Cnl1CAHI1E HA B'bJlfAPCKOTO fEOJ10fW1ECKO .UPY)I(l!C'l'BO, ro)l. XLII, KH. 2, 1981 REVIEW OF THE BULGARIAN GEOLOGICAL SOCIETY, vol. XLII, part 2, 1981

·nporpaMH 33 e~HOMepeH aHaJIH3 . Ha eMnHpH4HI1

reOJIO}I{KH ~3HHI1

E ecmamu HeaHttee

HayttHOU3CAeaoeameAcKu uHcmumym no noAe3HU usKonae,!lu, 1505 Cot/Jtt!!

E . Iuancheu- Programs for One-Dimensional Analysis of Empirical Geologic Data. The paper presents programs for analysis of one-dimensional empirical distributions. Their practical application is illustrated by parts of analysed data from the engineering-geological studies in the Dobrudza coal basin (DCB).

The initial treatment of input data is described - determination of quantitative characteristics, choice of qualitative parameters and their coding. The DCB data are record­ed on magnetic tape. On the basis of the qualitative feature "lithology" samples are com­piled. The empiric distribution of volume weight , pore volume, compression and tension strength and the cohesion of limestones and dolomites are analysed. Hystograms and cum­mutative curves are obtained, the elementary statistics are computed, the optimum boun· daries of the parameters and the statistics within these boundaries are determined. The equa· tions of the distribution curves of all studied parameters are derived.

It is established that the limestones and dolomites from DCB are of intermediate strenght, the dolomites having higher physicomechanical properties. The theoretical dis­tribution curves of all parameters considerably deviate from the normal curve.

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rp~HHUH .ce- H3q-H_cJJHBaT M~TeMa:;~wma~a Ha.n.em.n.a Xt, cTaH.n.apThT· 6t H ~ce ()'f'IJ~~' qaTBaT (Ta6JJ . 3). · . .. .. . . . .

2. I1scJJe)l.Ba Ce 33BHCHMOCTTa Ha H3MeHeHHeTO Ha CTaH)l.apTa . 9T rp11HHq-: HHTe sepoHTHOCTH (qmr. 5). MaKCHMaJIHO pe3KHTe cna.n.ose B a1 onpe.n.eJIHT . ~d~. HaTa Me2I<)l.y )l.Be HJJH noseqe nocJie)l.OBaTeJJHH npecHqaHHH Ha eMnHpHtiHOTO. pa3~, npe.n.eJJeHHe, B KOHTO nona.n.a rpaHHUaTa Ha yparaHHHTe npo'6H. - ~ ..

3. Hssnprusa ce onTHMHsaumi BbTpe B TaKa oqepTaH.aTa soHa o'I'.n.eJiHo 'sa: Hal\mpaHe H3 JIHBaTa H )l.5ICHaTa OnTHMaJIHa rpaHHUa x;in H X~ax Ra H3CJie)l.B37. HHH napaMeThp (cjmr. 4) . BnTpe B Te3H rpaHHUJ:I ce J13qH9JifiBSIT MaTeM~;fH1J:.H3T~

200

Ha.n.e>K.n.a X"', craH.n.apT'hT o* H Koe<jlHUHeH'f.'hT Ha B;i_pHaUJUI V*. Tipouec'hT Ha OnTHMH3aUJUI:~ MoiKe ll,<i C~ npocJieii.H no or·neqaTaHaTa Ta6JI . 4.

H Hmepnpemal{Uf/. Ha pe3yilmamume om' eih-wMepHuf/. cmamucmuttecKu aHa­/I.U3 Ha e.MnujJUttH.if:.f!l~ p_a3_npeoeAeHUf/.. B .. T~~JI. 5 .. ~~ )I.a.ll.~!.HLP.~~YJITaTJ1Te OT 06-

.G

22 .. ~89 21. 771

7.1.263

2CU 55 .. .

r 7.0 . 2!·6

19. 738

19 .229 .

18. 721

18.l13

17 .:704. . .

(;)"· 0 ? c-.. 0 .......

~ ~ .. 8·.

