ІНТЕГРОВАНЕ СТОХАСТИЧНЕ МОДЕЛЮВАННЯ ПЕТРОФІЗИЧНИХ ПАРАМЕТРІВ ДЛЯ ОЦІНКИ МІНЕРАЛОГІЧНОГО СКЛАДУ ЗЕМНОЇ КОРИ

І.  Віршило; І.  Пап

doi:10.17721/1728-2713.84.12

Authors

I. Virshylo Taras Shevchenko National University of Kyiv, 90 Vasylkivska Str., Kyiv, 03022, Ukraine
I. Pap Taras Shevchenko National University of Kyiv, 90 Vasylkivska Str., Kyiv, 03022, Ukraine

DOI:

https://doi.org/10.17721/1728-2713.84.12

Keywords:

deep seismic sounding, seismic and mineralogical models, global optimization methods, stochastic methods, direct problem of seismic acoustics, Monte Carlo method, method of conditional moment functions

Abstract

The construction of a new algorithm for spatial modeling of the composition of rocks, which is consistent with the results of geophysical, petrophysical and geochemical studies, is considered. The probability distributions of the quantities simulated – volume concentrations of rockforming minerals and voids and the parameters of the thermally stressed state of the medium – pressure and temperature are used as input parameters of the model. The determination of probability distributions is carried out by statistical processing of the results of geological and geochemical studies for the composition and the introduction of confidence intervals for the results of geophysical studies. The method of conditional moment functions for the problem of seismic acoustics, thermometry, magnetometry and electrometry is used as calculation algorithms. The algorithm is based on a multicomponent matrix model of a medium with ellipsoidal inclusions and has no restrictions on the concentration of components. The algorithm makes it possible to take into account arbitrary symmetry of the medium. The result of the simulation is a statistically significant set of decisions that have a geological meaning and are limited to the probability distribution of the concentrations of rock-forming minerals.

References

Anderson, O., Isaak, D., Oda, H. (1992). High-Temperature Elastic-Constant Data on Minerals Relevant to Geophysics. Reviews of Geophysics, 30 (1), 57-90. https://doi.org/10.1029/91RG02810

Bandy, B. (1988). Metody optimizacii. М.: Radio i svyas. [in Russian]

Christensen, N. I., Mooney, W. D. (1995). Seismic velocity structure and composition of the continental crust: A global view. Journal of Geophysical Research, 100(B6), 9761. doi:10.1029/95JB00259

Evtushenko, U.G., Malkov, V.U., Stanevichus, A.A. (2009). Parallelniy poise globalnogo ekstremuma funkcii mnogih peremennyh. Vychisl. matem. i mat. fis., 49, 2,255-269. [in Russian]

FENNIA Working Group. (1998). P- and S-velocity structure of the Baltic Shield beneath the FENNIA profile in southern Finland. Report. Univ. of Helsinki.

Gavrilov, V.P., (2005). Geotectonika. Neft i gas, 368, 30-66. [in Russian]

Golizdra, G.Ya. (1977). Osnovnye metody resheniya pryamoy zadachi gravirazvedki na EVM. Obzor ONTI VIEMS. Ser. Region., raved. I promysl. geofiz., 99. [in Russian]

Grad, M., Tripolsky, A. A. (1994). Structure of the Ukrainian shield. P. 3: Seismic and petrological models of the Ukrainian shield. Acta Geophysica Polonica, 42, 1, 23-44.

Grad M., Tripolsky, A. A. (1995). Crustal structure from P and S seismic waves and petrological models of the Ukrainian shield. Tectonophysics, 250, 89-112.

Grad, M., Luosto, U. (1994). Seismic velocities and Q-factors in the uppermost crust beneath the SVEKA profile in Finland. Tectonophysics, 230, 1-18. doi:10.1016/0040-1951(94)90144-9.

Janik, T., E. Kozlovskaya, P. Heikkinen, J. Yliniemi, and H. Silvennoinen. (2009) Evidence for preservation of crustal root beneath the Proterozoic Lapland-Kola orogen (northern Fennoscandian shield) derived from P and S wave velocity models of POLAR and HUKKA wide-angle reflection and refraction profiles and FIRE4 reflection transect J. Geophys. Res. 114, B06308, doi:10.1029/2008JB005689

Janik, T., Kozlovskaya, E., Yliniemi, J. (2007). Crust-mantle boundary in the central Fennoscandian shield: Constraints from wide-angle P and S wave velocity models and new results of reflection profiling in Finland. Journal of Geophysical Research, 112(B4), 1-28. http://doi.org/10.1029/2006JB004681

Kosminskaya, I.P, Davyidova, N.I. (1980). Seysmicheskie modeli litosfery I osnovnyih geostruktur territorii SSSR. Seysmicheskie modeli. М.: Nauka, 11-15. [in Russian]

Kozlovskaya, E., Elo, S., Hjelt, S.-E., Yliniemi, J., Pirttij?rvi, M. and SVEKALAPKO STWG. (2004). 3D density model of the crust of southern and central Finland obtained from joint interpretation of SVEKALAPKO crustal P-wave velocity model and gravity data. Geophysical Journal International, 158, 827-848.

Lines, L.R., Schultz, A.K., Treitel, S. (1988). Cooperative inversion of geophysical data. Geophysics, 53, 1, 8-20.

Luosto, U. et al. (1989). The crustal structure along the POLAR Profile from seismic investigation. doi:10.1016/0040-1951(89)90356-9

Mahdavi-Amiri, N., Bartels, R.H. (1989). Constrained nonlinear neast squares: An Exact Penalte Approach with Projected Structured Quasi-Newton Updates. ACM Trans. Mathem. Software, 15, 3, 220-242.

