 19 17 11 16 11 19 17 16 17 19 18 17 15 16 11 17 19
19 15 11 18 15 15 19 13 17 17 19 15 18 19 11 27 17 13 19 15 12 13 18 29  0]xS 
1236 318 M (the source boundaries \(small movement inward may happen )[11 19 17 15 15 18 19 13 16 17 15 19 18 19 19 19 17 13 11 17 15 14 13 15 29 17 11 11 14 29 18 18
17 29 17 19 11 14 11 19 27 17 13 19 14 29 17 17 14 19 17 19 19 17 19  0]xS 
1236 363 M (for narrow and thick blocks, but usually of small extent\). This )
[12 18 13 10 19 17 13 13 18 27 10 17 19 19 10 11 19 11 16 19 10 19 11 18 16 19 15 10 10 19 19 11
10 19 15 19 17 11 11 17 10 18 12 10 15 29 17 11 11 10 17 19 11 17 19 11 13 10 10 23 19 11 15  0]xS 
1236 408 M (gives a maximum limit to the block width, since we can )[18 11 18 17 15 20 17 20 29 17 19 11 29 19 29 20 11 11 29 11 11 19 11 18 19 11 19 17 19 19 11 18
16 19 19 27 11 19 11 19 10 19 15 11 19 16 17 19 27 17 19 16 17 19  0]xS 
1236 453 M (expect it should not exceed the horizontal distance between )[17 19 19 17 16 11 15 11 11 15 15 19 18 19 11 19 15 19 18 11 15 17 19 16 17 17 19 15 11 19 17 15
19 18 13 11 16 18 19 11 17 11 14 19 11 15 11 17 19 16 17 14 19 17 11 27 17 17 19  0]xS 
1236 498 M (the edges on the two flanks of the anomaly.)[11 19 17 10 17 19 18 17 15 10 18 19 10 11 19 17 10 11 27 18 10 12 11 17 19 19 15 10 18 12 10 11
19 17 10 17 19 18 29 17 11 17  0]xS 
1897 498 M ( )S 
1236 543 M ( )S 
1236 588 M (Finally, we often know whether the source crops out or not, )[21 11 19 17 11 11 17 10 14 27 17 14 18 12 11 17 19 14 19 19 18 27 14 27 19 17 11 19 17 13 14 11
19 17 14 15 18 19 13 16 17 14 16 13 18 19 15 14 18 19 11 13 18 13 13 19 18 11 10  0]xS 
1236 633 M (and we obviously always know that the sourc)[17 19 19 18 27 17 18 18 19 18 11 18 19 15 11 17 18 17 11 27 17 17 15 18 19 19 18 27 17 11 19 17
11 17 11 19 17 17 15 18 19 13  0]xS 
1977 633 M (e can not be )[17 17 16 17 19 17 19 18 11 17 19 17  0]xS 
1236 678 M (more elevated that the ground itself. This offers further )[29 18 13 17 23 17 11 17 18 17 11 17 19 23 11 19 17 11 23 11 19 17 23 18 13 18 19 19 19 23 11 11
15 17 11 12 10 23 23 19 11 15 23 18 12 12 17 13 15 23 12 19 13 11 19 17 13  0]xS 
1236 723 M (constraints to the shape as it limits the minimum depth to the )
[16 18 19 15 11 13 17 11 19 11 15 11 11 18 11 11 19 17 11 15 19 17 19 17 11 17 15 11 11 11 11 11
11 29 11 11 15 11 11 19 17 11 29 11 19 11 29 19 29 11 19 17 19 11 19 11 11 18 10 11 19 17  0]xS 
1236 768 M (top.)[11 18 19  0]xS 
1294 768 M ( )S 
1236 813 M ( )S 
1236 858 M (All these visual clues allowed for a reliable application of the )
[26 11 11 11 11 19 17 15 17 11 18 11 15 19 17 11 11 16 11 19 17 15 11 17 11 11 18 27 17 19 11 12
18 13 11 17 11 13 17 11 11 17 19 11 17 10 17 19 19 11 11 16 17 11 11 18 19 10 18 12 10 11 19 17
 0]xS 
1236 903 M (technique to real profiles, as demonstrated below.)[11 17 16 19 19 11 19 19 17 10 11 18 10 13 17 17 11 10 19 13 18 12 11 11 17 15 10 10 17 15 10 19
17 29 18 19 15 11 13 17 11 17 19 10 19 17 11 18 27  0]xS 
1996 903 M ( )S 
1236 948 M ( )S 
F4S26 Ji 
1236 994 M (Test case)[25 17 15 13 10 17 19 15  0]xS 
1384 994 M ( )S 
F1S26 Ji 
1236 1038 M ( )S 
1236 1083 M (In Figure 4 \(see chart cross)[11 19 16 21 11 18 19 13 17 16 19 16 13 15 17 17 16 16 19 17 13 11 15 16 13 18 15  0]xS 
1678 1083 M (-)S 
1690 1083 M (cutting the geological model\) a )[16 19 11 11 11 19 18 15 11 19 17 15 18 17 18 11 18 18 11 16 17 11 15 29 18 19 17 11 13 15 17  0]xS 
1236 1128 M (gravity profile across a Devonian age granite body intrusion )
[18 13 17 18 11 11 17 15 19 13 18 12 11 11 17 15 17 16 13 18 15 15 15 17 14 27 17 18 18 19 11 17
19 14 17 18 17 14 18 13 17 19 11 11 17 14 19 18 19 17 14 11 19 11 13 19 15 11 18 19  0]xS 
1236 1173 M (into Cambrian age volcanics in Tasmania is shown \(data and )[11 19 11 18 13 25 17 29 19 13 11 17 19 12 17 18 17 12 18 18 11 16 17 19 11 16 15 12 11 19 12 23
17 15 29 17 19 11 17 12 11 15 12 15 19 18 27 19 12 13 19 17 11 17 12 17 19 19  0]xS 
1236 1218 M (processing courtesy of Fractal Graphics Pty Ltd / Pasminco )[19 13 18 16 17 15 15 11 19 18 16 16 18 19 13 11 17 15 17 16 18 12 16 21 13 17 16 11 17 11 16 27
13 17 19 19 11 16 15 16 21 11 17 16 22 11 19 16 11 15 21 17 15 29 11 19 16 18  0]xS 
1236 1263 M (Expl)[23 19 19  0]xS 
1308 1263 M (oration Ltd\).)[18 13 17 11 11 18 19 10 22 11 19 13  0]xS 
1500 1263 M ( )S 
1236 1308 M ( )S 
1236 1353 M (Figure 4 shows also the reconstruction of the possible source, )
[21 11 18 19 13 17 11 19 11 15 19 18 27 15 11 17 11 15 18 11 11 19 17 11 13 17 16 18 19 15 11 13
19 16 11 11 18 19 11 18 12 11 11 19 17 11 19 18 15 15 11 19 11 17 11 15 18 19 13 16 17 10  0]xS 
1236 1398 M (produced by geologists at Fractal Graphics Pty Ltd and )[19 13 18 19 19 16 17 19 24 19 17 24 18 17 18 11 18 18 11 15 11 15 24 17 11 24 21 13 17 16 11 17
