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RESOLUTION ESTIMATION OF REFLECTED AND REFRACTED WAVES IN CROSS-WELL STUDIES BASED ON FRESNEL VOLUME MODELING
Mining Institute of the Ural Branch of the Russian Academy of Sciences
Journal: Geophysical research
Tome: 24
Number: 3
Year: 2023
Pages: 69-86
UDK: 550.832.4:534.213
DOI: 10.21455/gr2023.3-4
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Chugaev A.V. RESOLUTION ESTIMATION OF REFLECTED AND REFRACTED WAVES IN CROSS-WELL STUDIES BASED ON FRESNEL VOLUME MODELING
// . 2023. Т. 24. № 3. С. 69-86. DOI: 10.21455/gr2023.3-4
@article{ChugaevRESOLUTION2023,
author = "Chugaev, A. V.",
title = "RESOLUTION ESTIMATION OF REFLECTED AND REFRACTED WAVES IN CROSS-WELL STUDIES BASED ON FRESNEL VOLUME MODELING
",
journal = "Geophysical research",
year = 2023,
volume = "24",
number = "3",
pages = "69-86",
doi = "10.21455/gr2023.3-4",
language = "English"
}
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Keywords: first Fresnel zone, Fresnel volume, head waves, seismic exploration, cross-well survey, resolution.
Аnnotation: The principles of propagation and registration of seismoacoustic pulses in three-dimensional space are considered using the case of cross-well survey near the boundary with abrupt change in the velocities of elastic waves. Modeling of constructive interference was performed to estimate the volume of the first Fresnel zone and the resolution of seismic studies on refracted and reflected waves in wells with 2D and 3D versions. It is shown that the Fresnel volume of head waves is compressed along the boundary plane in accordance with the distance in-creasing between the source and the receiver from the boundary. Calculations of the Fresnel volume of refract-ed and reflected waves are given for various variants of the relative positions of sources and receivers. It is concluded that the projection of the Fresnel volume of the head wave onto the plane of the high-speed refractive layer can be found by moving the excitation and reception points along the normal to this layer. As a conse-quence, if during cross-well survey the wells are perpendicular to the refractive layer, then the projection of the Fresnel volume of head waves onto this layer is practically independent of the position of the source and receiver in the well. Quantitative estimates of the resolution of borehole seismoacoustic techniques for studying the rock mass have been obtained.
Bibliography: Babich V.M., Matskovskiy A.A., An Interference Head Wave (Buldyrev Wave) and the Locality Principle, Journal of Mathematical Sciences, 2017, vol. 224, pp. 20-26. https://doi.org/10.1007/s10958-017-3390-8
Bai C., Li X., Huang G., Greenhalgh S., Simultaneous Inversion for Velocity and Reflector Geometry Using Mul-ti-phase Fresnel Volume Rays, Pure and Applied Geophysics, 2014, vol. 171, pp. 1089-1105.
Bolgarov A.G., Roslov Y.V., Borehole seismic tomography for near surface investigations, Tehnologii sejsmora-zvedki (Seismic exploration technologies), 2009, no. 1, pp. 105-111. [In Russian].
Cerveny V., Soares J.P., Fresnel volume ray tracing, Geophysics, 1992, vol. 57, pp. 902-915.
Chugaev A.V., Lisin V.P., Babkin A.I., Tomilov K.J., The analysis of the head waves registered in crosshole sur-vey for calculation velocities in the vicinity of boreholes, in Tezisy dokladov 16-j mezhdunarodnoj nauch-no-prakticheskoj konferencii “Inzhenernaja i rudnaja geofizika–2020”. Perm' (Abstracts of the reports of the 16th International Scientific and Practical Conference “Engineering and Ore Geophysics–2020”. Perm.), Moscow, OOO “EAGE GEOMODEL”, 2020a, 8 p. [In Russian].
Chugaev A.V., Lisin V.P., Sanfirov I.A., Nikiforov V.V., Zelenin V.P., Сross-section velocity characteristics de-termination by seismic acoustic borehole methods, in Inzhenernaja geofizika 2017. Kislovodsk (Engineer-ing Geophysics 2017. Kislovodsk), 2017, 10 p. [In Russian].
