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DETERMINATION OF DENSITY, VELOCITY, AND BOUNDARIES OF THE GEOLOGICAL MEDIUM WITH ARBITRARY BOUNDARIES AROUND A BOREHOLE
Murmansk State Technical University, Murmansk, Russia
Journal: Geophysical research
Tome: 17
Number: 4
Year: 2016
Pages: 67-77
UDK: 550.34.013
DOI: 10.21455/gr2016.4-6
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Rozhkov A.S. DETERMINATION OF DENSITY, VELOCITY, AND BOUNDARIES OF THE GEOLOGICAL MEDIUM WITH ARBITRARY BOUNDARIES AROUND A BOREHOLE // . 2016. Т. 17. № 4. С. 67-77. DOI: 10.21455/gr2016.4-6
@article{RozhkovDETERMINATION2016,
author = "Rozhkov, A. S.",
title = "DETERMINATION OF DENSITY, VELOCITY, AND BOUNDARIES OF THE GEOLOGICAL MEDIUM WITH ARBITRARY BOUNDARIES AROUND A BOREHOLE",
journal = "Geophysical research",
year = 2016,
volume = "17",
number = "4",
pages = "67-77",
doi = "10.21455/gr2016.4-6",
language = "English"
}
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Keywords: combined inverse problem of geophysics, vicinity of borehole, density, velocity
Аnnotation: This work is dedicated to a combined inverse problem using seismic and gravimetric data. For the case of two-dimensional geological medium in the vicinity of borehole, the problem of determining density, seismic wave velocities and layer boundaries is solved for arbitrary surface of discontinuity. The acoustic impedance (density-velocity product), and travel times of seismic waves, as a function of horizontal coordinate x, are assumed to be known in each layer. These functions do not impose any restrictions, i.e. these functions are arbitrary. The position of the upper border of the first layer is also known and seismic and gravimetric data are given on it.
A borehole is considered with density p and velocity V known in each layer based on GIS (Geographical information systems) data. The relation between density and velocity is assumed to be V=mp^l, where m and l are constants to be determined. According to these data, densities, velocities, and locations of discontinuity surfaces are determined as a function of horizontal coordinate for each layer.
Bibliography: Alekseev A. S. O postanovke sovmeshchennykh obratnykh zadach geofiziki. Uslovno-korrektnye obratnye zadachi matematicheskoy fiziki i analiza (On statement of combined inverse problems of Geophysics. Conditionally correct inverse problems of mathematical physics and analysis), Novosibirsk: Nauka, 1992, pp. 3-12. (in Russian)
Alekseev A. S. and Bubnov B.A. Ob odnoy sovmeshchennoy postanovke obratnykh zadach seysmiki i gravimetrii (One combined the formulation of inverse problems of seismology and gravimetry), Doklady Earth Sciences, 1981, vol. 251, no. 5, p. 1086-1090 (in Russian)
Alekseev A. S. and Bubnov B.A. Ustoychivost' resheniya obratnoy zadachi kompleksirovaniya seysmiki i gravimetrii (The stability of the solution of the inverse problem of integration of seismic and gravimetry), Doklady Earth Sciences, 1984, vol. 275, no. 2, p. 332-335 (in Russian)
Bakhvalov N. S. Chislennye metody (Numerical methods), Moscow: Nauka, 1975, (in Russian)
Blokh Yu. I. Reshenie pryamykh zadach gravirazvedki i magnitorazvedki (The solution of the direct problem of magnetic and gravitational exploration), Moscow: Moscow State Geological Exploration Academy, 1993 (in Russian)
Boganik G.N. and Gurvich I. I., Seismorazvedka (Exploration seismology), Tver': AIS Publ., 2006 (in Russian)
Faddeev D. K. and Faddeeva V. N. Vychislitel'nye metody lineynoy algebry (Computational methods of linear algebra), Saint-Petersburg: Lan' Publ., 2002. (in Russian)
Fikhtengol'ts G. M. Kurs differentsial'nogo i integral'nogo ischisleniya (A course of differential and integral calculus), Moscow: Nauka, 1970. (in Russian)
Gardner G. H. F., Gardner L. W., and Gregory A. R. Formation velocity and density - the diagnostic basics for stratigraphic traps. Geophysics, 1974, vol 39, p. 770-849.