11 24 27 13 17 19 19 11 16 15 24 21 11 17 23 22 11 19 23 17 19 19  0]xS 
1236 1443 M (Pasminco Exploration Ltd. The model was constructed by )[21 17 15 29 11 19 16 18 20 23 19 19 11 18 13 17 11 11 18 19 20 22 11 19 10 20 23 19 17 19 29 18
19 17 11 19 27 17 15 19 16 18 19 15 11 13 19 16 11 17 19 19 19 17  0]xS 
1236 1488 M (geological interpretation based on occasional field out)[18 17 18 11 18 18 11 16 17 11 14 11 19 11 17 13 19 13 17 11 17 11 11 18 19 14 19 17 15 17 19 13
18 19 13 18 16 16 17 15 11 18 19 17 11 13 12 11 17 11 19 13 18 19  0]xS 
2078 1488 M (-)S 
2090 1488 M (crops, )[16 13 18 19 15 10  0]xS 
1236 1533 M (seismic data, sparse drilling information and interpretation of )
[15 17 11 15 29 11 16 12 19 17 11 17 10 11 15 19 17 13 15 17 11 19 13 11 11 11 11 19 18 11 11 19
12 18 13 29 17 11 11 18 19 11 17 19 19 11 11 19 11 17 13 19 13 17 11 17 11 11 18 19 11 18 12  0]xS 
1236 1578 M (the gravity data via Euler deconvolution.)[11 19 17 10 18 13 17 18 11 11 17 10 19 17 11 17 10 18 11 17 10 23 19 11 17 13 10 19 17 16 18 19
18 18 11 19 11 11 18 19  0]xS 
1855 1578 M ( )S 
1236 1623 M ( )S 
1236 1668 M (From geological studies on the area we can assume that the )[21 13 18 29 15 18 17 18 11 18 18 11 16 17 11 14 15 11 19 19 11 17 15 14 18 19 14 11 19 17 14 17
13 17 17 14 27 17 14 16 17 19 14 17 15 15 19 29 17 14 11 19 17 11 14 11 19 17  0]xS 
1236 1713 M (density contrast of the source may vary between )[19 17 19 15 11 11 17 11 16 18 19 11 13 17 15 11 10 18 12 10 11 19 17 10 15 18 19 13 16 17 10 29
17 17 10 18 17 13 17 10 19 17 11 27 17 17 19  0]xS 
1976 1713 M (-)S 
1988 1713 M (.16 and )[10 19 19 10 17 19 19  0]xS 
2111 1713 M (-)S 
2123 1713 M (.25. )[10 19 19 10  0]xS 
1236 1758 M (Notice that this leaves quite a )[27 18 11 11 16 17 19 11 19 17 11 19 11 19 11 15 18 11 17 17 18 17 15 18 19 19 11 11 17 18 17  0]xS 
1749 1758 M (wide range in the possible )[27 11 19 17 18 13 17 19 18 17 18 11 19 18 11 19 17 18 19 18 15 15 11 19 11 17  0]xS 
1236 1803 M (density contrast of the source.)[19 17 19 15 11 11 17 10 16 18 19 11 13 17 15 11 10 18 12 10 11 19 17 10 15 18 19 13 16 17  0]xS 
1690 1803 M ( )S 
1236 1848 M ( )S 
: 520 385 24 1560 941 697 1236 1857 F F 3 [ 0 0 0 ] F 
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F /F7 0 /256 T /Courier mF 
/F7S32 F7 [50 0 0 -50 0 0 ] mFS
F7S32 Ji 
2177 2554 M ( )S 
F4S26 Ji 
1236 2591 M (Figure 4. Gravity profile \(yellow line in top chart\) and )[24 11 19 21 17 17 17 19 10 17 30 17 19 18 11 13 18 17 21 17 18 13 11 11 17 17 13 18 17 11 11 18
27 17 11 11 21 17 17 11 21 17 13 18 21 17 17 21 19 17 13 13 17 19 21 21  0]xS 
1236 2636 M (reconstruction of the possible source from geophysical )[17 17 17 18 21 15 13 17 21 17 13 11 18 21 22 18 13 21 13 21 17 21 21 18 15 15 11 21 11 17 21 15
18 21 17 17 17 21 13 17 18 31 21 19 17 18 21 21 18 15 11 17 19 11  0]xS 
1236 2681 M (and geological information.)[19 21 21 10 19 17 18 11 18 19 11 17 19 11 10 11 21 13 18 17 31 19 13 11 18 21  0]xS 
1680 2681 M ( )S 
/F7S2A F7 [42 0 0 -42 0 0 ] mFS
F7S2A Ji 
1236 2722 M ( )S 
F1S26 Ji 
1236 2770 M (In Figure 5 we can see the results of our reconstruction. The )
[11 19 13 21 11 18 19 13 17 13 19 13 27 17 13 16 17 19 13 15 17 17 13 11 19 17 13 13 17 15 19 11
11 15 12 18 12 12 18 19 13 12 13 17 16 18 19 15 11 13 19 16 11 11 18 19 10 12 23 19 17  0]xS 
1236 2815 M (outermost block \(d\) is the result obtained assuming a density )
[18 19 11 17 13 29 18 15 11 12 19 11 18 16 19 12 13 19 13 12 11 15 12 11 19 17 12 13 17 15 19 11
11 12 18 19 11 17 11 19 17 19 12 17 15 15 19 29 11 19 18 12 17 11 19 17 19 15 11 11 17  0]xS 
1236 2860 M (contrast of  )[16 18 19 11 13 17 15 11 11 18 12 11  0]xS 
1419 2860 M (-)S 
1431 2860 M (.16. In this case a very large block is required, to )[10 19 19 10 11 11 19 11 11 19 11 15 11 16 17 15 17 11 17 11 18 17 13 17 11 11 17 13 18 17 11 19
11 18 16 19 10 11 15 10 13 17 19 19 11 13 17 19 10 10 11 18  0]xS 
1236 2905 M (the point that the block top exceeds the topography. Clearly )
[11 19 17 15 19 18 11 19 11 14 11 19 17 11 14 11 19 17 14 19 11 18 16 19 14 11 18 19 14 17 19 16
17 17 19 15 14 11 19 17 14 11 18 19 18 18 13 17 19 19 17 10 14 25 11 17 17 13 11 17  0]xS 
1236 2950 M (this model had to be rejected. The innermost block \(b\) is)[11 19 11 15 18 29 18 19 17 11 18 19 17 19 18 11 18 18 19 17 18 13 17 11 17 16 11 17 19 10 18 23
19 17 18 11 19 19 17 13 29 18 15 11 18 19 11 18 16 19 18 13 19 13 17 11  0]xS 
2181 2950 M ( )S 
1236 2995 M (obtained for a density contrast of )[18 19 11 17 11 19 17 19 27 12 18 13 27 17 27 19 17 19 15 11 11 17 26 16 18 19 11 13 17 15 11 26
18 12  0]xS 
1845 2995 M (-)S 
1857 2995 M (.25. This model is )[10 19 19 10 26 23 19 11 15 26 29 18 19 17 11 26 11 15  0]xS 
1236 3040 M (reasonable and should be preferred as s possible )[13 17 17 15 18 19 17 19 11 17 40 17 19 19 40 15 19 18 19 11 19 40 19 17 40 19 13 17 12 17 13 13