Chugaev A.V., Pugin A.V., Lisin V.P., Tarakanov S.A., Particular Features of Wave-Field Forming in the Process of Ice Wall Fencing Study at the Mine Shaft by the Borehole Seismic Methods, in Tezisy dokladov 15-j mezhdunarodnoj nauchno-prakticheskoj konferencii “Inzhenernaja i rudnaja geofizika–2019”. Gelen-dzhik (Abstracts of the 15th International Scientific and Practical Conference “Engineering and Ore Geo-physics–2019”. Gelendzhik), Netherlands, EAGE Publishing BV, 2019, 10 p. [In Russian].
Chugaev A.V., Sanfirov I.A., Babkin A.I., Tomilov K.Yu., Near vertical fractured zones imaging using refracions in the vertical seismic profiling, in Tezisy dokladov 17-j mezhdunarodnoj nauchno-prakticheskoj konfer-encii “Inzhenernaja i rudnaja geofizika–2021”. Gelendzhik (Abstracts of the 17th International Scien-tific and Practical Conference “Engineering and Ore Geophysics–2021”. Gelendzhik), Netherlands, EAGE Publishing BV, 2021, 7 p. [In Russian]. https://doi.org/10.3997/2214-4609.202152014
Chugaev A.V., Sanfirov I.A., Tarantin M.V., Tomilov K.Yu., The analysis of head waves secondary field in crosshole seismic method, Geofizika (Geophysics), 2020b, no. 5, pp. 4-12. [In Russian].
de Kool M., Rawlinson N., Sambridge M., A practical grid-based method for tracking multiple refraction and re-flection phases in three-dimensional heterogeneous media, Geophysical Journal International, 2006, vol. 167, pp. 253-270. https://doi.org/10.1111/j.1365-246X.2006.03078.x
Denham L.R., The limits of seismic resolution, SEG Technical Program Expanded Abstracts, 2000, pp. 2401-2404. https://doi.org/10.1190/1.1815946
Han B., Gu H., Liu S., Yan Z., Tang Y., Liu C., Wavelength-dependent Fresnel beam propagator and migration in VTI media, J. Appl. Geophys., 2018, vol. 155, pp. 176-186.
Hubral P., Schleicher J., Tygel M., Hanitzsch C., Determination of Fresnel zones from traveltime measurements, Geophysics, 1993, vol. 58, pp. 703-712. https://doi.org/10.1190/1.1443454
Kondrat'ev O.K., Resolution of seismic exploration MOV-OGT, Geofizika (Geophysics), 2006, no. 2, pp. 3-12. [In Russian].
Kravtsov Yu.A., Orlov Yu.I., Limits of applicability of the method of geometric optics and related problems, Sov. Phys. Usp., 1980a, vol. 23, pp. 750-762.
Kravtsov Yu.A., Orlov Yu.I., Geometricheskaja optika neodnorodnyh sred (Geometric optics of inhomogeneous media), Moscow, Nauka, 1980b, 304 p. [In Russian].
Lazaratos S.K., Harris J.M., Rector J.W., Van Schaack M., High resolution cross well imaging of a west Texas carbonate reservoir. Part 4. Reflection imaging, Geophysics, 1995, vol. 60, pp. 702-711. https://doi.org/10.1190/1.1822130
Li V.O., Vladov M.L., Efficiency of 2D CDP during section subsurface investigations, Moscow University Geol-ogy Bulletin, 2012, vol. 67, no. 3, pp. 193-201. DOI: 10.3103/S0145875212030039
Lisin V.P., Chugaev A.V., Sanfirov I.A., Potentially dangerous zones investigation on the mine fields by methods of ground and borehole seismic, in Inzhenernaja i rudnaja geofizika 2018. Almaty, Kazahstan, 23-27 aprelja (Engineering and Ore Geophysics 2018. Almaty, Kazakhstan, April 23-27), Netherlands, EAGE Publishing BV, 2018, pp.1-12. [In Russian]. DOI: 10.3997/2214-4609.201800521
Liu Y., Dong L., Wang Y., Zhu J., Ma Z., Sensitivity kernels for seismic Fresnel volume tomography, Geophysics, 2009, vol. 74, pp. U35-U46. https://doi.org/10.1190/1.3169600
Matskovskiy A.A., Interference head wave in diffraction of waves from a point source by an inhomogeneous half-plane, Computational Mathematics and Mathematical Physics, 2015, vol. 55, pp. 1867-1883.