<l>l!i'. 5.: 3aaHcHMQCT oi=f(PrP) ~a R.L"aa aapoB!IUH OT .l{o6pyll.>K8H· CK-HH B'l>rJIH!l(eH 6ace1\lf { · O -

pa(OTKHTe, Ha_~:?p!:IJe~iH .. B C'bOTBeTCTBHe .c .. !~~-HOJ19.rHtiHa'I'a ,C::XeM~. ·,flO-C'blll,eCTBe• HHTe H3BO.ll.H.r: KOHTO MOraT .n.a Ce HanpaB.HT, Ca CJie.ll.HHTe: ..

1. ·C)nocraB~HTe Mem.n.y X0, M; H MJ sa BCH':IKH napaMerpH roBop .srr 3a

acuMerp~plfOC.-'1' ·Ira pasnpe.n.e.neHu.srTa, ·<5co6eHo cwrBo .HspaseHa sa o6eMa aa nopH:re. · ·

2. PascefmaHero Ha .n.aHHHTe oKoJio XO e Hali-cJia6o sa o6eMHOTO rerJio H HaH-CHJIHO Sa o6eMa Ha I)OpHTe. 5IKOCTHH'I'e xapaKTepHCTHKH Ha BapoBHUHTe H .IJ.OJIOMHTHTe HMaT DO"!ITH e.n.HaK'bB CTaH.n.apT. PaSJIHKHTe B'bB V Ce .IJ.bJI.>KaT Ha pasJilfliHHTa .. . B .. .. X0 • . ·- . . .

3. EJIH!'1.tiHHpaHero Ha Jif!BOeKcrpeMaJIHHTe H JI.HCHpeKcrpeM"aJIHHTe c:roli­HOCTH no.n.o6p.srBa:-xoMrraKtHocr:ra 'Ha .n.aHHH,re. Hali:·srp&o 'nspaseHo e BJIHSIHHero Ha ypara HH_'!'.I:~.-I].P~6.~.-BO.P~Y . x a p·a ~:r~P.!'!<:!H_!~_Hre_ -~? ... ~MI1!1PH':I.I:i.OT9 pasnpe.n.eJie­HHe Ha nopHCTOCTTa Ha .ll.OJIOMHTI-I'~e. 0TXBbpJI51HeTO CaMO Ha e.n.Ha: .ll.SICHOeKCTpe­M3JIHa CTOHJiOCT )IaMaJISI~a Koe<jlHii.HeH"I:a Ha BapHaU.HSI OT 70,·15% Ha 44,35 %.

4. 06Ul,aTa·TeH.zteHI.I;HSI Ha H3MeHeHHeTO·Ha X° C;1Ie.IJ. OTXBbpJISiH~TO Ha eKcrpe­M3JIHHTe 3HatreHJ{~ .. e .K'bM HaMaJieHHe. J1S~JI!QtreHHe npaBH, KOXe3HSIT3 Ha JI.OJIO·

MHTHTe. 5. Cpe.n.Horo o6eMHo :rerJIQ Ha .n.oJIOMHTHTe e no-roJI.srMo or rosa Ha BapoBH­

UHTe C 5,8% H fOBOpH 3a cpe.n.HaTa s.n.paBHHa Ha CKaJIHTe (.IT 0 M T a .11. S e, 1970) . 6. Tiop.HcrocTXa . Ha .n.oJIOMHTHTe. e. no-HHCKa . c 11,1%. TosH . noKasareJI

C'blll,O KOCBeHO .CB.H.IJ.eTMCTByBa Sa cpe.n.f!aTa 3.IJ.paBHHa Ha CKaJIHTe" (C e p f e e B H .n.p., 1973k ..

to.:) 0 t-;)

T:t6nuna 5

Pe3yAmamu om eiJHo.MepftuR aHa.AU3 Ha e.Mnupu~tnume pa3npeiJeAeHUF: Ha u~cAeiJsanume napaMempu -.--~-.-------.. ------,,,--------.--------.. --------.. --------.--------

~ :i ~ - I ' CKua I m.lx!ta X max Xi

n .. oeKC• .U•tHOtKC•

ITI)eM8ABH T p e MAJIHM

• lt{J . Mo v'l ' o., .: I . e I. : 0 I . ,'I• 6p. j '1. 6p. I %

. I .