Malovichko, A.K., Kosticyn, V.I. (1992). Gravirazvedka. M.: Nedra. [in Russian]

Maslov, B.P., Prodayvoda, G.T. (1998). Dispersiya I rasseyanie uprugih voln v treschinovatoy geologicheskoy srede. Geofizicheskiy zhurnal, 20, 2, 47-55. [in Russian]

Mironov, V.S. (1980). Kurs gravirazvedki. L.: Nedra. [in Russian]

Noleta, G. (Edc.). (1990). Seysmicheskaya tomografiya. М.: Mir. [in Russian]

Prodaivoda, H. T., Hryshchuk, P. I. (2007). Hravimetrychnyi metod heokartuvannia strukturno-rechovynnykh kompleksiv Ukrainskoho shchyta. Visnyk of Taras Shevchenko National University of Kyiv. Geology, 41, 7-10. [in Ukrainian]

Prodaivoda, G.T, Maslov, B.P., Prodaivoda, T.G. (2003). Seismomineralogical model of the continental upper mantle. Fizika Zemli, 2,3-14. [in Russian]

Prodaivoda, G. T., Khoroshun, L. P., Nazarenko, L. V., Vyzhva, S. A. (2000). Mathematical modeling of the azimuthal anisotropy in thermoelasic properties of the oceanic upper mantle. Izvestiya Physics of the Solid Earth, 36(5), 394-405. [in Russian]

Prodajvoda, G., Zinchenko, O., Kozionova, O. (2005). Methodological principle of formation of main lithotypes database for determination of Earth crust composition of north-west region of Ukrainian shield by seismogravitational method. Visnyk of Taras Shevchenko National University of Kyiv. Geology, 34,11-18. [in Ukrainian]

Prodayvoda, G.T., Vyzhva, S.A., Virshylo, I.V. (2012). Matematychne modelyuvannya geofizychnykh parametriv. Kyiv: VTS "Kyivskyi universytet". [in Ukrainian].

Riznichenko, O.Yu. (2016). GSZ: Ot glubinnoy seysmorazvedki k seysmologii kontroliruemyih istochnikov. K stoletiyu so dnya rozhdeniya I.P. Kosminskoy. Geofizicheskie issledovaniya, 17, 2, 77-82. [in Russian]

Sharov, N. V. (2012) Comparison of the geophysical sections of the earth crust with the results of deep drilling in the Fennoscandian shield. Karelian Research Centre of the Russian Academy of Sciences. [in Russian]

Shary, S.P. (2008). Randomized algorithms in interval global optimization. Siberian J. Num. Math., 11, 4, 457-474. [in Russian]

Silvennoinen, H., Kozlovskaya, E. (2007). 3D structure and physical properties of the Kuhmo Greenstone Belt (eastern Finland): Constraints from gravity modelling and seismic data and implications for the tectonic setting. Journal of Geodynamics, 43(3), 358–373. http://doi.org/10.1016/j.jog.2006.09.018

Silvennoinen, H., Kozlovskaya, E. (2010). Upper crustal velocity and density models along FIRE4 profile. Geophysica, 46(1-2), 21-46.

Sollogub, V. B. (1986). Litosfera Ukrainyi. Kiev: Nauk. dumka. [in Russian]

Sollogub, V. B., Chekunov, A. V., Tripolskiy, A. A., Babinets, V. A. (1978). Rezul'taty issledovaniya glubinnogo stroyeniya Ukrainskogo shchita. Stroyeniye kory i verkhney mantii Tsentral'noy i Vostochnoy Yevropy. Kiev: Nauk. dumka, 136-147. [in Russian]

Starostenko, V.I. (1978). Ustoychivye chislennye metody v zadachah gravimetrii. K.: Nauk. dumka. [in Russian]

Starostenko, V.I., Kostyukevich, A.S., Kozlenko, V.G. (1988). Kompleksnaya interpretatsiya seysmometrii i gravimetrii. Printsipy i metodika. Izv. AN SSSR. Fizika Zemli, 4, 33-49. [in Russian]

Starostenko, V.I., Shvantsara, Ya. (1994). Seysmogravitatsionnoe modelirovanie pri izuchenii litosfery. K.: Nauk. dumka. [in Russian]

Stixrude, L., Lithgow-Bertelloni, C. (2005). Thermodynamics of mantle minerals - I. Physical properties. Geophysical Journal International, 162 (2), 610-632.

Tripolsky, A. A., Sharov, N. V. (2004). Structure of the precambrian shields of the northern hemisphere of the Earth lithosphere by seismic data. Petrozavodsk. Karelian research centre Russian academy of sciences, Institute of Geology. National academy of sciences of Ukraine, Institute of Geophysics. [in Russian]

Tulina, Yu.V., Burmin, V.Yu., Shemeleva, I.B. (2011). To ambiguity problem of interpretation of deep seismic sounding data. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia. [in Russian]

Vyzhva, S., Prodaivoda, G., Virshilo, I., Kozionova, O. (2013). The problems of information support of geophysical tomography interpretive technologies. Visnyk of Taras Shevchenko National University of Kyiv. Geology, 62, 57-62. [in Ukrainian]

Vyzhva, S., Prodayvoda, G., Virshylo, I. (2010). Metodolohichni i teoretychni pryntsypy seysmohravitatsiynoyi tomohrafiyi. Visnyk of Taras Shevchenko National University of Kyiv. Geology, 48, 29-33. [in Ukrainian]