%PDF-1.3 % 1 0 obj [ ] endobj 2 0 obj << /Length 8124 >> stream 0 0 0 rg 0 0 0 RG q 1 0 0 1 0 0 cm 576 0 0 792 0 0 cm /background_1 Do Q BT 0 0 0 rg 0 0 0 RG 1 0 0 1 121 734 Tm 99 Tz 3 Tr /OPBaseFont0 14 Tf (ON 3D NONLINEAR) Tj 1 0 0 1 255 734 Tm 96 Tz /OPBaseFont1 14 Tf (ELECTROMAGNETIC INVERSE) Tj 1 0 0 1 50 733 Tm 103 Tz /OPBaseFont1 20 Tf (F008) Tj 1 0 0 1 122 718 Tm 87 Tz /OPBaseFont0 14 Tf (PROBLE) Tj 1 0 0 1 174 718 Tm 94 Tz (M) Tj 1 0 0 1 67 612 Tm 110 Tz /OPBaseFont2 11 Tf (Electromagnetic methode are) Tj 1 0 0 1 213 611 Tm 106 Tz (. now widely used in geophysicai=proepecting) Tj 1 0 0 1 432 611 Tm 109 Tz (.) Tj 1 0 0 1 50 598 Tm 112 Tz (The interpretation of data obtained bythese methode) Tj 1 0 0 1 310 598 Tm 102 Tz (. involves coneiderable dif-) Tj 1 0 0 1 50 585 Tm 111 Tz (ficulties becanse in a general case the inverse problem is reduce to an operator) Tj 1 0 0 1 50 571 Tm 113 Tz (equation of the first kind witti implicitly atipulated) Tj 1 0 0 1 310 571 Tm 108 Tz (.operator) Tj 1 0 0 1 353 571 Tm 119 Tz (. The nnmerical) Tj 1 0 0 1 50 557 Tm 109 Tz (solntion of such equations requires coneiderable expenditures of computertime) Tj 1 0 0 1 433 557 Tm 72 Tz (.) Tj 1 0 0 1 50 544 Tm 110 Tz (We have obtained the new inverse problem) Tj 1 0 0 1 263 544 Tm 106 Tz (. egnations of electromagnetic Relde) Tj 1 0 0 1 50 530 Tm 109 Tz (which satisfy the telegrapher's, difnsion and Helmholtz equationa) Tj 1 0 0 1 372 530 Tm 111 Tz (. We've used) Tj 1 0 0 1 50 516 Tm 108 Tz (representations of field functions throngh the valnes of the functions themeelves) Tj 1 0 0 1 50 503 Tm 113 Tz (and the derivatives at the bonndary of the anomaly-forming object There) Tj 1 0 0 1 420 502 Tm 101 Tz (.sre) Tj 1 0 0 1 50 489 Tm 112 Tz (the first generation equations with explicit operators) Tj 1 0 0 1 311 489 Tm 110 Tz (.The primary field) Tj 1 0 0 1 403 488 Tm 36 Tz /OPBaseFont3 11 Tf (.) Tj 1 0 0 1 406 488 Tm 102 Tz /OPBaseFont2 11 Tf (sourse) Tj 1 0 0 1 50 476 Tm 120 Tz (can be arbitrary type) Tj 1 0 0 1 160 475 Tm 114 Tz (. Uniqueness of representation is shown) Tj 1 0 0 1 362 475 Tm 126 Tz (. The method) Tj 1 0 0 1 50 462 Tm 112 Tz (for solving of 3-D nonlineaz electromagnetic inverse problem was diviced \(in) Tj 1 0 0 1 51 449 Tm 109 Tz (the cases potential and monochromatic fields\)) Tj 1 0 0 1 275 448 Tm 116 Tz (. It's based on the algorithm for) Tj 1 0 0 1 50 435 Tm 109 Tz (solving explicit equations of the 3-D inverse problem) Tj 1 0 0 1 309 435 Tm 114 Tz (. We apply the Tikhonov) Tj 1 0 0 1 50 421 Tm 113 