Estimation of the generalized characteristics of spatial movements of the Earth crust using the data of GPS measurements/ Erdviniu Zemes plutos judesiu apibendrintuju charakteristiku nustatymas pagal GPS matavimu duomenis.

Zakarevicius, Algimantas ; Aksamitauskas, Vladislovas Ceslovas ; Stanionis, Arminas 等

1. Ivadas

Zemes plutos judesiams tirti naudojami tikslus geodeziniu tinklu kartotiniu matavimu duomenys (Badawy et al. 2008; Borghi et al. 2009; Ching et al. 2007; Song, Yun 2008; Zakarevicius 2003; Zakarevicius et al. 2008a; Zakarevicius et al. 2008b). Precizinio tikslumo erdviniai geodeziniai tinklai dazniausiai sudaromi taikant globalines padeties nustatymo sistemas--GPS (Kahmen 2006; Petroskevicius 2004; Skeivalas 2008).

Horizontaliosios, vertikaliosios bei erdvines Zemes plutos judesiu charakteristikos Ignalinos atomines elektrines rajone nagrinetos daugelyje darbu (Aksamitauskas et al. 2006; Stanionis 2005; Sliaupa et al. 2006; Zakarevicius 1994; Zakarevicius 2003; Zakarevicius et al. 2007; Zakarevicius, Stanionis 2006; Zakarevicius, Stanionis 2007). Tokiu tyrimu rezultatai skelbti ir kituose mokslo darbuose, taciau nera nustatytos Ignalinos atomines elektrines teritorijos erdvines Zemes plutos judesiu apibendrintosios charakteristikos. Pagal nustatytas charakteristikas galima vertinti bei interpretuoti lokalios teritorijos bendruosius Zemes plutos judesiu ypatumus atsizvelgiant i sasajas su regioninemis tektoninio fono savybemis bei strukturomis.

Atsizvelgiant i geodinaminiu procesu raida ir ypatumus (Gailius et al. 1991; Vanicek, Krakiwsky 1986), patobulinta Zemes plutos judesiu tyrimu metodika pritaikant trigonometrini metoda svarbiausiuju itempiu pokyciams ivertinti.

Darbo tikslas--sudaryti svarbiausiuju erdviniu Zemes plutos itempiu pokyciu ivertinimo algoritma taikant trigonometrini metoda bei ivertinti erdvines Zemes plutos judesiu apibendrintasias charakteristikas Ignalinos atomines elektrines rajone.

2. Erdviniu zemes plutos judesiu apibendrintuju charakteristiku tyrimo metodika

Vertinant Zemes plutos apibendrintasias erdvines deformacijas, taikyta mazuju deformaciju prielaida. Laikytasi prielaidos, kad erdvines deformacijos pagal pobudi yra vienalytes bei izotropines.

Blokiniu strukturu apibendrintuju erdviniu Zemes plutos deformaciju parametru vektorius ivertinamas maziausiuju kvadratu metodu (Zakarevicius, Stanionis 2006):

T = [([H.sup.T] * H).sup.-1] * [H.sup.T] * [DELTA]E, (1)

cia

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

cia T--blokines strukturos apibendrintuju erdviniu Zemes plutos deformaciju parametru vektorius, H--punktu erdviniu koordinaciu nuokrypiu nuo ju vidurkio matrica, [DELTA][gamma]--punktu erdviniu koordinaciu poslinkiu vektorius.

Reiksmes is (1-4):

[DELTA][X.sub.i] = [X'.sub.t] - [X.sub.i], [DELTA][Y'.sub.i] = [Y'.sub.i] - [Y.sub.i], [DELTA][Z.sub.i] = [Z'.sub.i] - [Z.sub.i], [X.sub.i], [Y.sub.i], [Z.sub.i]--pirmojo matavimo erdvines staciakampes geocentrines geodezinio tinklo punktu koordinates, [X'.sub.i], [Y'.sub.i], [Z'.sub.i]--antrojo matavimo erdvines staciakampes geocentrines geodezinio tinklo punktu koordinates, i = 1, 2,...,n--punktu numeriai, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]--erdvinio geodezinio tinklo punktu koordinaciu nuokrypiai nuo ju vidurkio, [[alpha].sub.X], [[alpha].sub.Y], [[alpha].sub.Z]--poslinkiai koordinaciu asiu kryptimis, [gamma] - blokines strukturos posukis, [[epsilon].sub.XX], [[epsilon].sub.YY], [[epsilon].sub.ZZ] - santykines linijines deformacijos, [[epsilon].sub.XY], [[epsilon].sub.XZ], [[epsilon].sub.YZ]--santykines slyties deformacijos.

