Appendix I 259
Appendix I Fortran Program for Regional-Residual Separation by Finite Element Method
C AG-BOUGUER,GN-REGIONAL,D-RESIDUAL C PROGRAM FOR SEPARATION OF REGIONAL & RESIDUAL USING FEM METHOD C PROGRAM NEEDS THE GRAVITY VALUES ALSO IN ADDITION TO THE A(I)& B(I)VALUES DIMENSION G(12),X(12),Y(12) DIMENSION A(200000),B(200000),GN(200000),AG(200000),D(200000) OPEN(UNIT=3,FILE=‘F1-8.DAT’, STATUS=‘OLD’) OPEN(UNIT=4,FILE=‘A1.DAT’, STATUS=‘NEW’) OPEN(UNIT=11,FILE=‘A2.DAT’, STATUS=‘NEW’) OPEN(UNIT=12,FILE=‘A3.DAT’, STATUS=‘NEW’) OPEN(UNIT=13,FILE=‘A4.DAT’, STATUS=‘NEW’) READ (3,*) N,NN WRITE (*,*)‘GIVE OUTPUT DATA FILE NAME AS UNIT 4’ WRITE (4,*)‘NUMBER OF NODES{A(I)& B(I)} AND DATA(8 or 12) POINTS’ WRITE (4,*)N,NN WRITE (4,*)‘INPUT VALUES X,Y,AND GRAVITY DATA’ DO 10 I=1,NN READ (3,*) X(I),Y(I),G(I) 10 WRITE (4,*) X(I),Y(I),G(I) WRITE (4,*)‘INPUT VALUES OF A(I) & B(I)’ DO 20 I=1,N READ (3,*) A(I),B(I),AG(I) 20 WRITE (4,*)A(I),B(I),AG(I) WRITE (4,*)‘OUTPUT X , Y , REGIONAL GRAVITY & RESIDUAL VALUES’ DO 100 I=1,N A1=1+A(I) A2=1-A(I) AA=1-A(I)*A(I)
K. Mallick et al., Bouguer Gravity Regional and Residual Separation: Application to Geology 259 and Environment, DOI 10.1007/978-94-007-0406-0, © Capital Publishing Company 2012 260 Bouguer Gravity Regional and Residual Separation
B1=1+B(I) B2=1-B(I) BB=1-B(I)*B(I) C1=(9*AA)/32 C2=(9*BB)/32 C3=(-10+9*(2-AA-BB))/32 AN1=0.25*A2*B2*(A2+B2-3) AN3=0.25*A1*B2*(B2-A2-1) AN5=0.25*A1*B1*(1-A2-B2) AN7=0.25*A2*B1*(A2-B2-1) AN2=0.5*AA*B2 AN6=0.5*AA*B1 AN4=0.5*BB*A1 AN8=0.5*BB*A2 T1=AN1*G(1)+AN2*G(2)+AN3*G(3)+AN4*G(4) GN(I)=T1+AN5*G(5)+AN6*G(6)+AN7*G(7)+AN8*G(8) T2=AN1*X(1)+AN2*X(2)+AN3*X(3)+AN4*X(4) A(I)=T2+AN5*X(5)+AN6*X(6)+AN7*X(7)+AN8*X(8) T3=AN1*Y(1)+AN2*Y(2)+AN3*Y(3)+AN4*Y(4) B(I)=T3+AN5*Y(5)+AN6*Y(6)+AN7*Y(7)+AN8*Y(8) D(I)=AG(I)-GN(I) WRITE (4,*) A(I),B(I),GN(I),D(I) 100 CONTINUE WRITE (*,*)‘GIVE THE FILE NAME FOR STORING GRAVITY VALUES’ WRITE (11,*)‘VALUES FOR X,Y AND THE MEASURED GRAVITY VALUES’ DO 101 I=1,N 101 WRITE (11,*)A(I),B(I),AG(I) WRITE (*,*)‘GIVE FILE NAME FOR STORING REGIONAL GRAVITY VALUES’ WRITE (12,*)‘VALUES FOR X,Y AND THE CALCULATED REGIONAL VALUES’ DO 102 I=1,N 102 WRITE (12,*)A(I),B(I),GN(I) WRITE (*,*)‘GIVE FILE NAME FOR STORING RESIDUAL GRAVITY VALUES’ WRITE (13,*)‘VALUES FOR X,Y AND THE RESIDUAL VALUES’ DO 103 I=1,N 103 WRITE (13,*)A(I),B(I),D(I) SUMAG2=0.0 SUMDAG=0.0 SUMGNAG=0.0 SUMAG=0.0 SUMDGN=0.0 Appendix I 261