Tz (regnlarization method to) Tj 1 0 0 1 177 421 Tm 86 Tz /OPBaseFont3 11 Tf (3-) Tj 1 0 0 1 186 421 Tm 106 Tz /OPBaseFont2 11 Tf (D EMD inveraion) Tj 1 0 0 1 272 421 Tm 114 Tz (. As a result of interpretation we) Tj 1 0 0 1 50 408 Tm 108 Tz (obtain the bodies stellate relative to some point with different valnes of conduc-) Tj 1 0 0 1 50 394 Tm 109 Tz (tivity which generated the same \(electrical or magnetic\) field) Tj 1 0 0 1 346 394 Tm 115 Tz (. We) Tj 1 0 0 1 373 394 Tm 108 Tz /OPBaseFont3 11 Tf (have) Tj 1 0 0 1 400 394 Tm 111 Tz /OPBaseFont2 11 Tf (stadied) Tj 1 0 0 1 50 381 Tm 106 Tz (the possibilities for nniquenesa solution seeking on the) Tj 1 0 0 1 311 381 Tm 109 Tz (:based joint interpretation) Tj 1 0 0 1 50 367 Tm 110 Tz (of diffrent EMD) Tj 1 0 0 1 131 367 Tm 112 Tz (. We have lome examples with good results of interpretation) Tj 1 0 0 1 433 367 Tm 72 Tz (.) Tj 1 0 0 1 50 353 Tm 108 Tz (Thus, we have snch inverse problem equation for monohromatic field \(electrical) Tj 1 0 0 1 50 340 Tm 113 Tz (- E\(r\) and magnetic - H\(r\)\)) Tj 1 0 0 1 186 340 Tm 109 Tz (. We have obtained) Tj 1 0 0 1 281 340 Tm 36 Tz (.) Tj 1 0 0 1 383 689 Tm 75 Tz /OPBaseFont1 8 Tf (P) Tj 1 0 0 1 388 689 Tm 79 Tz (.S) Tj 1 0 0 1 396 689 Tm 100 Tz (. MARTYSHKO and A) Tj 1 0 0 1 477 689 Tm 89 Tz (.L) Tj 1 0 0 1 484 689 Tm 95 Tz (. RUBLEV) Tj 1 0 0 1 232 679 Tm 106 Tz /OPBaseFont4 8 Tf (lnstitute of Geophysics, Amundsen Street 100, 620016 Ekaterinburg, Russi) Tj 1 0 0 1 515 678 Tm 90 Tz (a) Tj 1 0 0 1 50 299 Tm 120 Tz /OPBaseFont2 11 Tf (Ei \(ri\) =) Tj 1 0 0 1 97 289 Tm 74 Tz /OPBaseFont5 24 Tf (J) Tj 1 0 0 1 110 299 Tm 98 Tz /OPBaseFont5 11 Tf ({\() Tj 1 0 0 1 120 299 Tm 111 Tz /OPBaseFont6 11 Tf (n,E1\)grad\(G3-G1) Tj 1 0 0 1 215 299 Tm 115 Tz /OPBaseFont3 11 Tf (\)+\(n) Tj 1 0 0 1 239 299 Tm 109 Tz /OPBaseFont2 11 Tf (,) Tj 1 0 0 1 244 299 Tm 108 Tz /OPBaseFont3 11 Tf (ES\)gradG2+iw[n x H) Tj 1 0 0 1 354 299 Tm 109 Tz (1) Tj 1 0 0 1 94 264 Tm 114 Tz (+ '2[n x H8]G2 + [n x) Tj 1 0 0 1 213 264 Tm 98 Tz /OPBaseFont2 11 Tf (E1`]\(v1G1) Tj 1 0 0 1 264 264 Tm 128 Tz /OPBaseFont5 11 Tf (- aiGi\) + [) Tj 1 0 0 1 322 264 Tm 111 Tz /OPBaseFont6 11 Tf (n,ES]o1G) Tj 1 0 0 1 374 264 Tm 105 Tz /OPBaseFont5 11 Tf (}ds) Tj 1 0 0 1 391 264 Tm 264 Tz (. \(1) Tj 1 0 0 1 431 264 Tm 106 Tz (\)) Tj 1 0 0 1 50 216 Tm 100 Tz /OPBaseFont2 11 Tf (HO\(r1) Tj 1 0 0 1 79 216 Tm 106 Tz (\)) Tj 1 0 0 1 66 215 Tm 101 Tz /OPBaseFont6 11 Tf (\(rI) Tj 1 0 0 1 79 215 Tm 135 Tz /OPBaseFont5 11 Tf (\) = f {\() Tj 1 0 0 1 121 216 Tm 123 Tz /OPBaseFont6 