17 19 40 17 15 39 15 39 19 18 15 15 11 19 11 17  0]xS 
1236 3085 M (approximation to the source. Finally the middle block \(c\) is )
[17 19 19 13 18 19 11 29 17 11 11 18 19 15 11 18 15 11 19 17 15 15 18 19 13 16 17 10 14 21 11 19
17 11 11 17 14 11 19 17 14 29 11 19 19 11 17 14 19 11 18 16 19 14 13 16 13 14 11 15  0]xS 
1236 3130 M (the largest possible due to the location of the centre of )[11 19 17 22 11 17 13 18 17 15 11 22 19 18 15 15 11 19 11 17 22 19 19 17 22 11 18 22 11 19 17 22
11 18 16 17 11 11 18 19 22 18 12 22 11 19 17 22 16 17 19 11 13 17 21 18 12  0]xS 
LH
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0 0 0 1 scol F2S26 Ji 
173 122 M ( )S 
F1S2A Ji 
173 3285 M ( )S 
2162 127 M ( )S 
F1S26 Ji 
173 273 M (gravity, the amount of mass, and the ground level. In absence )
[18 13 17 18 11 11 17 10 12 11 19 17 12 17 29 18 19 19 11 11 18 12 11 29 17 15 15 10 11 17 19 19
11 11 19 17 11 18 13 18 19 19 19 11 11 17 18 17 11 10 11 11 19 11 17 19 15 17 19 16 17  0]xS 
173 318 M (of further information we should assume that the last two )[18 12 18 12 19 13 11 19 17 13 18 11 19 12 18 13 29 17 11 11 18 19 18 27 17 18 15 19 18 19 11 19
18 17 15 15 19 29 17 18 11 19 17 11 18 11 19 17 18 11 17 15 11 17 11 27 18  0]xS 
173 363 M (blocks represent the maximum and minimum extent of the )[19 11 18 16 19 15 17 13 17 19 13 17 15 17 19 11 17 11 19 17 17 29 17 19 11 29 19 29 17 17 19 19
17 29 11 19 11 29 19 29 16 17 19 11 17 19 11 16 18 12 16 11 19 17  0]xS 
173 408 M (possible solution. Overlying them a section of the Fractal )[19 18 15 15 11 19 11 17 20 15 18 11 19 11 11 18 19 10 20 27 18 17 13 11 17 11 19 18 19 11 19 17
29 19 17 19 15 17 16 11 11 18 19 19 18 12 19 11 19 17 19 21 13 17 16 11 17 11  0]xS 
173 453 M (Graphics/Pasminco 3D model is plotted \(a\). It can be s)[27 13 17 19 19 11 16 15 11 21 17 15 29 11 19 16 18 17 19 27 17 29 18 19 17 11 17 11 15 17 19 11
18 11 11 17 19 16 13 17 13 10 16 11 11 16 16 17 19 16 19 17 16  0]xS 
1065 453 M (een )[17 17 19  0]xS 
173 498 M (that the two smaller models match the geologically )[11 19 17 11 35 11 19 17 35 11 27 18 34 15 29 17 11 11 17 13 34 29 18 19 17 11 15 34 29 17 11 16
19 34 11 19 17 34 18 17 18 11 18 18 11 16 17 11 11 17  0]xS 
173 543 M (reconstructed section moderately well. This, again, is mostly )
[13 17 16 18 19 15 11 13 19 16 11 17 19 14 15 17 16 11 11 18 19 13 29 18 19 17 13 17 11 17 11 17
13 27 17 11 11 10 13 23 19 11 15 10 13 17 18 17 11 19 10 13 11 15 13 29 18 15 11 11 17  0]xS 
173 588 M (due to the proper estimation of the centre of gravity. )[19 19 17 10 11 18 10 11 19 17 10 19 13 18 19 17 13 10 17 15 11 11 29 17 11 11 18 19 10 18 12 10
11 19 17 10 16 17 19 11 13 17 10 18 12 10 18 13 17 18 11 11 17 10  0]xS 
977 588 M ( )S 
173 633 M ( )S 
173 678 M (Finally it should be noted that satisfactory results have been )
[21 11 19 17 11 11 17 14 11 11 14 15 19 18 19 11 19 14 19 17 13 19 18 11 17 19 13 11 19 17 11 13
15 17 11 11 15 12 17 16 11 18 13 17 13 13 17 15 19 11 11 15 13 19 17 18 17 13 19 17 17 19  0]xS 
173 723 M (obtained by applying a 2D technique to a 3D problem \(in )[18 19 11 17 11 19 17 19 18 19 17 18 17 19 19 11 17 11 19 18 18 17 18 19 27 18 11 17 16 19 19 11
19 19 17 17 11 18 17 17 17 19 27 17 19 13 18 19 11 17 29 17 13 11 19  0]xS 
173 768 M (standard geophysical application 2D models are assumed to )[15 11 17 19 19 17 13 19 16 18 17 18 19 19 17 15 11 16 17 11 15 17 19 19 11 11 16 17 11 11 18 19
15 19 27 15 29 18 19 17 11 15 15 17 13 17 15 17 15 15 19 29 17 19 15 11 18  0]xS 
173 813 M (have infinite extension in the Y axis, while the 3D model )[19 17 18 17 17 11 19 12 11 19 11 11 17 17 17 19 11 17 19 15 11 18 19 17 11 19 17 11 19 17 17 27
17 17 19 11 15 10 17 27 19 11 11 17 17 11 19 17 17 19 27 16 29 18 19 17 11  0]xS 
173 858 M (presented in Figure 4 is not particularly elongated\). )[19 13 17 15 17 19 11 17 19 10 11 19 10 21 11 18 19 13 17 10 19 10 11 15 10 19 18 11 10 19 17 13
11 11 16 19 11 17 13 11 17 10 17 11 18 19 18 17 11 17 19 13 10  0]xS 
967 858 M ( )S 
173 903 M (.)S 
183 903 M ( )S 
/F1S1E F1 [30.027 0 0 -30.027 0 0 ] mFS
F1S1E Ji 
173 939 M ( )S 
: : N 173 912 764 430 irp C 
1 1 1 1 scol O ; 486 275 1 61 764 430 173 912 F F 3 [ 0 ] F 
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o`"p[p\t6k`W#r9q>UHno`"pKp&>$jo`"p[p\t6k`W#r9q>UHno`"pKp&>$jo`"p[p\t6k`W#r9
!<(=$!6t;p!T3gorrDu9rrDu9rrDu9rrDu9rrDu9rrDr~> Z
; 1 Lj 1 Lc 6 Lw solid N 1041 1049 M 843 1109 I : 0.297 0.297 +S K 
; N 841 1100 M 825 1115 I 847 1119 I C 
 O N 1037 1121 M 881 1164 I : 0.297 0.297 +S K 
; N 879 1154 M 863 1169 I 884 1173 I C 
 O N 1043 1192 M 911 1223 I : 0.297 0.297 +S K 
; N 910 1213 M 892 1227 I 914 1232 I C 
 O N 1043 976 M 786 1054 I : 0.297 0.297 +S K 
; N 784 1044 M 768 1060 I 790 1063 I C 
 O : N 1035 939 67 68 rp C 