X• a• ~

v% x* min xm:~

r3 .. IBapoBHUH 79 ~I 2,70 2,431~ :·2,49 ': 2,63 ~;~111_.!.:_ ~ o.o I 2,41 0,19 I 7,95 1,83 2,70

. AOnOMHTM 65 . ~ ,61 2,75 2,57 0,16 , 2,59 · : 2,67 ~~07 2 3,1 0 0,0 2,51 0,11 4,43 2,37 2,75 • I I 0 ' ' ' ' ' • • ' • • '

n 5 1aapoaunu 178 ~~~ 46,20 ~~~ :8.42 t ~,72 1 : 4,59 1 75~~1~~~ 0,0 1--=-12.6 1 10,36 I 6,26 I 60,46 I 1,82 1 42,56

· AOJIOMHTH 65 2,20 57,30 9,89 6,94 8,8q . 6,14 7(};15 0 0,0 1 1,5 9,21 4,08 44,35 2,2.0 23,38

9 I aapoauuu I 71 I 43,00

R.L H AOnOMIITM I 55 I 49,00

1274,0 1581,60,285,6,516,00 ~27,70 4~·-:~0 11_15,61_:_17,0 I 541,80 I 205,8 I 38,00 I

1441,0 810,10 284, 6j 846,00 ,943,90 :~5.13 1 1,8 3 5,5 780,40 234.0 29,98 ': • !

,76

119,90

159,10

15 181p0BHUH 1621 3,20 I 105,0 140,96 , 21,871 ~4,301 25,01 sa.~o 12 13,21314,81 39,30 I 19,16 I 48.

RJ- AO.IIOMHTH 42 4,40 102.0 58,23 19,59 61,~ 61,33 :~~64 -~- 2.4 - 1- 2,4 56,66 15,80 27,89 I 16,55

c.l.. AOnOMIITH

19 laaposuua I 69 I 0,33 121,64162,68l12o,oo ·140,16 :~\.33 4 5,8 6 8,7 116,13 45.88 39,50

541 7,20 I 287,0 1182,63 63,52 2~.00 1S7,07 :34,'78 S is 4 7.5 201,99 44,81 22,18 ' ' . . : . ~

280,0 20,31

106,66

1041,3

1332.1

86,73

93,61

218,89

267,01

Ta611Hua 6

lle<tam npu aHa.llusa Ha adeKtJamHocmma -Ha nodtJpaHUJI. meope· mu<teH .1tode.11 Ha pa3npede.lleHue Ha Rif- sa Mposuqume om Jlo­tJpydJfCaHCKUJI. 8&MUtqeH. (JacelJH.

HoMep HI EMnHpH'IHA TeopeTH'IHI Pasni(Ka aunpaana qecrora qecroTI

1 7,000 9.629 -2,629 2 14.1-00 12.827 1,173 3 12,000 8,685 3,315 4 4,000 6,958 -2,958 5 8,000 5,887 2,113 6 3,000 5,083 -2,083 7 5,000 4,376 0,624 8 4,000 3,558 0,442

7. 0THOllleHHeTo RuiR0 3a sapoBHU.HTe H .AOJIOMHTHTe e :::::: I4, Ru/C 3a Ba· pOBHU.HTe e 4,7, a 3a ,AOJIOMHTHTe e 4,4.

8. 5JKOCTHHTe xapaKtepHCTHKH Ha )J.OJIOMHTHTe npeBHlllaBaT Te3H Ha Ba· poBHU.HTe 3a R~ c 39,3 %, 3a Rif c 42,2% H 3a C.L c 50, I %.