SUMD2=0.0 SUMGN2=0.0 SUMD=0.0 SUMGN=0.0 DO 110 I=1,N SUMAG2=SUMAG2+AG(I)*AG(I) SUMDAG=SUMDAG+D(I)*AG(I) SUMGNAG=SUMGNAG+GN(I)*AG(I) SUMAG=SUMAG+AG(I) SUMDGN=SUMDGN+D(I)*GN(I) SUMD2=SUMD2+D(I)*D(I) SUMGN2=SUMGN2+GN(I)*GN(I) SUMD=SUMD+D(I) SUMGN=SUMGN+GN(I) 110 CONTINUE NR1=SUMGNAG-(SUMAG*SUMGN/N) DR1=(SUMGN2-(SUMGN*SUMGN/N))*(SUMAG2-(SUMAG*SUMAG/ N)) DR1=SQRT(DR1) R1=NR1/DR1 NR2=SUMDAG-(SUMD*SUMAG/N) DR2=(SUMD2-(SUMD*SUMD/N))*(SUMAG2-(SUMAG*SUMAG/N)) DR2=SQRT(DR2) R2=NR2/DR2 NR3=SUMDGN-(SUMD*SUMGN/N) DR3=(SUMD2-(SUMD*SUMD/N))*(SUMGN2-(SUMGN*SUMGN/N)) DR3=SQRT(DR3) R3=NR3/DR3 WRITE (*,*) ‘R BET. BOU-REG,BOU-RES, REG-RES=’ WRITE (*,*)R1,R2,R3 WRITE (4,*)‘R BET. BOU-REG,BOU-RES,REG-RES’ WRITE (4,*)R1,R2,R3 WRITE (4,*)‘VALUES OF BOUGUER REGIONAL RESIDUAL’ DO 111 I=1,N 111 WRITE (4,*)AG(I),GN(I),D(I) STOP END 262 Bouguer Gravity Regional and Residual Separation
Appendix II C++ Program for Regional-Residual Separation by Finite Element Method
/* C++ Program for separation of regional and residual using FEM method */ /* Program needs Gravity values in addition to A[i] & B[i] values */
#include
/* Opening the file for reading */
262 AppendixAppendix III 263
fin.open(“f1-8.DAT”); if(!fin) { cout<<“\n Cannot Open File!!!!”; }
/* Creating output files A1,A2,A3,A4 */
fout.open(“8A1.DAT”); if(!fout) { cout<<“\n Cannot open [A1.DAT] File!!!!”; }
fout1.open(“8A2.DAT”); if(!fout1) { cout<<“\n Cannot open [A2.DAT] File!!!!”; }
fout2.open(“8A3.DAT”); if(!fout2) { cout<<“\n Cannot open [A3.DAT] File!!!!”; }
fout3.open(“8A4.DAT”); if(!fout3) { cout<<“\n Cannot open [A4.DAT] File!!!!”; }
fin>>N>>NN; cout<<“\n GIVE OUTPUT DATA FILE NAME AS UNIT 4”; fout<<“ NO OF NODES {A[i] & B[i]} AND DATA (8 OR 12) POINTS”; fout< for(i=0;i fout<<“\n INPUT VALUES OF A[i] AND B[i] and AG[i]”; for(i=0;i { fin>>A[i]>>B[i]>>AG[i]; fout<<“\n”< fout<<“\n OUTPUT X,Y, REGIONAL GRAVITY AND RESIDUAL VALUES”; /* Calculating Zeeta , Eeta Coefficients */ for(i=0;i T1=AN1*G[0]+AN2*G[1]+AN3*G[2]+AN4*G[3]; GN[i]=T1+AN5*G[4]+AN6*G[5]+AN7*G[6]+AN8*G[7]; T2=AN1*X[0]+AN2*X[1]+AN3*X[2]+AN4*X[3]; A[i]=T2+AN5*X[4]+AN6*X[5]+AN7*X[6]+AN8*X[7]; T3=AN1*Y[0]+AN2*Y[1]+AN3*Y[2]+AN4*Y[3]; B[i]=T3+AN5*Y[4]+AN6*Y[5]+AN7*Y[6]+AN8*Y[7]; D[i]=AG[i]-GN[i]; // Calculating Residual values fout<<“\n”< cout<<“\n GIVE THE FILE NAME FOR STORING GRAVITY VALUES”; fout1<<“\n VALUES FOR X,Y AND MEASURED GRAVITY VALUES”; for(i=0;i cout<<“\n GIVE FILE NAME FOR STORING REGIONAL GRAVITY VALUES”; fout2<<“\n VALUES FOR X,Y AND CALCULATED REGIONAL VALUES”; for(i=0;i cout<<“\n GIVE FILE NAME FOR STORING RESIDUAL GRAVITY VALUES”; fout3<<“\n VALUES FOR X,Y AND RESIDUAL VALUES”; for(i=0;i /* Calculating the correlation coefficients */ SUMAG2=0.0; SUMDAG=0.0; SUMGNAG=0.0; SUMAG=0.0; SUMDGN=0.0; SUMD2=0.0; SUMGN2=0.0; SUMD=0.0; SUMGN=0.0; for(i=0;i NR1=SUMGNAG-(SUMAG*SUMGN/N); DR1=(SUMGN2-(SUMGN*SUMGN/N))*(SUMAG2-(SUMAG*SUMAG/ 266 Bouguer Gravity Regional and Residual Separation N)); DR1=sqrt(DR1); R1=NR1/DR1; NR2=SUMDAG-(SUMD*SUMAG/N); DR2=(SUMD2-(SUMD*SUMD/N))*(SUMAG2-(SUMAG*SUMAG/N)); DR2=sqrt(DR2); R2=NR2/DR2; NR3=SUMDGN-(SUMD*SUMGN/N); DR3=(SUMD2-(SUMD*SUMD/N))*(SUMGN2-(SUMGN*SUMGN/N)); DR3=sqrt(DR3); R3=NR3/DR3; cout<<“\n”<<“ R BET, BOU-REG, BOU-RES, REG-RES”; cout<<“\n”< for(i=0;i<=N;i++) { fout<<“\n”< cout<<“\n PROGRAM TERMINATED”; getch(); fin.close(); fout.close(); fout1.close(); fout2.close(); fout3.close(); } /* end function gcalc*/ void main() { clrscr(); gravity gr; /* Creating Object of the class gravity */ gr.gcalc(); /* Calling the Calc function of the class gravity */ } /* end main */ References 267 References Abdoh, A., Cowan, D. and Pilkington, M., 1990. 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Index 85 degrees East 156 Nagapatnam depression 143 90 degrees East 156 Offshore magnetic anomaly 143, 151 Accuracy 24 Palk Bay 143 Nevada Batholith 26 Pondicherry 2001 earthquake 144, Synthetic model 24 147, 153 Agra-Shahjahanpur ridge 136 Pondicherry basin 141 Airborne gravity 69 River piracy 143 Analytical methods 13 Sub-canyon structure 153 Aravali 140 Tanjavur depression 143 Tirucherapalli Basin 151 Bafi river 72 Traquebar depression 143 Bandpass filter 37 Chambal river 139, 141 Barringer impact crater 234 Chamoli 200 Bhima river 71 Chelima 71, 73 Botuobiya Kimberlite Field 73 Chigicherla kimberlites 85 Bouguer correction 5, 7, 167 Chocolate mountain range region 8, 69 Bouguer gravity anomaly 6, 9 Chromite 69, 110, 118 Bundelkhand Massif 136 Clairaut 2 Congo river 72 California 168 Contact metamorphism 68 Camaugue province, Cuba 111 Cascade Range 167, 168, 169, 171, 173, Coordinate transformation 24 182 Correction to gravity data 4 Cauvery Basin 141, 150 Craton 68 Bathymetry 145 Aravali-Bundelkhand 71 Circular feature 145 Bastar 71 Fault pattern 143, 144, 145 Dharwar 71 Geology 142 Heat flow 85 Gravity studies 147 Singbhum 71 Gulf of Mannar 143 Crustal movement in Himalaya 196 Kumbakonam ridge 143, 154 Indo-Nepal levelling line 197 Madanam ridge 143 Pathankot-Dalhousie levelling Marine magnetic map 152 line 196 Marine magnetic regional anomaly Saharanpur-Dehradun-Mussorie map 153 line 197 Marine magnetic residual map 155 Crustal movement in Swiss Alps 188 285 286 Index Cuba 69 Greenstone belt 76 Cuddapah Basin 8, 10, 69, 74, 77, 82, 98 Greneville province 234 Diamond field 