1 1 1 1 scol  L ; /F4S23 F4 [35.129 0 0 -35.129 0 0 ] mFS
F4S23 Ji 
1053 982 M (A)S 
: 1078 950 6 40 rc 1078 982 M ( )S 
; : N 1035 1014 67 67 rp C 
1 1 1 1 scol  L ; 1053 1056 M (B)S 
: 1076 1024 8 40 rc 1076 1056 M ( )S 
; : N 1035 1088 67 68 rp C 
1 1 1 1 scol  L ; 1053 1130 M (C)S 
: 1078 1098 6 40 rc 1078 1130 M ( )S 
; : N 1035 1162 67 68 rp C 
1 1 1 1 scol  L ; 1053 1205 M (D)S 
: 1078 1173 6 40 rc 1078 1205 M ( )S 
; F7S32 Ji 
1117 1342 M ( )S 
F4S26 Ji 
173 1379 M (Figure 5. Reconstruct)[24 11 19 21 17 17 17 19 10 17 27 17 17 18 21 15 13 17 21 17  0]xS 
541 1379 M (ion of the source with the method )[11 18 21 16 18 13 16 13 21 17 16 15 18 21 17 17 17 16 27 11 13 21 16 13 21 17 16 31 17 13 21 18
21  0]xS 
173 1424 M (discussed in this paper. The outermost block \(d\) is the )[21 11 15 17 21 15 15 17 21 18 11 21 18 13 21 11 15 18 21 19 21 17 17 10 18 25 21 17 18 18 21 13
17 17 31 18 15 13 17 21 11 18 17 20 17 13 21 13 17 11 15 17 13 21 17  0]xS 
173 1469 M (result for the low density contrast model. The innermost )[17 17 15 21 11 13 14 13 18 17 14 13 21 17 14 11 18 27 14 21 17 21 15 11 13 18 14 17 18 21 13 17
19 15 13 14 31 18 21 17 11 10 14 25 21 17 14 11 21 21 17 17 31 18 15 13  0]xS 
173 1514 M (block \(b\) represents the high density contrast model. The )[21 11 18 17 20 13 13 21 13 13 17 17 21 17 17 15 17 21 13 15 12 13 21 17 12 21 11 19 21 12 21 17
21 15 11 13 18 12 17 18 21 13 17 19 15 13 12 31 18 21 17 11 10 12 25 21 17  0]xS 
173 1559 M (middle block \(c\) is the largest possible given the location )[31 11 21 21 11 17 14 21 11 18 17 20 14 13 17 13 14 11 15 14 13 21 17 13 11 19 17 19 17 15 13 13
21 18 15 15 11 21 11 17 13 19 11 18 17 21 13 13 21 17 13 11 18 17 19 13 11 18 21  0]xS 
173 1604 M (of the centre of gravity, the amount of mass, and the )[18 13 20 13 21 17 20 17 17 21 13 17 17 20 18 13 20 19 17 19 18 11 13 18 10 20 13 21 17 20 19 31
18 21 21 13 20 18 13 20 31 19 15 15 10 19 19 21 21 19 13 21 17  0]xS 
173 1649 M (ground level..)[19 17 18 21 21 21 10 11 17 18 17 11 10  0]xS 
F1S26 Ji 
394 1649 M ( )S 
173 1693 M ( )S 
F4S2A Ji 
518 1743 M (DISCUSSION)[30 16 23 30 30 23 23 16 33  0]xS 
772 1743 M ( )S 
F1S26 Ji 
173 1788 M ( )S 
173 1833 M (We are very well aware of the problems due to the non)[35 17 19 17 13 17 19 18 17 13 17 19 27 17 11 11 19 17 27 17 13 17 19 18 12 19 11 19 17 19 19 13
18 19 11 17 29 15 19 19 19 17 19 11 18 18 11 19 17 18 19 18  0]xS 
1106 1833 M (-)S 
173 1878 M (uniqueness of the inversion of potential field data. An in )[19 19 11 19 19 17 19 17 15 15 20 18 12 20 11 19 17 20 11 19 18 17 13 15 11 18 19 19 18 12 19 19
18 11 17 19 11 11 17 11 19 12 11 17 11 19 19 19 17 11 17 10 19 26 19 19 11 19  0]xS 
173 1923 M (depth analysis of the issue, as well as our approach)[19 17 19 11 19 15 17 19 17 11 17 15 11 15 15 18 12 15 11 19 17 15 11 15 15 19 17 10 14 17 15 14
27 17 11 11 14 17 15 14 18 19 13 14 17 19 19 13 18 17 16  0]xS 
992 1923 M ( to such )[14 11 18 14 15 19 16 19  0]xS 
173 1968 M (problem can be found in Hornby et al \(2000\). From a purely )[19 13 18 19 11 17 29 13 16 17 19 13 19 17 13 12 18 19 19 19 13 11 19 13 27 18 13 19 19 17 13 17
11 13 17 11 12 13 19 19 19 19 13 10 12 21 13 18 29 12 17 12 19 19 13 17 11 17  0]xS 
173 2013 M (mathematical point of view, uniquely reconstructing the )[29 17 11 19 17 29 17 11 11 16 17 11 26 19 18 11 19 11 26 18 12 26 18 11 17 27 10 26 19 19 11 19
19 17 11 17 25 13 17 16 18 19 15 11 13 19 16 11 11 19 18 25 11 19 17  0]xS 
173 2058 M (source from gravity or magnetic profiles is simply impossible. )
[15 18 19 13 16 17 11 12 13 18 29 11 18 13 17 18 11 11 17 10 18 13 10 29 17 18 19 17 11 11 16 10
19 13 18 12 11 11 17 15 10 11 15 10 15 11 29 19 11 17 10 11 29 19 18 15 15 11 19 11 17 10  0]xS 
173 2103 M (All algorithms published in the literature, as well as ours, )
[26 11 11 18 17 11 18 18 13 11 11 19 29 15 17 19 19 19 11 11 15 19 17 19 17 11 19 17 11 19 17 17
11 11 11 17 13 17 11 19 13 17 10 17 17 15 17 27 17 11 11 17 17 15 17 18 19 13 15 10  0]xS 
173 2148 M (attempt, in one way or another, to achieve the impossible. )[17 11 11 17 29 19 11 10 18 11 19 17 18 19 17 17 27 17 17 17 18 13 17 17 19 18 11 19 17 13 10 17
11 18 17 17 16 19 11 17 18 17 17 11 19 17 17 11 29 19 18 15 15 11 19 11 17 10  0]xS 
173 2193 M (This is done via a number of a priori assumptions, as well as )
[23 19 11 15 12 11 15 12 19 18 19 17 12 18 11 17 12 17 12 19 19 29 19 17 13 12 18 12 12 17 11 19
13 11 18 13 11 11 17 15 15 19 29 19 11 11 18 19 15 10 11 17 15 11 27 17 11 11 11 17 15  0]xS 
173 2238 M (a great deal of approximation. The requirement of strong a )[17 16 18 13 17 17 11 16 19 17 17 11 16 18 12 16 17 19 19 13 18 19 11 29 17 11 11 18 19 10 16 23
19 17 16 13 17 19 19 11 13 17 29 17 19 11 16 18 12 15 15 11 13 18 19 18 15 17  0]xS 