9. MareMaTHtiHHTe Ha,nem.nw 3a R;, Rd- H C ,AoKa3BaT cpep,Hata 3,npaBHHa

Ha BapOBHU.HTe H P,OJIOMHTHTe OT llo6py,nmaHCKH51 BbfJIHlll.eH 6acefiH. A t-taAus H.a eoH.oMepH.ume meopemwmu pasnpeoeAeHuR. l13BeCTHO e. tie BCH·

Ka cJiytiafiHa aeJIHtiHHa npHremaaa HHKaKBo pa3npe,neJieHHe. H eroBHSIT BH,n H xapaKrep 3aBHCSIT or ecrecrsoro Ha pa3r Jiemp,aHara aeJIUtiHHa. Hafi-tiecro cpe­lll.aHaTa 3a,natia B reOJIOfHSITa e no Cblll.eCTBYBalll.H e_~cnepHMeHTaJIHH ,naHHH 3a cJiytJafiHaTa BMHtiHHa Xt .na ce onpe,AeJIH HeHH_o.1'({" pa3npe,neJieHHe.

TeopeTHtiHHTe pasnpe,neJieHHSI HMaT roJI51Mo 3HatieHHe 3a BHHKBaHe ·B CblU· HOCTTa Ha pa3rJiemp,aHHSI napaMeTbp. KpafiHa u.eJl npH H3CJie,ABaHe Ha pa3npe­p,eJieHHeTo Ha CJiytiaHHaTa BeJIHtiHHa npe,nCTaBJISIBa yctaHOB51BaHeTO Ha ypaBHe· HHeTO Ha Heii:HaTa KpHBa Ha pa3npe,AeJieHHe (M H T p 0 n 0 Jl b C K H ll, 197I) .

E,nHH or Hafi-o61ll.HTe ctaTHCTHtiecKH Mop,eJIH 3a anpoKCHMaUHH Iia eMnH· pHtiHH -pag-n_pg,neJietiH51 Ha ep,Ha cJiytJai1Ha BeJIHtJHHa e Mo,neJibT Ha MapKoB -KoJIMoropoB. To3H Mo,neJI BOAH .no npe,neJIHHTe croxacTHtJHH KpHBH Ha I1 H p • C b H (K e H A a JI 11 C T b 10 a p T, 1966). CHCTeMaTa OT KpHBHTe Ha I111 p C b H o6xBalll.a BCHtJKH Bb3M0)KHH pa3npep,eJieH H51 (M H T p 0 n 0 JI b C K H H, I971) 11 no ta311 npHtiHHa e MHoro no.nxo.nHlll.a 3a Hym,nHre ua reoJiorH HTa. CJiomHOCT­ra Ha npHJIO)l<eHHeTo H ce Cb CToH npep,HMHO B r pyp,oeMKara H3tJHCJIHTeJIHa pa-6ora, HO H3rorBeHata sa ra3H u.eJI nporpaMa {H B a H q e B, _1978) npeMaxaa T83H tpy,nHOCT.

. AHaJIH3bT Ha reopetHtJHOTO pa3npe,neJieHHe Ha H3cJie,nBaHara BeJIHtiHHa ce H3Bbpmaa 3a,nbJimHTeJIHO cJie,n npeMHHaBaHe npes eran 2 Ha aHaJIH3a Ha eMnH· pHtiHOTO pasnpe.neiieHHe. Toaa ce HaJiara nopa.nw o6croHT~lcTBOTO, tie HaJIHtiHeto Aa yparaHHH CTOHHOCTH B H3Ba,nKaTa MO)Ke 3H8tJHTeJIHO p,a npOMeHH H 3aMbfJIH reopetHtJHoro pa3npe,neJieHHe. Ero 3alll.O B nporpaMata PIRCUR sa H3CJieP.BaHe Ha TeopeTHlJHOTO pa3npe,neJieHHe Ce BJIH3a B OllTHMaJIHHTe rp aHHll,H X~ln H X~ax 38 H3CJie,nBaHH51 napaMeTbp. OnepaU.HHTe, KOHTO ce H3BbplllB8T OT Ta3H npo• rpaMa, ca :

I. I1o.npep,emne no roJieMHHa p,aHHH ce npotiHTaT or MJ12. 2. Orneqaraar ce sxo,nHHTe .naHHH 6e3 yparaHHHTe croi1HOCTH. 3. YI3'IHCJI51Bar ce e~mupwmare sec.ronL h.JL .cpe,nHTe Ha HHTepsa.TIH-Te xm,. 4. l13tJHCJI5IB8T ce HatJaJIHJ1Te MQ·MeHTH -.