V. N. Glaznev, Kompleksnye geofizicheskie modeli litosfery Fennoskandii (Integrated geophysical models of the lithosphere in Fennoscandia), Apatity: KaeM JSC, 2003, 252 p. (in Russian)
Gogonenkov G.N., Zakharov E.T., and El'manovich S.S. Prognoz detal'nogo skorostnogo razreza po seysmicheskim dannym (Forecast of the detailed velocity section from seismic data), Prikladnaya geofizika, vol. 97, p. 58-72, 1980. (in Russian)
Gogonenkov G.N. Izuchenie detal'nogo stroeniya osadochnykh tolshch seysmorazvedkoi (The study of the detailed structure of the sedimentary strata by the seismic survey), Moscow: Nedra, 1987. (in Russian)
Golizdra G. Ya. Kompleksnaya interpretatsiya geofizicheskikh poley pri izuchenii glubinnogo stroeniya zemnoy kory (Integrated interpretation of geophysical fields in the study of the deep structure of the earth's crust), Moscow: Nedra, 1988. (in Russian)
Kantorovich L. V. and Akilov G. P. Funktsional'nyi analiz (Functional analysis), Moscow: Nauka, 1977 (in Russian)
Kakhaner D., Mouler K., and Nesh S. Chislennye metody i programmnoe obespechenie (Numerical methods and software), Moscow: Mir, 1998 (in Russian)
Kobrunov A.I. The principles of integrated interpretation of gravimetric data, Geofizicheskiy zhurnal (Geophysical journal), 2003, no. 6, vol. 25, p. 95-105. (in Russian)
Nedyalkov I. P. Integrated interpretation of potential fields, Doklady Earth Sciences, 1957, vol. 10, no. 6, p. 67. (in Russian)
Nedyalkov I. P. Integrated interpretation of potential fields], Izv. Phys. Solid Earth, 1965, no. 11, p. 48-65. (in Russian).
Rozhkov A. S. The density calculations for the model of layered geological medium using seismic and gravimetric data, Vestnik Moskovskogo universiteta (Bulletin of the Moscow state University), 4th series Geology, vol. 2, 2005, Moscow, 2005, p. 65-69. (in Russian)
Rozhkov A. S. Algoritm chislennogo resheniya zadachi opredeleniya plotnosti v sloistoy geologicheskoy srede (The algorithm for numerical solution of the problem of determining the density in a layered geological environment). All-Union Institute of Scientific and Technical Information of the Russian Academy of Sciences, no. 585-V2010, 6 p., 2010. (in Russian)
Starostenko V. I., Kostyukevich A. S., and Kozlenko V. G. Integrated interpretation of seismic and gravimetry, Izv. Phys. Solid Earth, no. 4, 1988, pp. 33-49. (in Russian)
Strakhov V. N. and Romanyuk T. V. Restoring the density of the earth's crust and upper mantle according to data from the NHS and gravimetry, section I, Izv. Phys. Solid Earth, 1984, no. 6, p. 44-63. (in Russian)
Strakhov V. N. and Romanyuk T. V. Restoring the density of the earth's crust and upper mantle according to data from the NHS and gravimetry, section II, Izv. Phys. Solid Earth, 1984, no. 7, p. 64-80. (in Russian)
Sheriff R. and Geldart L. Seysmorazvedka. Obrabotka i interpretatsii dannykh (Exploration seismology. Processing and interpretation of data), vol. 2, Moscow: Mir, 1987. (in Russian) Tal-Virsky B. B. and Tabakov A. A. High-resolution prediction of acoustic impedances below bottom-of-hole, Geoph. Prosp., 1983,vol. 31, no. 2, p. 225-236.
Veselov K. E. and Sagitov M.U. Gravimetricheskaya razvedka (Gravity exploration), Moscow, 1968. (in Russian)
Alekseev A. S. and Bubnov B.A. Ob odnoy sovmeshchennoy postanovke obratnykh zadach seysmiki i gravimetrii (One combined the formulation of inverse problems of seismology and gravimetry), Doklady Earth Sciences, 1981, vol. 251, no. 5, p. 1086-1090 (in Russian)
Alekseev A. S. and Bubnov B.A. Ustoychivost' resheniya obratnoy zadachi kompleksirovaniya seysmiki i gravimetrii (The stability of the solution of the inverse problem of integration of seismic and gravimetry), Doklady Earth Sciences, 1984, vol. 275, no. 2, p. 332-335 (in Russian)
Bakhvalov N. S. Chislennye metody (Numerical methods), Moscow: Nauka, 1975, (in Russian)
Blokh Yu. I. Reshenie pryamykh zadach gravirazvedki i magnitorazvedki (The solution of the direct problem of magnetic and gravitational exploration), Moscow: Moscow State Geological Exploration Academy, 1993 (in Russian)
Boganik G.N. and Gurvich I. I., Seismorazvedka (Exploration seismology), Tver': AIS Publ., 2006 (in Russian)
Faddeev D. K. and Faddeeva V. N. Vychislitel'nye metody lineynoy algebry (Computational methods of linear algebra), Saint-Petersburg: Lan' Publ., 2002. (in Russian)
Fikhtengol'ts G. M. Kurs differentsial'nogo i integral'nogo ischisleniya (A course of differential and integral calculus), Moscow: Nauka, 1970. (in Russian)
Gardner G. H. F., Gardner L. W., and Gregory A. R. Formation velocity and density - the diagnostic basics for stratigraphic traps. Geophysics, 1974, vol 39, p. 770-849.