173 2283 M (priori assumption is well known in the literature. )[19 13 11 18 13 11 10 17 15 15 19 29 19 11 11 18 19 10 11 15 10 27 17 11 11 10 19 19 18 27 19 10
11 19 10 11 19 17 10 11 11 11 17 13 17 11 19 13 17 10  0]xS 
932 2283 M ( )S 
173 2328 M ( )S 
173 2373 M (In our opinion, what justifies )[11 19 15 18 19 13 15 18 19 11 19 11 18 19 10 14 27 19 17 11 14 11 19 15 11 11 12 11 17 15  0]xS 
646 2373 M (the simplified approach to the )[11 19 17 14 15 11 29 19 11 11 12 11 17 19 14 17 19 19 13 18 17 16 19 14 11 18 14 11 19 17  0]xS 
173 2418 M (problem presented in this paper is the requirement for a great )
[19 13 18 19 11 17 29 11 19 13 17 15 17 19 11 17 19 11 11 19 11 11 19 11 15 11 19 17 19 17 13 11
11 15 11 11 19 17 11 13 17 19 19 11 13 17 29 17 19 11 10 12 18 13 10 17 10 18 13 17 17 11  0]xS 
173 2463 M (deal of approximation. Potential field data can be seen as a )
[19 17 17 11 15 18 12 15 17 19 19 13 18 19 11 29 17 11 11 18 19 10 15 21 18 11 17 19 11 11 17 11
15 12 11 17 11 19 15 19 17 11 17 14 16 17 19 14 19 17 14 15 17 17 19 14 17 15 14 17  0]xS 
173 2508 M (smoothed version of the source, where the response due to )[15 29 18 18 11 19 17 19 17 18 17 13 15 11 18 19 17 18 12 16 11 19 17 16 15 18 19 13 16 17 10 16
27 19 17 13 17 16 11 19 17 16 13 17 15 19 18 19 15 17 16 19 19 17 16 11 18  0]xS 
173 2553 M (material at different depth is summed linearly in a way that is )
[29 17 11 17 13 11 17 11 11 17 11 11 19 11 12 12 17 13 17 19 11 11 19 17 19 11 19 10 11 15 10 15
19 29 29 17 19 10 11 11 19 17 17 13 11 17 10 11 19 10 17 10 27 17 17 10 11 19 17 11 10 11 15  0]xS 
173 2598 M (impossible to unravel. Accordingly, precise reconstruction is )
[11 29 19 18 15 15 11 19 11 17 14 11 18 14 19 19 13 17 18 17 11 10 14 26 16 16 18 13 19 11 19 18
11 17 10 14 19 13 17 16 11 15 17 14 13 17 16 18 19 15 11 13 19 16 11 11 18 19 13 11 15  0]xS 
173 2643 M (beyond the ability of the technique. In the absence of strong )
[19 17 17 18 19 19 14 11 19 17 14 17 19 11 11 11 11 17 14 18 12 14 11 19 17 14 11 17 16 19 19 11
19 19 17 10 14 11 19 13 11 19 17 13 17 19 15 17 19 16 17 13 18 12 13 15 11 13 18 19 18  0]xS 
173 2688 M (additional geological information, approximate estimation of )
[17 19 19 11 11 11 18 19 17 11 14 18 17 18 11 18 18 11 16 17 11 14 11 19 12 18 13 29 17 11 11 18
19 10 14 17 19 19 13 18 19 11 29 17 11 17 14 17 15 11 11 29 17 11 11 18 19 14 18 12  0]xS 
173 2733 M (shape and depth is all one can hope for. )[15 19 17 19 17 10 17 19 19 10 19 17 19 11 19 10 11 15 10 17 11 11 10 18 19 17 10 16 17 19 10 19
18 19 17 10 12 18 13 10  0]xS 
787 2733 M ( )S 
173 2778 M ( )S 
173 2823 M (Also, w)[26 11 15 18 10 12  0]xS 
292 2823 M (e argue that non)[17 12 17 13 18 19 17 11 11 19 17 11 11 19 18  0]xS 
541 2823 M (-)S 
553 2823 M (uniqueness should not be completely )[19 19 11 19 19 17 19 17 15 15 11 15 19 18 19 11 19 11 19 18 11 11 19 17 11 16 18 29 19 11 17 11
17 11 17  0]xS 
173 2868 M (removed. Presenting the user with multiple solutions, )[13 17 29 18 18 17 19 10 32 21 13 17 15 17 19 11 11 19 18 32 11 19 17 32 19 15 17 13 31 27 11 11
19 31 29 19 11 11 11 19 11 17 31 15 18 11 19 11 11 18 19 15 10  0]xS 
173 2913 M (possibly as some sort of maximum and minimum source )[19 18 15 15 11 19 11 17 22 17 15 21 15 18 29 17 21 15 18 13 11 21 18 12 21 29 17 19 11 29 19 29
21 17 19 19 21 29 11 19 11 29 19 29 21 15 18 19 13 16 17  0]xS 
173 2958 M (extent \(as in our real case test\) will help the user remember )
[17 19 11 17 19 11 14 13 17 15 14 11 19 13 18 19 13 13 13 17 17 11 13 16 17 15 17 13 11 17 15 11
13 13 27 11 11 11 13 19 17 11 19 13 11 19 17 13 19 15 17 13 13 13 17 29 17 29 19 17 13  0]xS 
173 3003 M (the limitations of the method and possibly help the geological )
[11 19 17 11 11 11 29 11 11 17 11 11 18 19 15 11 18 12 11 11 19 17 11 29 17 11 19 18 19 11 17 19
19 11 19 18 15 15 11 19 11 17 10 19 17 11 19 10 11 19 17 10 18 17 18 11 18 18 11 16 17 11  0]xS 
173 3048 M (interpretation. In this scenario, some sort of interactivity is )
[11 19 11 17 13 19 13 17 11 17 11 11 18 19 10 17 11 19 17 11 19 11 15 17 15 16 17 19 17 13 11 18
10 16 15 18 29 17 16 15 18 13 11 16 18 12 16 11 19 11 17 13 17 16 11 11 18 11 11 17 16 11 15  0]xS 
173 3093 M (welcome. For this reason, a fast method, not requiring )[27 17 11 16 18 29 17 10 25 21 18 13 25 11 19 11 15 25 13 17 17 15 18 19 10 25 17 25 12 17 15 11
25 29 17 11 19 18 19 10 25 19 18 11 25 13 17 19 19 11 13 11 19 18  0]xS 
1236 273 M (iterative calculation seems best suited to sit inside a )[11 11 17 13 17 11 11 18 17 29 16 17 11 16 19 11 17 11 11 18 19 29 15 17 17 29 15 29 19 17 15 11
29 15 19 11 11 17 19 29 11 18 29 15 11 11 29 11 19 15 11 19 17 28 17  0]xS 
1236 318 M (geological 3D visualisation package for real time ana)[18 17 18 11 18 18 11 16 17 11 19 19 27 18 18 11 15 19 17 11 11 15 17 11 11 18 19 18 19 17 16 19