203

204

,, mh= ..:::::_, xm7 * ft, k= 1, 2, 3, 4.

i=l

5. J.btiHCJU!BaT ce H Ce OTlletiaTBaT UeHTpaJIHHTe MOMeHTH

p

0.5

0.4

0.3

1!1

0.2

0. 1

.--+--- 1·

--' N w t.J s- s- U1 U1 0') :::1 "-l CP a> .... 0 0') N :--'1 ~ !.() U1 :--' N

a> (}'> .,... N 0 <D "" U1 w ~ 0 CP 0 N ·- (}) Cf) 0 N .... 0) a> 0 '"

<l>Hr. o. TeopetHlJHa KpHaa Ha pa3npe.neJJeHHer o Ha RJ. Ha sapoBHUH or Ll,o· 6py,n>KaHCKHJI B'bfJJHIUeH 6 aceHH O

., .·,u8 = m3 ~ 3m1 m'l + 2mt,

ll4 = m4 - ~~3m1 + 6m2mi- 3mi.

6. J13tiHCJI5IBaT ce H Ce OTlletiaTBaT OCHOBHHTe MOMeHTH

rh= :~' h=3, 4.

7. H 3tiHCJI5IBa ce H ce OTlletiaTBa KoeqmuHeHT'hT Ha nHpCbH

r~ (r4 +3)2 ------~ -~---4 (4r4 -3r~) (2r4.-3r~-6)

~. 0

· (11·

Ta6nuua 7

XapaKmepucmUICU Ita meopemu'IHOmo paanpeiJe.lleHue Ha U3C.AeiJeaH.ume ~H:HCeHepf.IOUO.AO:JfCICU napa.Mempu om Jl,otJpyiJ:m:aHCICUJl 81>Z.I!Ul/4eH (JacedH,

X I Tun-~ napa>teT'hp 1 CKana A ' E

- -

3 BllpOBHUH - 9,978 ----:0,039 -0,321 I

------·- ·-

r AOnOMHTH - 0,088 - 0,934 -0.003 . r

5 B3pOBHllH 1,100 0,536 -0,480 I

- -

n )(O.IIOMHTH · 0,802 1,755 0,358 IV

9 BapOBHUH 0,312 - 0,799 - 0,041 I

- -

R~ )(OnOMHTH -0,192 - 0,891 -0,015 I

15 B3pOBHitH 0,621 - 0,818 -0,122 I

--R J. 0

)(OnOMHTH -0,172 - 1,312 - 0,009 I

19 aapOBHUH -0,104 -0,904 - 0,005 I I

C J. )(On OMHTll - 0,291 -1,077 -0,029 I

YpaBHeHae

';; .= ] 788 ( t+~~-r527 ( 1-~~-r0.482 J , 0,557 0,189

. n ·=IO 496 (t+_!"l_ r772 (I-___2_ r·582

. J ' 0,213 0,160

n1= 13,942 1+- L -- ( X ) 0,331 . 6,645

(t-~/-r-439 . 24,244

';; .=I 519 (1+-=:L) - 6,9 e8,823 a rctg ~ J , 8,8462 8,846

-----;; .= u I48 (1 . 2 L r 404 (1-~r098

J · • \ T 249,7 . 679,0

n ·= 10 704 ( 1 ~ r909 ( I- ---=2__ r482 J , + 619,9 335,4

'ii ·= 7 348 ( 1 ---=2__) -0.426 ( 1-___2_ r 139 J ' + 19.819 39,356

11 = 6 153 ( 1 +~L) -o.2o~ ( 1-___2_) - o.alo j , 28,386 23,500

nj=9.574 (I+~r888 (t - ___:2__r469 . . 107,3 . 78,4

~=6.454 (1 + ___2_ r 219 (~-~ )-0.129 . . 78,8 - 56,3

I x•

2,637

3,165

1,781

4,25I

7,202

1,343

2,225

-1,068

3,053

' 5,996

l CTeneHH H8 CB060.A8

1

3

1

I

I

1

1

1

2

1

4 pe3 Hero ce onpe.n.em1 K'hM Kofl nm KpHsa no ITHpC'hH .ce OTHaCll pa3r Jie*.n.~· HOTO pa3npe.n.eJiemle ..