11 Tf (n,Hi\)grad) Tj 1 0 0 1 178 216 Tm 137 Tz /OPBaseFont5 11 Tf (\(lGz-G1\)+ l) Tj 1 0 0 1 260 216 Tm 80 Tz /OPBaseFont2 11 Tf (\() Tj 1 0 0 1 264 216 Tm 111 Tz /OPBaseFont3 11 Tf (n,HS\)gradG2+) Tj 1 0 0 1 343 216 Tm 81 Tz /OPBaseFont2 11 Tf ([) Tj 1 0 0 1 346 216 Tm 112 Tz /OPBaseFont3 11 Tf (n,HI']) Tj 1 0 0 1 380 216 Tm 105 Tz /OPBaseFont6 11 Tf (xgrad\(G3) Tj 1 0 0 1 430 215 Tm 160 Tz (-) Tj 1 0 0 1 105 206 Tm 515 Tz /OPBaseFont2 11 Tf (s A2 9) Tj 1 0 0 1 253 206 Tm 72 Tz (2) Tj 1 0 0 1 63 181 Tm 115 Tz (- G1\) + [n, HS]) Tj 1 0 0 1 146 181 Tm 112 Tz /OPBaseFont5 11 Tf (x gradG2 + [n) Tj 1 0 0 1 220 181 Tm 115 Tz /OPBaseFont2 11 Tf (x E1]\(ozG2 - vi Gl\) +) Tj 1 0 0 1 335 181 Tm 111 Tz /OPBaseFont5 11 Tf ([n, ES]c2G}ds) Tj 1 0 0 1 408 181 Tm 72 Tz (.) Tj 1 0 0 1 419 180 Tm 100 Tz /OPBaseFont2 11 Tf (.\(2) Tj 1 0 0 1 432 180 Tm 80 Tz (\)) Tj 1 0 0 1 50 156 Tm 107 Tz (where v-condactivity p^permeability, s-permittivity,) Tj 1 0 0 1 301 155 Tm 140 Tz /OPBaseFont3 11 Tf (i = \() Tj 1 0 0 1 329 155 Tm 178 Tz (;i - s\)) Tj 1 0 0 1 376 155 Tm 111 Tz /OPBaseFont6 11 Tf (divs[n,) Tj 1 0 0 1 413 155 Tm 106 Tz /OPBaseFont3 11 Tf (H1]) Tj 1 0 0 1 434 155 Tm 72 Tz (,) Tj 1 0 0 1 49 138 Tm 109 Tz /OPBaseFont2 11 Tf (since \() Tj 1 0 0 1 81 138 Tm 128 Tz /OPBaseFont3 11 Tf (n, EDS\) _ --) Tj 1 0 0 1 153 138 Tm 104 Tz /OPBaseFont6 11 Tf (divs[n) Tj 1 0 0 1 188 138 Tm 136 Tz /OPBaseFont2 11 Tf (x N) Tj 1 0 0 1 211 138 Tm 110 Tz (. The algorithm for solving equations \(1\) - \(2\)) Tj 1 0 0 1 49 124 Tm 109 Tz (in the clase of atellate bodies was developed) Tj 1 0 0 1 268 124 Tm 112 Tz (. The right-hand aide of the egna-) Tj 1 0 0 1 50 111 Tm 109 Tz (tion of the surface S can be represented by a double Foerier series in such case) Tj 1 0 0 1 433 111 Tm 36 Tz (.) Tj 1 0 0 1 50 97 Tm 111 Tz (Hence we aeek the TIP solution) Tj 1 0 0 1 212 97 Tm 91 Tz /OPBaseFont3 11 Tf (as) Tj 1 0 0 1 226 97 Tm 60 Tz /OPBaseFont2 11 Tf (a) Tj 1 0 0 1 229 97 Tm 72 Tz (.) Tj 1 0 0 1 235 97 Tm 103 Tz /OPBaseFont3 11 Tf (segment) Tj 1 0 0 1 279 97 Tm 108 Tz /OPBaseFont2 11 Tf (of the double Foerier, series \(we) Tj 1 0 0 1 49 84 Tm 111 Tz (must determin twenty five coefi) Tj 1 0 0 1 207 84 Tm 98 Tz /OPBaseFont3 11 Tf (icienta) Tj 1 0 0 1 239 84 Tm 80 Tz /OPBaseFont2 11 Tf (\)) Tj 1 0 0 1 243 83 Tm 115 Tz (. There are some theoretical) Tj 1 0 0 1 391 83 Tm 98 Tz /OPBaseFont3 11 Tf (examplea) Tj 1 0 0 1 50 69 Tm 121 Tz /OPBaseFont5 11 Tf (\(i = s\)) Tj 1 0 0 1 97 70 Tm 72 Tz (.) 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