17 18 17 18 12 18 13 18 13 17 17 11 18 11 11 29 17 18 17 19  0]xS 
2102 318 M (lysis. )[11 17 15 11 15 10  0]xS 
1236 363 M (This is how we envisage the use of the technique presented in )
[23 19 11 15 11 11 15 10 19 18 27 10 27 17 10 17 19 18 11 15 17 18 17 10 11 19 17 10 19 15 17 10
18 12 10 11 19 17 10 11 17 16 19 19 11 19 19 17 10 19 13 17 15 17 19 11 17 19 10 11 19  0]xS 
1236 408 M (this work.)[11 19 11 15 10 27 18 13 19  0]xS 
1389 408 M ( )S 
: N 1230 417 957 45 rp C 
1 1 1 1 scol  L ; 1236 453 M ( )S 
F4S2A Ji 
1555 503 M (CONCLUSIONS)[30 33 30 30 28 30 23 16 33 30  0]xS 
1861 503 M ( )S 
1708 553 M ( )S 
F1S26 Ji 
1236 598 M (We present a method to reconstruct a block)[35 17 34 19 13 17 15 17 19 11 34 17 34 29 17 11 19 18 19 34 11 18 34 13 17 16 18 19 15 11 13 19
16 11 34 17 33 19 11 18 16  0]xS 
2063 598 M (-)S 
2075 598 M (shaped )[15 19 17 19 17 19  0]xS 
1236 643 M (approximation to the source of a gravity anomaly. Such a )[17 19 19 13 18 19 11 29 17 11 11 18 19 19 11 18 19 11 19 17 19 15 18 19 13 16 17 19 18 12 19 17
19 18 13 17 18 11 11 17 18 17 19 18 29 17 11 17 10 18 21 19 16 19 18 17  0]xS 
1236 688 M (problem could be solved as a simple 5 parameter inversion. )[19 13 18 19 11 17 29 15 16 18 19 11 19 15 19 17 14 15 18 11 18 17 19 14 17 15 14 17 14 15 11 29
19 11 17 14 19 14 19 17 13 17 29 17 11 17 13 14 11 19 18 17 13 15 11 18 19 10  0]xS 
1236 733 M (The advantage of our technique lies in the fact that the )[23 19 17 22 17 19 18 17 19 11 17 18 17 22 18 12 22 18 19 13 21 11 17 16 19 19 11 19 19 17 21 11
11 17 15 21 11 19 21 11 19 17 21 12 17 16 11 21 11 19 17 11 21 11 19 17  0]xS 
1236 778 M (reconstruction is performed by direct calculation. No iterative )
[13 17 16 18 19 15 11 13 19 16 11 11 18 19 11 11 15 11 19 17 13 12 18 13 29 17 19 11 19 17 11 19
11 13 17 16 11 11 16 17 11 16 19 11 17 11 11 18 19 10 11 27 18 10 11 11 17 13 17 11 11 18 17  0]xS 
1236 823 M (search is needed. This makes the calculation fast enough to )[15 17 17 13 16 19 15 11 15 15 19 17 17 19 17 19 10 15 23 19 11 15 15 29 17 19 17 15 15 11 19 17
15 16 17 11 16 19 11 17 11 11 18 19 14 12 17 15 11 14 17 19 18 19 18 19 14 11 18  0]xS 
1236 868 M (envisage its use in real time for 3D geological visualisation )
[17 19 18 11 15 17 18 17 15 11 11 15 15 19 15 17 15 11 19 15 13 17 17 11 15 11 11 29 17 15 12 18
13 14 19 27 14 18 17 18 11 18 18 11 16 17 11 14 18 11 15 19 17 11 11 15 17 11 11 18 19  0]xS 
1236 913 M (packages.)[19 17 16 19 17 18 17 15  0]xS 
1384 913 M ( )S 
1236 958 M ( )S 
1236 1003 M (The algorithm is designed for the unfortunate, but frequent, )
[23 19 17 15 17 11 18 18 13 11 11 19 29 15 11 15 15 19 17 15 11 18 19 17 19 15 12 18 13 15 11 19
17 14 19 19 12 18 13 11 19 19 17 11 17 10 14 19 19 11 14 12 13 17 19 19 17 19 11 10  0]xS 
1236 1048 M (scenario where little or no information is available about the )
[15 16 17 19 17 13 11 18 13 27 19 17 13 17 13 11 11 11 11 11 17 13 18 13 13 19 18 13 11 19 12 18
13 29 17 11 11 18 19 12 11 15 12 17 18 17 11 11 17 19 11 17 12 17 19 18 19 11 12 11 19 17  0]xS 
1236 1093 M (source, except for a guessed estimate of the density contrast. )
[15 18 19 13 16 17 10 13 17 19 16 17 19 11 13 12 18 13 13 17 13 18 19 17 15 15 17 19 13 17 15 11
11 29 17 11 17 13 18 12 12 11 19 17 12 19 17 19 15 11 11 17 12 16 18 19 11 13 17 15 11 10  0]xS 
1236 1138 M (Should this estimate be only approximate, the algorithm can )[21 19 18 19 11 19 14 11 19 11 15 14 17 15 11 11 29 17 11 17 14 19 17 13 18 19 11 17 13 17 19 19
13 18 19 11 29 17 11 17 10 13 11 19 17 13 17 11 18 18 13 11 11 19 29 13 16 17 19  0]xS 
1236 1183 M (generate different solutions that describe the range of models )
[18 17 19 17 13 17 11 17 12 19 11 12 12 17 13 17 19 11 12 15 18 11 19 11 11 18 19 15 12 11 19 17
11 12 19 17 15 16 13 11 19 17 12 11 19 17 11 13 17 19 18 17 11 18 12 11 29 18 19 17 11 15  0]xS 
1236 1228 M (allowed by the data.)[17 11 11 18 27 17 19 10 19 17 10 11 19 17 10 19 17 11 17  0]xS 
1543 1228 M ( )S 
1236 1273 M ( )S 
1236 1318 M (Finally, the algorithm can be extended to the analysis of )[21 11 19 17 11 11 17 10 20 11 19 17 20 17 11 18 18 13 11 11 19 29 20 16 17 19 20 19 17 20 17 19
11 17 19 19 17 19 20 11 18 20 11 19 17 20 17 19 17 11 17 15 11 15 20 18 12  0]xS 
1236 1363 M (magnetic data via pseudo)[29 17 18 19 17 11 11 16 18 19 17 11 17 18 18 11 17 17 19 15 17 19 19  0]xS 
1644 1363 M (-)S 
1656 1363 M (gravity transformation, which we )[18 13 17 18 11 11 17 17 11 13 17 19 15 12 18 13 29 17 11 11 18 19 10 17 27 19 11 16 19 17 27 17
 0]xS 
1236 1408 M (tested on synthetic data.   )[11 17 15 11 17 19 10 18 19 10 15 17 19 11 19 17 11 11 16 10 19 17 11 17 10 10 10  0]xS 
1633 1408 M ( )S 
1236 1453 M ( )S 
F4S26 Ji 
1582 1499 M (REFERENCES)[27 25 24 25 27 25 27 27 25  0]xS 
F1S26 Ji 
1835 1499 M ( )S 