8 . .i13tJHCJIHBaT Ce Koeqmu.HeHTHTe Ha C'bOTBeTHaTa TeopenrliHa KpHBa 11 ce OTnetJaTBa HeHHOTO ypaBHeHHe.

9. l.Jpe3 TaKa llOJiytJeHOTO ypaBHeHHe Ce l13tJHCJIHBaT TeopeTWIHHTe lleCTOTH 3a cpe.n.Hre· Ha lfHTepsaJIHTe · (TaoJI: 6). · · · ··

10. l13tiHCJISIBaT ce H ce oTnettaTBaT Koop.n.HHaTHTe Ha TeopeTHtiHaTa Kp11Ba 3a 6poii TOtiKH l= IOk. .

II. C TaKa H3tJHCJieHHTe Koop.n.HHaTH trpe3 nporparvta GRAPI.R ce H3tiep-rasa TeopetHtiHata kjYmia (cpl!r. 6). ·· · · ·· · · · ·· · ·-

12. l13tJHCJIHBa ce H ce ometJaTBa KpHTepHllT 3a c'brJiaCHe Ha ITupC'hH 7.2 ,

tipe3 KOHTO ce yctaHoBSIBa 6JIH3ocrra Me:>K.n.y eMnHpHtiHHre H TeopeTHtiHHTe tieCTOTH.

13. Onpe.n.eJIHT ce creneHHTe Ha csooo.n.a 3a c'LorserHara Kpwsa 11 ce or­nel!aTBaT. · ·

Pe3yJiraTHTe or aHaJIH3a Ha TeopeTHlJHHTe pa3npe.n.eneHHH 3a pa3rJie:>K.n.a­HHTe HH:>KeHepHOreOJIO:>KKH napaMeTpH (TaO.TJ. · 7) ll03BOJ!l'IB3T .n.a Ce HanpaBHT CJie.ll.HHTe H3BO.U.H: .

I. BcFitiKH H3CJie.n.saHH napaMeTpH HMar reopeTiftJHH KpHBH Ha pa3npe.n.e· JieHHe, KOHTO ce OTJIHtiaBaT 3llalJHTeJIHQ OT Kpl-f~aTa Ha HOpMaJIHOTO pa3npe­.n.eJieHJ-Ie. · ··

2. Koeqmu.HeHT'bT Ha acl-IMeTpfiH A 11a KpHBHTe 3a n r-ia sapoBHU.HTe It .n.o­JIOMHTHTe e HaH-BHCOK - Te HM3T HaH·CHJIHO H3pa3eHa ,Il.HCHa 3CHMeTplf1li-IOCT Ha pa3npe.n.eJieHHero. · . .. .. . . .

3. Jlllsa acHMeTp-H-t:fHocT--·Ha ·· pa3npe.n.eJieFmero ce yctaHOBHBa 3a r u C.L. 4. 5IKOCTHHTe llOK33aTeJIH Ha .ll.OJIOMHTHTe npHTe:>KaBaT JIHBa aCHMe'l'pHH.