Turint apskaiciuotas apibendrintasias erdvines deformacijas, galima nustatyti apibendrintuju erdviniu normaliniu bei tangentiniu tektoniniu itempiu pokycius. Erdviniams tektoniniu itempiu pokyciams modeliuoti taikytas atvirkstinis Huko desnis. Fizines priklausomybes, itempius isreiskus deformacijomis, uzrasomos (Zakarevicius, Stanionis 2007):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

cia

G = E/2(1 + v), (6)

G - slyties modulis, E--tamprumo modulis (7 * [10.sup.10] N/[m.sup.2]), [??] = [[epsilon].sub.XX] + [[epsilon].sub.YY] + [[epsilon].sub.ZZ]--pirmasis deformaciju tenzoriaus [bar.[epsilon]] invariantas [I.sub.1], v--Puasono koeficientas (0,25), [[sigma].sub.XX], [[sigma].sub.YY], [[sigma].sub.ZZ]--normaliniu tektoniniu itempiu pokyciai, [[sigma].sub.XY], [[sigma].sub.XZ], [[sigma].sub.YZ]--tangentiniu tektoniniu itempiu pokyciai. Apibendrintuju svarbiausiuju erdviniu itempiu pokyciai apskaiciuojami is kubines lygties (Atkociunas, Nagevicius 2004; Stanionis 2008):

[[sigma].sup.3] - [I.sub.1] * [[sigma].sup.2] + [I.sub.2] * [sigma] - [I.sub.3] = 0, (7)

cia

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

[sigma]--svarbiausiuju erdviniu itempiu pokyciai, [I.sub.1], [I.sub.2], [I.sub.3] - itempiu tenzoriaus invariantai.

Kubinei lygciai (7) spresti trigonometriniu budu galima pakeisti kintamuosius (Atkociunas, Nagevicius 2004):

[sigma] = x + 1/3 [I.sub.1]. (9)

Tuomet (7) lygtis uzrasoma:

[x.sup.3] + 3px + 2q = 0, (10)

cia

p = 1/3([I.sub.2] - 1/3 [I.sup.2.sub.1]), (11)

q = -1/27[I.sup.3.sub.1] + 1/6[I.sub.1][I.sub.2] -1/2[I.sub.3]. (12)

Visos trys kubines lygties (10) saknys yra realiosios, jeigu diskriminantas [DELTA] = [p.sup.3] + [q.sup.2] < 0. Nagrinejamame uzdavinyje diskriminantas [DELTA] visada neigiamas (Atkociunas, Nagevicius 2004; [TEXT NOT REPRODUCIBLE IN ASCII.], T. 1970). Kai [DELTA] < 0, kubine lygtis (10) gali buti sprendziama trigonometriniu metodu. Lygties (10) saknys [x.sub.1], [x.sub.2], [x.sub.3] isreiskiamos taip:

[x.sub.1] = 2[square root of ([absolute value of p] cos [phi])], (13)

[x.sub.1] = 2[square root of ([absolute value of p] cos ([phi] + 120[degrees]), (14)

[x.sub.3] = 2[square root of ([absolute value of p] cos ([phi] - 120[degrees]), (15)

cia

[phi] = 1/3 arccos -q/[[absolute value of p].sup.3/2], (16) . = - 1

[absolute value of p]--absoliucioji koeficiento reiksme.

[ILLUSTRATION OMITTED]

Paeiliui irasius lygties (10) gautasias [x.sub.1], [x.sub.2], [x.sub.3] reiksmes i priklausomybe (9), gaunamos svarbiausiuju itempiu pokyciu [[sigma].sub.1], [[sigma].sub.2], [[sigma].sub.3] reiksmes ([[sigma].sub.1] = [[sigma].sub.2], = [[sigma].sub.3]).