1236 1543 M ( )S 
1236 1588 M (Blakely, R. J., 1995)[25 11 17 19 17 11 17 10 12 25 10 12 15 10 10 12 19 19 19  0]xS 
1545 1588 M (, Potential theory in gravity and magnetic )[10 12 21 18 11 17 19 11 11 17 11 11 11 19 17 18 13 17 11 11 19 11 18 13 17 18 11 11 17 11 17 19
19 11 29 17 18 19 17 11 11 16  0]xS 
1236 1633 M (applications: Cambridge University Press.)[17 19 19 11 11 16 17 11 11 18 19 15 9 10 25 17 29 19 13 11 19 18 17 10 27 19 11 18 17 13 15 11
11 17 10 21 13 17 15 15  0]xS 
1877 1633 M ( )S 
1236 1678 M ( )S 
1236 1723 M (F. Boschetti, Y. Kammoun, F. Horowitz and P. Hornby, )[21 10 22 25 18 15 16 19 17 11 11 11 10 22 27 10 22 27 17 29 29 18 19 19 10 22 21 10 22 27 18 13
18 27 11 11 16 22 17 19 19 22 21 10 21 27 18 13 19 19 17 10  0]xS 
1236 1768 M (2000, Feature removal and stable downward continuation of)[19 19 19 19 10 10 21 17 17 11 19 13 17 10 13 17 29 18 18 17 11 10 17 19 19 10 15 11 17 19 11 17
10 19 18 27 19 27 17 13 19 10 16 18 19 11 11 19 19 17 11 11 18 19 10 18  0]xS 
2153 1768 M ( )S 
1236 1813 M (potential field data by multiscale edge suppression, )[19 18 11 17 19 11 11 17 11 38 12 11 17 11 19 37 19 17 11 17 37 19 17 37 29 19 11 11 11 15 16 17
11 17 37 17 19 18 17 37 15 19 19 19 13 17 15 15 11 18 19 10  0]xS 
1236 1858 M (Submitted to Geophysics.)[21 19 19 29 11 11 11 17 19 10 11 18 10 27 17 18 19 19 17 15 11 16 15  0]xS 
1626 1858 M ( )S 
1236 1903 M ( )S 
1236 1948 M (Hornby, P., Boschetti, F., and Horowitz, F.G., 1999a. )[27 18 13 19 19 17 10 29 21 10 10 29 25 18 15 16 19 17 11 11 11 10 29 21 10 10 29 17 19 19 28 27
18 13 18 27 11 11 16 10 28 21 10 27 10 10 28 19 19 19 19 17 10  0]xS 
1236 1993 M (Ambiguity analysis and the constrained inversion of potential )
[26 29 19 11 18 19 11 11 17 12 17 19 17 11 17 15 11 15 12 17 19 19 12 11 19 17 11 16 18 19 15 11
13 17 11 19 17 19 11 11 19 18 17 13 15 11 18 19 11 18 12 11 19 18 11 17 19 11 11 17 11  0]xS 
1236 2038 M (fields. Submitted to Geophysics)[12 11 17 11 19 15 10 10 21 19 19 29 11 11 11 17 19 10 11 18 10 27 17 18 19 19 17 15 11 16  0]xS 
1721 2038 M ( )S 
1236 2083 M ( )S 
1236 2128 M (Hornby, P., Boschetti, F. and Horowitz, F., 1999b,  Analysis )
[27 18 13 19 19 17 10 13 21 10 10 13 25 18 15 16 19 17 11 11 11 10 13 21 10 13 17 19 19 13 27 18
13 18 27 11 11 16 10 13 21 10 10 12 19 19 19 19 19 10 12 12 26 19 17 11 17 15 11 15  0]xS 
1236 2173 M (of potential field data in)[18 12 18 19 18 11 17 19 11 11 17 11 18 12 11 17 11 19 18 19 17 11 17 18 11  0]xS 
1636 2173 M ( the wavelet domain. Geophysical )[18 11 19 17 18 27 17 18 17 11 17 11 17 19 18 29 17 11 19 10 17 27 17 18 19 19 17 15 11 16 17 11
 0]xS 
1236 2218 M (Journal International, 137, 175)[15 18 19 13 19 17 11 10 11 19 11 17 13 19 17 11 11 18 19 17 11 10 10 19 19 19 10 10 19 19  0]xS 
1706 2218 M (-)S 
1718 2218 M (196.)[19 19 19  0]xS 
1785 2218 M ( )S 
1236 2263 M ( )S 
1236 2308 M (Moreau, F., Gibert, D., Holschnider, M. and Saracco G., )[34 18 13 17 17 19 10 21 21 10 10 21 27 11 19 17 13 11 10 20 27 10 10 20 27 18 11 15 16 19 19 11
19 17 13 10 20 34 10 20 17 19 19 20 21 17 13 17 16 16 18 20 27 10 10  0]xS 
1236 2353 M (1997. Wavelet analysis of potential fields, Inverse Problems, )
[19 19 19 19 10 13 35 17 18 17 11 17 11 13 17 19 17 11 17 15 11 15 13 18 12 13 19 18 11 17 19 11
11 17 11 13 12 11 17 11 19 15 10 12 11 19 18 17 13 15 17 12 21 13 18 19 11 17 29 15 10  0]xS 
1236 2398 M (Vol. 13, pp165)[27 18 11 10 10 19 19 10 10 19 19 19 19  0]xS 
1465 2398 M (-)S 
1477 2398 M (178.)[19 19 19  0]xS 
1544 2398 M ( )S 
1236 2443 M ( )S 
1236 2488 M (Lyubimov, G., A., Lyubimov, A., 1970, Opredeleniye glubiny )[22 17 19 19 11 29 18 18 10 11 27 10 10 11 26 10 10 11 22 17 19 19 11 29 18 18 10 11 26 10 10 11
19 19 19 19 10 11 27 19 13 17 19 17 11 17 19 11 17 17 10 18 11 19 19 11 19 17  0]xS 
1236 2533 M (zaleganiya tsentra tyazhesti vytyanutykh tel poanomaliyam )[16 17 11 17 18 17 19 11 17 17 21 11 15 17 19 11 13 17 21 11 17 17 16 19 17 15 11 11 21 18 17 11
17 17 19 19 11 17 19 19 20 11 17 11 20 19 18 17 19 18 29 17 11 11 17 17 29  0]xS 
1236 2578 M (deltag \(Determination of depth to the center of gravity of )[19 17 11 11 17 18 19 13 27 17 11 17 13 29 11 19 17 11 11 18 19 19 18 12 19 19 17 19 11 19 19 11
18 19 11 19 17 19 16 17 19 11 17 13 19 18 12 19 18 13 17 18 11 11 17 18 18 12  0]xS 
1236 2623 M (elongated bodies from deltag anomalies\), Geologiya i )[17 11 18 19 18 17 11 17 19 32 19 18 19 11 17 15 32 12 13 18 29 32 19 17 11 11 17 18 32 17 19 18
29 17 11 11 17 15 13 10 32 27 17 18 11 18 18 11 17 17 32 11  0]xS 
1236 2668 M (razvedka. 6, 122)[13 17 16 18 17 19 19 17 10 10 19 10 10 19 19  0]xS 
1488 2668 M (-)S 
1500 2668 M (125. )[19 19 19 10  0]xS 
1577 2668 M ( )S 
1236 2713 M ( )S 
1236 2758 M (Managadze, G. Glonti, V., Rusadze, I., 1976, Opre)[34 17 19 17 18 17 19 16 17 10 16 27 10 16 27 11 18 19 11 11 10 16 27 10 10 16 25 19 15 17 19 16