Matskovskiy A.A., Wave front sets of the Buldyrev head wave and whispering gallery waves, Journal of Math-ematical Sciences, 2016, vol. 214, pp. 337-343. https://doi.org/10.1007/s10958-016-2781-6
Pica A., Fast and accurate finite difference solution of the 3D eikonal equation parameterized in celerity, in 67th Annual International Meeting, SEG, Exp. Abstr., 1997, pp. 774-1777. https://doi.org/10.1190/1.1885777
Podvin P., Lecomte I., Finite difference computation of traveltimes in very contrasted velocity models: a mas-sively parallel approach and its associated tools, Geophysical Journal International, 1991, vol. 105, pp. 271-284. http://dx.doi.org/10.1111/j.1365-246X.1991.tb03461.x
Rawlinson N., Sambridge M., Wave front evolution in strongly heterogeneous layered media using the fast marching method, Geophysical Journal International, 2004, vol. 156, pp. 631-647. https://doi.org/10.1111/j.1365-246X.2004.02153.x
Sanfirov I.A., Chugaev A.V., Babkin A.I., Lisin V.P., Bobrov V.Y., Minetechnical applications of seismic in shal-low wells, Geofizika (Geophysics), 2018, no. 5, pp. 24-30. [In Russian].
Schuster G.T., Quintus-Bosz A., Wavepath eikonal traveltime inversion: Theory, Geophysics, 1993, vol. 58, pp. 1314-1323. https://doi.org/10.1190/1.1443514
Sheriff R.E., Nomogram for Fresnel-zone calculation, Geophysics, 1980, vol. 45, pp. 968-972. https://doi.org/10.1190/1.1441101
Shishkina M.A., Fokin I.V., Tikhotskiy S.A., Resolution of cross-well travel-time tomography, Tehnologii sejsmorazvedki (Seismic exploration technologies), 2015, no.1, pp. 5-21. [In Russian]. http://dx.doi.org/10.18303/1813-4254-2015-1-5-21
Spetzler J., Snieder R., The effect of small-scale heterogeneity on the arrival time of waves, Geophysical Journal International, 2001, vol. 145, pp. 786-796. https://doi.org/10.1046/j.1365-246x.2001.01438.x
Spetzler J., Snieder R., The Fresnel volume and transmitted waves, Geophysics, 2004, vol. 69, pp. 653-663. https://doi.org/10.1190/1.1759451
Spetzler J., Šijačić D., Wolf K., Application of a linear finite-frequency theory to time-lapse crosswell tomogra-phy in ultrasonic and numerical experiments, Geophysics, 2007, vol. 72, pp. O19-O27. https://doi.org/10.1190/1.2778767
Tverdohlebov D.N., Korolev E.K., Practice of using the 1st Fresnel zone in seismic exploration, in 5th EAGE In-ternational Scientific and Practical Conference and Exhibition on Engineering and Mining Geophysics. Gelendzhik, Russia, Netherlands, EAGE Publishing BV, 2009, pp. 1-4. [In Russian]. https://doi.org/
10.3997/2214-4609.20147351
Vasco D.W., Nihei K.T., A trajectory mechanics approach for the study of wave propagation in an anisotropic elastic medium, Geophysical Journal International, 2019, vol. 219, pp. 1885-1899.
Vasco D.W., Peterson J.E., Majer E.L., Beyond ray tomography: wave paths and Fresnel volumes, Geophysics, 1995, vol. 60, pp. 1790-1804.