3. Erdviniu zemes plutos judesiu apibendrintuju charakteristiku skaiciavimo rezultatai

Erdvinems Zemes plutos judesiu charakteristikoms tirti Ignalinos atomines elektrines rajone 1998 m. irengtas specialus GPS tinklas. Tinkla sudaro 10 gruntiniu punktu, isdestymo schema pateikta paveiksle. Erdvinio GPS tinklo sudarymo darbai, matavimu programa, prietaisai bei kartotiniu matavimu duomenys pateikti C. Aksamitausko ir kitu (2006), A. Stanionio (2005; 2008), A. Zakareviciaus (2003), A. Zakareviciaus, A. Stanionio (2003) darbuose.

Pagal (1-16) formules, naudojant kartotinius GPS tinklo matavimu duomenis (antras ciklas atliktas 1999 m.), ivertintos Ignalinos atomines elektrines teritorijos erdvines apibendrintosios Zemes plutos judesiu charakteristikos: poslinkiai koordinaciu asiu kryptimis, blokines strukturos posukis, santykines linijines bei slyties deformacijos, normaliniu ir tangentiniu itempiu pokyciai, svarbiausiuju tektoniniu itempiu pokyciai.

Ignalinos atomines elektrines teritorijos, kaip vientiso bloko, poslinkis [[alpha].sub.X] yra teigiamas (0,006 1 m), ordinaciu kryptimi poslinkio kitimo nenustatyta, [[alpha].sub.Z]--neigiamas (-0,000 3 m), lokalios teritorijos blokines strukturos posukis [omega] - 0,101.

Ivertintos erdviniu Zemes plutos judesiu apibendrintosios charakteristikos pateiktos 1 ir 2 lentelese.

Erdviniu apibendrintuju santykiniu linijiniu deformaciju kitimo ribos - nuo -0,012 * [10.sup.-6] iki -0,472 * [10.sup.-6], santykines slyties deformacijos kinta nuo -0,233 * [10.sup.-6] iki -0,760 * [10.sup.-6] (1 lentele).

Erdviniu Zemes plutos normaliniu itempiu pokyciai svyruoja nuo -0,017 4 MPa iki -0,043 1 MPa bei tangentiniu itempiu pokyciai kinta nuo -0,006 5 MPa iki -0,021 3 MPa (2 lentele).

Svarbiausiuju apibendrintuju itempiu pokyciu reiksmes nustatytos trigonometriniu budu: [[sigma].sub.1] = -0,003 3 MPa, [[sigma].sub.2] -0,021 7 MPa bei [[sigma].sub.3] -0,058 5 MPa.

Erdviniu Zemes plutos judesiu Ignalinos atomines elektrines teritorijoje apibendrintuju charakteristiku reiksmes yra neigiamos. Remiantis tyrimo rezultatais galima teigti, kad Ignalinos atomines elektrines teritorija yra veikiama bendrojo tektoninio spaudimo.

Erdviniai apibendrintieji deformaciju bei itempiu pokyciu Ignalinos atomines elektrines teritorijoje rezultatai koreliuoja su lokaliaisiais bei regioniniais Zemes plutos judesiu tyrimu rezultatais (Aksamitauskas et al. 2006; Stanionis 2005; Sliaupa et al. 2006; Zakarevicius 1994; Zakarevicius 2003; Zakarevicius, Stanionis 2002; Zakarevicius, Stanionis 2003; Zakarevicius, Stanionis 2005).

Ivertintos Zemes plutos judesiu charakteristikos apibendrina ankstesniu tyrimu rezultatus, galima kompleksiskai vertinti ir interpretuoti dabartiniu geodinaminiu procesu kaitos desningumus sisteminio poziurio principu.

Pateikti rezultai atpsindi bendra geodinamine situacija Ignalinos AE rajone--modelyje tiriamas plotas traktuojamas, kaip vientisas blokas. Taciau butina atsizvelgti i tikimybe, kad tektonines deoformacijos ir itempiai bloko viduje greiciausiai pasiskirste netolygiai ir yra kontroliuojamu stambiu luziniu zonu, kurios kerta tyrimu plota (pav.).

4. Isvados

1. Sudarytas erdviniu svarbiausiuju itempiu pokyciu skaiciavimo algoritmas taikant trigonometrini metoda.

2. Gauti nauji erdviniu Zemes plutos judesiu Ignalinos atomines elektrines rajone duomenys--apibendrintosios erdvines santykines deformacijos bei apibendrintieji erdviniu tektoniniu itempiu pokyciai.