96 Griffin’s method 30, 76 Kimberlite pipe 109 Gulbarga 86 Guntakal 80 Dahuki fault 219, 222 Deep drilling in Ganga Basin 135 Hazra Thrust (HT) 204, 212 Deep Seismic Sounding (DSS) 37 Hayford anomalies of Shillong Delhi-Aravali range 136 Plateau 220 Delhi-Haridwar ridge 141 Dharwar orogeny 83 Indian plate 133 Diamond 70 Indo-Burma Syntax 133 Great Moghul 73 Indo-Nepal region 8, 134 Kohinoor 73 Indravati river 71 Orloff 73 Inner Moray Firth Basin 7, 41 Pitt 73 Bouguer gravity map 43 Regent 73 FEA regional gravity map 44 Drawbacks in regional computation 16 FEA residual map 45 Drift correction 5 Great Glen fault 42 Helmsdate fault 42 Earthquakes in Himalaya 206 Model-based residual map 44 Focal depth-Magnitude plot 207 Old Red Sandstone (ORS) 42, 43, 45 Eastern Ghats Mobile Belt 85, 94 Wick fault 42 Elevation correction 5 International reference ellipsoid 2 Isostasy 160 Finite Element Analysis 19 Airy-Heiskanen model 162, 164, 166, Computation procedures 28 171 Isoparametric elements 21 Archimedes Principle 161 Types of elements 20 Pratt-Hayford model 164, 166, 172 Free-air correction 5, 7, 167 Buoyancy force 165 Frequency domain 15 Vening-Meinsz model 166 Isostatic correction 6, 7, 168 Gani-Kalwa fault 85 George Everest 161 Jacobian matrix 117 Golconda 73 Gold mineralization 69 Kaladgi-Badami Basin 7 Gondwanaland 48 Basement geometry 67 Gorda Plate 8, 167, 171, 175 Bouguer gravity map 64 Gradiometry 69 Karakoram Thrust (KT) 204, 212 Graphical method 12 Kasai river 72 Grants method 30 Klamath mountains 167, 168, 169, 171, Gravimeter 1, 4 173, 182 Gravity gradient 1, 2, 3, 69 Kangra 191, 196, 199, 200 Gravity method 1, 2 Kathmandu 199, 217 Gravity studies over Narayanpet Kimberlite 68 Kimberlite Field 82 Kimberlite pipes 69, 82, 83 Great Boundary Fault (GBF) 137 Kimberly 70 Green’s equivalent layer 37 Krishna-Godavari (K-G) Basin 44 Index 287 Krishna river gravels 71, 73 Muzaffarabad 2005 earthquake 203, 205, 208 Lagrange polynomial 22 Aftershock patterns 216 Lambert rift 48 FEA residual and isoseismal lines 214 Lamproite 73 Resistivity variation 209 Banganapalle 73 Chelima 73 Nagasamudram granite 76, 79, 80 Ramannapet 73 Narayanpet-Maddur region 69, 73 Lamprophyres 70 Nepal Himalaya 215 Latitude correction 6 Earthquake epicenters 217 Lattavaram 75, 76, 82 FEA residual anomalies 217 Lena river 72 Vertical movements 217 Lesser Himalayas 190, 192 Nettleton’s method 30 Bouguer gravity anomalies 193 Nevada test site 225 FEA residual map 196 North Sea oil and gas 41 Main Boundary Thrust (MBT) 191, Northwest Ganga Basin 8, 134 194, 