BapoBHU.HTe o6atre HMaT KaKro JJHBa acHMeTpl-IH (R ~), TaKa _ 11 .ll.HCHa acHMeT-pHH (C.L). . · . . ·

5. Koecpnu.MeHTbT Ha eKcu.ec E caMe 3a n e noJimrmTeJieH - KpHBHTe ca OCTpOBopXCBFI.

6. OoeMHoro rerJio H SIKOCTHHte nof<:a3aTeJtH rrpKTe:l{(aBat orpfn..r;aTe-JieH eKe· u.ec- KpHBHTe ca llJIOCI<OBbpXOBH.

7. ITotrTH BCHtiKH pa3r Jie:>K.n.aHH napaMeTpH .IJOKa3sar . p<;~3npe.n.eJieHHe or I THn no ITHpcoH, Koero cosna.n.a c ,8-pa3npe.n.eJieHHeTo. l13KJIIOtieHHe npas11 nop!1crocTTa Ha .n.oJIOMHTHTe, KOHTO !1Ma pa3npe.n.eJietme or IV Tlfn..

8. KpHrep!1HTe 33 CbrJiacHe noKa3sar ~moro .n.o6pa anpOKCHMaU.HH aa·· eM­nHpHtiHHTe .n.aHHH 3a BCHtJKH 113CJie.n.saHH napaMeTpH. CJJe.n.osareJI.lro. ooJiytie­HHTe ypaBHeHHH (Ta6JI. 7) MOraT .n.a Ce npHeMaT KaTO 3a.U.OBOJIHTeJIHH CTaTHCTH· tJeCKH Mo.n.eJIH Ha H3C.TJe.n.saH!11'e napaMeTpH.

3aKAIOI.feH.ue. AsroMaTH3aU.HHTa Ha npou.eca Ha cTaTHCTHllecKa o6pa6oTI<a Ha e.n.HOMep-HH· eMHHpHtiHH .ll.aHHH· .n.a-sa· POJieMH Bb3MO:>KHOCTH ·3a ·npeM-HHaBaHe KoM MacosH. H3CJie.n.BaH!1H oT T03H po.n.. ToBa oT csoH crpaHa no3BOJIHBa Ha HHTep­npeTaropa .n.a .n.asa apryMeHTtl:paHH 3aKJIIOtJeHHH, 6a3Hpalll.H ce Ha KoMnJieKCHH, crporo KOJIHtrecTBeHH ou.eHKH 3a pa3rJie)K.n.aHHTe seJIHlJHHH. HaJIHtJHero Ha .Ko­.n.HpaHa 11HcpOpMatVIH, 33TIHCaHa Ha ·:r-.n:rrmrTIIa JieFITa, .n.asa Bb3MO:>KHOCT 3a MHO· fOKpaTHO OOpolll.eHHe l<'bM HeH 33 pewaBaHeTO H Ha .ll.PYfH Ha)'tiHH HJIH npaK· THtieCKH 3a.U.atiH.

206

JI H·T e p aT y p a

11 8 a H 'I e B, E. 1978. HcnOJJb3083HHe KpHBbiX n upcoua .ll;JIH annpoKCHMiiUHH 3MnHpH'IHbiX pacnpe.n;eJJeHHH HH>KeHepHo-reoJJorH'IeCKHX napaMeTpOB. C6. 25 eoa. BM r H, 4, 195- 200.

K e H .A a JJ, M ., A. C r b 10 apr. 1966. TeopuR pacnpeael!eHuR. M., H ayKa. 428 c. JI oM T a .A 3 e, B. 1970. HH:J~CeHepHaR eeo11oeuR. HH:J~CeHepHaR nempo11oeuR. JI ., HayKa. 479 c. M H T p on o JJ b c K H A, A. 1971. TexHuKa cmamucmu'leCKUX Bbl'lUCI!eHut1. M ., <l>H3MaTrH3 .

584 c. c e pre e B, E., r. r 0 JJ 0 .A K 0 B c K a H H .n;p. 1973. FpyHmOBeaeHue. M ., l13.n;. MocK.

yH-Ta. 383 C. T 11M o a, X., E. 11 a a H 11 ea. 1978. To'!KOBII oueHKH Ha HH<jlopMaUHOHHHTe noroun npH

asroMaTH3HpaHH cacreMH 3a ynpasJJeHHe, IV- Half. H.ay.'l-Ho-mexH. MapKmauiJepi:Ka KOHrjJepeHifUR, I , Bapua . 124- 129.

(llocm?JnuAa 1-ta 18. VII . 1980 e.)

201