3. Metines apibendrintosios santykines deformacijos kinta nuo -0,012 * [10.sup.-6] iki -0,760 * [10.sup.-6], tektoniniu itempiu pokyciai svyruoja nuo -0,003 MPa iki -0,059 MPa.

4. Erdvines Zemes plutos judesiu apibendrintosios charakteristikos yra neigiamo zenklo, t. y. Ignalinos atomines elektrines teritorija veikia tektoninis spaudimas.

Straipsnis parengtas tyrimus remiant Lietuvos valstybiniam mokslo ir studiju fondui (sutartis Nr. V-05/2009).

doi: 10.3846/1392-1541.2009.35.126-130

Iteikta 2009 06 22; priimta 2009 09 23

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[TEXT NOT REPRODUCIBLE IN ASCII.] 1970. [TEXT NOT REPRODUCIBLE IN ASCII.] [TEXT NOT REPRODUCIBLE IN ASCII.] [Korn, G.; Korn, T. Mathematical handbook for scientists and engineers]. [TEXT NOT REPRODUCIBLE IN ASCII.]. 720 c.

Algimantas Zakarevicius (1), Vladislovas Ceslovas Aksamitauskas (2), Arminas Stanionis (3), Daiva Levinskaite (4)

(1, 2, 3, 4) Geodezijos ir kadastro katedra, Vilniaus Gedimino technikos universitetas, Sauletekio al. 11, LT-10223 Vilnius, Lietuva El. pastas: gkk@vgtu.lt

Algimantas ZAKAREVICIUS. Prof., Dr. Habil. at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania, Ph +370 5 237 0630, Fax +370 5 274 4705, e-mail Algimantas. Zakarevicius@ap.vgtu.lt.

A graduate from Kaunas Polytechnic Institute (now Kaunas University of Technology), geodetic engineer, 1965. Doctor's degree at Vilnius University, 1973. Dr Habilis degree at VGTU, 2000. A member of the Geodetic Commission of Estonia, Latvia and Lithuania. Research training at Geodetic Institute of Norwegian Mapping Authority, 1994. The author of more than 150 publications and 3 monographs.

Research interests: investigations into the recent geodynamic processes, formation of geodetic networks.

Vladislovas Ceslovas AKSAMITAUSKAS. Assoc. Prof., Dr. at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania, Ph +370 5 2744 701, Fax +370 5 2744 705, e-mail caks@ap.vgtu.lt.

Doctor of Science (1993). The author of two teaching books and more than 50 scientific papers. Participated in a number of international conferences.

Research interests: geodetic instrumentation, automation of measurements, angular and distance measurements.

Arminas STANIONIS. Assoc. Prof., Dr. at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 237 0629, Fax +370 5 274 4705, e-mail Arminas.Stanionis@ap.vgtu.lt.

A graduate from Vilnius Gediminas Technical University (VGTU) (Master of Science, 2002). Doctor's degree at VGTU, 2005. The author and co-author of more than 30 research papers. Participated in a number of international conferences.

Research interests: investigation of geodynamic processes, GIS, investigations of deformations.

Daiva LEVINSKAITE. Doctoral student at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail gkk@ap.vgtu.lt.

A graduate from Vilnius Gediminas Technical University (Master of Science, 2008). A co-author of 2 publications.

Research interests: investigation of geodynamic processes, investigations of deformations.

Table 1. Spatial deformations of the Earth-crust

1 lentele. Erdvines Zemes plutos deformacijos

[epsilon]XX.[10.sup.-6] -0,472 [epsilon]XY.[10.sup.-6] -0,233

[epsilon]yy.[10.sup.-6] -0,113 [epsilon]XZ.[10.sup.-6] -0,760

[epsilon]zz.[10.sup.-6] -0,012 [epsilon]YZ.[10.sup.-6] -0,377

Table 2. Changes of spatial tectonic stresses
2 lentele. Erdviniu tektoniniu itempiu pokyciai

[sigma]XX (MPa) -0,043 1 [sigma]XY (MPa) -0,006 5
[sigma]YY (MPa) -0,023 0 [sigma]XZ (MPa) -0,021 3
[sigma]ZZ (MPa) -0,017 4 [sigma]YZ (MPa) -0,010 6