17 10 16 11 10 10 16 19 19 19 19 10 15 27 19 13  0]xS 
2053 2758 M (deleniye )[19 17 11 17 19 11 17 17  0]xS 
1236 2803 M (vertikal'noy koordinaty tsentra vozmushchayushchikh mass )[18 17 13 11 11 19 17 11 5 19 18 17 22 19 18 18 13 19 11 19 17 11 17 22 11 15 17 19 11 13 17 22
18 18 16 29 19 15 19 16 19 17 17 19 15 19 16 19 11 19 19 22 29 17 15 15  0]xS 
1236 2848 M (polokalizovannoy anomalii sily tyazhesti \(Determining the )[19 18 11 18 19 17 11 11 16 18 18 17 19 19 18 17 22 17 19 18 29 17 11 11 11 21 15 11 11 17 21 11
17 17 16 19 17 15 11 11 21 13 27 17 11 17 13 29 11 19 11 19 18 21 11 19 17  0]xS 
1236 2893 M (vertical coordinate of the gravity center of an anomalous )[18 17 13 11 11 16 17 11 21 16 18 18 13 19 11 19 17 11 17 21 18 12 21 11 19 17 21 18 13 17 18 11
11 17 21 16 17 19 11 17 13 21 18 12 21 17 19 21 17 19 18 29 17 11 18 19 15  0]xS 
1236 2938 M (body, by using the local gravity anomaly\), Soobshcheniya )[19 18 19 17 10 21 19 17 21 19 15 11 19 18 20 11 19 17 20 11 18 16 17 11 20 18 13 17 18 11 11 17
20 17 19 18 29 17 11 17 13 10 20 21 18 18 19 15 19 16 19 17 19 11 17 17  0]xS 
1236 2983 M (Akademii Nauk Gruzinskoy SSR. 83, 2, 349)[26 19 17 19 17 29 11 11 10 27 17 19 19 10 27 13 19 16 11 19 15 19 18 17 10 21 21 25 10 10 19 19
10 10 19 10 10 19 19  0]xS 
1912 2983 M (-)S 
1924 2983 M (352.)[19 19 19  0]xS 
1991 2983 M ( )S 
1236 3028 M ( )S 
1236 3073 M (Mendelutsa, V., 1967, Graficheskiy sposob opredeleniya )[34 17 19 19 17 11 19 11 15 17 10 26 27 10 10 26 19 19 19 19 10 26 27 13 17 12 11 16 19 17 15 19
11 17 26 15 19 18 15 18 19 26 18 19 13 17 19 17 11 17 19 11 17 17  0]xS 
1236 3118 M (tsentra tyazhesti anomal'nogo ob'yekta ponormal'nomu )[11 15 17 19 11 13 17 41 11 17 17 16 19 17 15 11 11 41 17 19 18 29 17 11 5 19 18 18 18 40 18 19
5 17 17 19 11 17 40 19 18 19 18 13 29 17 11 5 19 18 29 19  0]xS 
LH
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0 0 0 1 scol F2S26 Ji 
173 122 M ( )S 
F1S2A Ji 
173 3285 M ( )S 
2162 127 M ( )S 
F1S26 Ji 
173 273 M (gradiyentu potentsiala \(A graphic method of determining the )[18 13 17 19 11 17 17 19 11 19 14 19 18 11 17 19 11 15 11 17 11 17 13 13 26 13 18 13 17 19 19 11
16 13 29 17 11 19 18 19 13 18 12 13 19 17 11 17 13 29 11 19 11 19 18 13 11 19 17  0]xS 
173 318 M (center of gravity of an anomalous object from the normal )[16 17 19 11 17 13 19 18 12 19 18 13 17 18 11 11 17 19 18 12 19 17 19 19 17 19 18 29 17 11 18 19
15 19 18 19 11 17 16 11 19 12 13 18 29 19 11 19 17 18 19 18 13 29 17 11  0]xS 
173 363 M (g)S 
191 363 M (radient of the potential\), Akad. nauk ukrain. ssr inst. )[13 17 19 11 17 19 11 26 18 12 26 11 19 17 26 19 18 11 17 19 11 11 17 11 13 10 26 26 19 17 19 10
25 19 17 19 19 25 19 19 13 17 11 19 10 25 15 15 13 25 11 19 15 11 10  0]xS 
173 408 M (geofiziki, geofiz. sbornik. 2\(13\), 77)[18 17 18 12 11 16 11 19 11 10 10 18 17 18 12 11 16 10 10 15 19 18 13 19 11 19 10 10 19 13 19 19
13 10 10 19  0]xS 
713 408 M (-)S 
725 408 M (79.)[19 19  0]xS 
773 408 M ( )S 
173 453 M ( )S 
173 498 M (Sokolovskii, K., 1978, Unitary method of determining the )[21 18 19 18 11 18 18 15 19 11 11 10 20 27 10 10 19 19 19 19 19 10 19 27 19 11 11 17 13 17 19 29
17 11 19 18 19 19 18 12 19 19 17 11 17 13 29 11 19 11 19 18 19 11 19 17  0]xS 
173 543 M (coordinates of the center of gravity and magnetic anomalies, )
[16 18 18 13 19 11 19 17 11 17 15 14 18 12 14 11 19 17 14 16 17 19 11 17 13 14 18 12 14 18 13 17
18 11 11 17 13 17 19 19 13 29 17 18 19 17 11 11 16 13 17 19 18 29 17 11 11 17 15 10  0]xS 
173 588 M (Soviet Geology and Geophysics. 19, 95)[21 18 18 11 17 11 10 27 17 18 11 18 18 17 10 17 19 19 10 27 17 18 19 19 17 15 11 16 15 10 10 19
19 10 10 19  0]xS 
770 588 M (-)S 
782 588 M (107.)[19 19 19  0]xS 
849 588 M ( )S 
173 633 M ( )S 
173 678 M (Tsaregradskiy, V., 1965, Kotsenke glubiny zaleganiya tsentra )
[23 15 17 13 17 18 13 17 19 15 19 11 17 10 12 27 10 10 12 19 19 19 19 10 11 27 18 11 15 17 19 19
17 11 18 11 19 19 11 19 17 11 16 17 11 17 18 17 19 11 17 17 11 11 15 17 19 11 13 17  0]xS 
173 723 M (mass po dannym Gravirazvedki \(On estimating the depth of )[29 17 15 15 15 19 18 15 19 17 19 19 17 29 15 27 13 17 18 11 13 17 16 18 17 19 19 11 15 13 27 19
14 17 15 11 11 29 17 11 11 19 18 14 11 19 17 14 19 17 19 11 19 14 18 12  0]xS 
173 768 M (the center of gravity from gravity survey data\), Prikladnaya )
[11 19 17 16 16 17 19 11 17 13 16 18 12 16 18 13 17 18 11 11 17 16 12 13 18 29 16 18 13 17 18 11
11 17 16 15 19 13 18 17 17 15 19 17 11 17 13 10 15 21 13 11 19 11 17 19 19 17 17 17  0]xS 
173 813 M (Geofizika. 46, 182)[27 17 18 12 11 16 11 19 17 10 10 19 19 10 10 19 19  0]xS 
456 813 M (-)S 
468 813 M (188. 1965. )[19 19 19 10 10 19 19 19 19 10  0]xS 
641 813 M ( )S 
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