V. N. Glaznev, Kompleksnye geofizicheskie modeli litosfery Fennoskandii (Integrated geophysical models of the lithosphere in Fennoscandia), Apatity: KaeM JSC, 2003, 252 p. (in Russian)
Gogonenkov G.N., Zakharov E.T., and El'manovich S.S. Prognoz detal'nogo skorostnogo razreza po seysmicheskim dannym (Forecast of the detailed velocity section from seismic data), Prikladnaya geofizika, vol. 97, p. 58-72, 1980. (in Russian)
Gogonenkov G.N. Izuchenie detal'nogo stroeniya osadochnykh tolshch seysmorazvedkoi (The study of the detailed structure of the sedimentary strata by the seismic survey), Moscow: Nedra, 1987. (in Russian)
Golizdra G. Ya. Kompleksnaya interpretatsiya geofizicheskikh poley pri izuchenii glubinnogo stroeniya zemnoy kory (Integrated interpretation of geophysical fields in the study of the deep structure of the earth's crust), Moscow: Nedra, 1988. (in Russian)
Kantorovich L. V. and Akilov G. P. Funktsional'nyi analiz (Functional analysis), Moscow: Nauka, 1977 (in Russian)
Kakhaner D., Mouler K., and Nesh S. Chislennye metody i programmnoe obespechenie (Numerical methods and software), Moscow: Mir, 1998 (in Russian)
Kobrunov A.I. The principles of integrated interpretation of gravimetric data, Geofizicheskiy zhurnal (Geophysical journal), 2003, no. 6, vol. 25, p. 95-105. (in Russian)
Nedyalkov I. P. Integrated interpretation of potential fields, Doklady Earth Sciences, 1957, vol. 10, no. 6, p. 67. (in Russian)
Nedyalkov I. P. Integrated interpretation of potential fields], Izv. Phys. Solid Earth, 1965, no. 11, p. 48-65. (in Russian).
Rozhkov A. S. The density calculations for the model of layered geological medium using seismic and gravimetric data, Vestnik Moskovskogo universiteta (Bulletin of the Moscow state University), 4th series Geology, vol. 2, 2005, Moscow, 2005, p. 65-69. (in Russian)
Rozhkov A. S. Algoritm chislennogo resheniya zadachi opredeleniya plotnosti v sloistoy geologicheskoy srede (The algorithm for numerical solution of the problem of determining the density in a layered geological environment). All-Union Institute of Scientific and Technical Information of the Russian Academy of Sciences, no. 585-V2010, 6 p., 2010. (in Russian)
Starostenko V. I., Kostyukevich A. S., and Kozlenko V. G. Integrated interpretation of seismic and gravimetry, Izv. Phys. Solid Earth, no. 4, 1988, pp. 33-49. (in Russian)
Strakhov V. N. and Romanyuk T. V. Restoring the density of the earth's crust and upper mantle according to data from the NHS and gravimetry, section I, Izv. Phys. Solid Earth, 1984, no. 6, p. 44-63. (in Russian)
Strakhov V. N. and Romanyuk T. V. Restoring the density of the earth's crust and upper mantle according to data from the NHS and gravimetry, section II, Izv. Phys. Solid Earth, 1984, no. 7, p. 64-80. (in Russian)
Sheriff R. and Geldart L. Seysmorazvedka. Obrabotka i interpretatsii dannykh (Exploration seismology. Processing and interpretation of data), vol. 2, Moscow: Mir, 1987. (in Russian) Tal-Virsky B. B. and Tabakov A. A. High-resolution prediction of acoustic impedances below bottom-of-hole, Geoph. Prosp., 1983,vol. 31, no. 2, p. 225-236.
Veselov K. E. and Sagitov M.U. Gravimetricheskaya razvedka (Gravity exploration), Moscow, 1968. (in Russian)