217 Bouguer gravity map 137 Main Central Thrust (MCT) 191, 194, Deep drilling 136 217 Regional gravity map 138 Regional anomaly map 195 Residual gravity map 139 Vertical crustal movement 197 Northwest Himalaya 203 Liquefaction zone 156 Bouguer gravity map 210 Slump belt 159 Bouguer residual map 213 Maddur-Kotakonda region 87 Orla-Delware Basin, Texas 7 Mahanadi Basin 7, 48 Basic body 57 Pacific Plate 68 3D view 57, 58 Pahute Mesa 8, 203, 225 FEA residual map 54 Panna 71 Oil India boreholes 51 Paradox Basin 7, 36 Mahanadi river 71 Bouguer gravity map 37 Ong river 71 FEA regional gravity map 38 Ib river 71 FEA residual gravity map 40 Maini river 71 Spectral regional gravity map 38 Mand river 71 Spectral residual gravity map 39 Manicougan crater 234 Penakacherla greenstone 76, 80 Basement geometry 245 Peninsular Gneissic Complex (PGC) 72, Regional gravity map 239 75, 82 Residual gravity map 240 Penner river 79 Main Mantle Thrust (MMT) 204, 212 Perry-Cratonic basins 48 Marine gravity 69 Polynomial fitting 16 Marine magnetics 69 Project Vasundhara (GSI) 84 Mesquite Gold Mine 8, 118 Proterozoic 70 Migmatite 75 Putnam anomaly 160, 182 Mississippi delta 47 Moon craters 233 Radial faults 76 Mt. Shasta 171, 173 Reference element 22 288 Index Shape (basis, weighting) functions 22, Space-domain operator 175 23, 175 Stratigraphic control 68 Resistivity variation during Structure control 68 earthquake 269 Sudbury Crater 234, 248 Rhein graben 47 Sukinda chromite 69 Rock density in Narayanpet Kimberlite Sulphur deposit in West Texas 126 Field 91 Swiss Alps 167, 183 FEA residual anomaly 187 Satellite microgravity 133 Isostatic anomalies 184 Schist belt 72 Seismic activities 189, 190 Kola-Kadiri-Raichur 72 Variation in crustal thickness 186 Nellore 72, 83, 84 Vertical movements 185, 190 Ramagiri-Penakacherla 72 Tsundapalli-Peddavuru 72 Topographic correction 5 Veligallu-Narayanpet 72 Torsion balance 1 Sedimentary basins in India 47 Tungabhadra lineament 85 Sewa river 72 Tungabhadra river 71 Shillong 1897 earthquake 203, 219 Epicenter 223 Venkatapalle kimberlite pipe 79 Iso-seismal line 224 Vertical crustal movement 160, 181, 182 Shillong plateau 133 Vilyui river 72 Sierra Nevada Batholith 167, 171, 177, Vindhayan Basin 136 178, 179, 181 FEA residual map 180 Vindhayan Plateau 71 Isostatic residual gravity map 180 Uttarkashi 200, 201 Seismic refraction studies 177 Silent Canyon 228 Wajra-Karur Kimberlite Field (WKF) 69, Siwalik formation 136 71, 72, 74 South Africa 72 Western Himalaya 8 Vaal river 72 Riet river 72 Yamuna river 139 Orange river 72