Vidale J., Finite-difference calculation of traveltimes in three dimensions, Geophysics, 1990, vol. 55, pp. 521-526. http://dx.doi.org/10.1190/1.1442863
Vidale J.E., Finite-difference traveltime calculation, Bull. Seis. Soc. Am., 1988, vol. 78, pp. 2062-2076. https://
doi.org/10.1785/BSSA0780062062
Vladov M.L., Struchkov V.A., Sudakova M.S., Shmurak D.V., Tomographic surveying at large cross-well dis-tances: negative factors, Inzhenernye izyskanija (Engineering Survey), 2020, vol. 14, no. 2, pp. 42-51. [In Russian]. DOI: 10.25296/1997-8650-2020-14-2-42-51
Watanabe T., Matsuoka T., Ashida Y., Seismic traveltime tomography using Fresnel volume approach, in 69th Annual International Meeting, SEG Expanded Abstracts, 1999, pp. 1402-1405. https://doi.org/10.1190/1.1820777
Xu S., Zhang Y., Huang T., Enhanced tomography resolution by a fat ray technique, in 76th Annual Interna-tional Meeting, SEG Expanded Abstracts, 2006, pp. 3354-3358. https://doi.org/10.1190/1.2370229
Zavalishin B.R., The use of first Fresnel zone radius in seismic exploration, Geofizika (Geophysics), 2008, no. 5, pp. 3-7. [In Russian].
Zhang L., Rector J.W., Hoversten G.M., Eikonal solver in the celerity domain, Geophysical Journal Internation-al, 2005, vol. 162, pp. 1-8. http://dx.doi.org/10.1111/j.1365-246X.2005.02626.x
Bai C., Li X., Huang G., Greenhalgh S., Simultaneous Inversion for Velocity and Reflector Geometry Using Mul-ti-phase Fresnel Volume Rays, Pure and Applied Geophysics, 2014, vol. 171, pp. 1089-1105.
Bolgarov A.G., Roslov Y.V., Borehole seismic tomography for near surface investigations, Tehnologii sejsmora-zvedki (Seismic exploration technologies), 2009, no. 1, pp. 105-111. [In Russian].
Cerveny V., Soares J.P., Fresnel volume ray tracing, Geophysics, 1992, vol. 57, pp. 902-915.
Chugaev A.V., Lisin V.P., Babkin A.I., Tomilov K.J., The analysis of the head waves registered in crosshole sur-vey for calculation velocities in the vicinity of boreholes, in Tezisy dokladov 16-j mezhdunarodnoj nauch-no-prakticheskoj konferencii “Inzhenernaja i rudnaja geofizika–2020”. Perm' (Abstracts of the reports of the 16th International Scientific and Practical Conference “Engineering and Ore Geophysics–2020”. Perm.), Moscow, OOO “EAGE GEOMODEL”, 2020a, 8 p. [In Russian].
Chugaev A.V., Lisin V.P., Sanfirov I.A., Nikiforov V.V., Zelenin V.P., Сross-section velocity characteristics de-termination by seismic acoustic borehole methods, in Inzhenernaja geofizika 2017. Kislovodsk (Engineer-ing Geophysics 2017. Kislovodsk), 2017, 10 p. [In Russian].
Chugaev A.V., Pugin A.V., Lisin V.P., Tarakanov S.A., Particular Features of Wave-Field Forming in the Process of Ice Wall Fencing Study at the Mine Shaft by the Borehole Seismic Methods, in Tezisy dokladov 15-j mezhdunarodnoj nauchno-prakticheskoj konferencii “Inzhenernaja i rudnaja geofizika–2019”. Gelen-dzhik (Abstracts of the 15th International Scientific and Practical Conference “Engineering and Ore Geo-physics–2019”. Gelendzhik), Netherlands, EAGE Publishing BV, 2019, 10 p. [In Russian].
Chugaev A.V., Sanfirov I.A., Babkin A.I., Tomilov K.Yu., Near vertical fractured zones imaging using refracions in the vertical seismic profiling, in Tezisy dokladov 17-j mezhdunarodnoj nauchno-prakticheskoj konfer-encii “Inzhenernaja i rudnaja geofizika–2021”. Gelendzhik (Abstracts of the 17th International Scien-tific and Practical Conference “Engineering and Ore Geophysics–2021”. Gelendzhik), Netherlands, EAGE Publishing BV, 2021, 7 p. [In Russian]. https://doi.org/10.3997/2214-4609.202152014
Chugaev A.V., Sanfirov I.A., Tarantin M.V., Tomilov K.Yu., The analysis of head waves secondary field in crosshole seismic method, Geofizika (Geophysics), 2020b, no. 5, pp. 4-12. [In Russian].
de Kool M., Rawlinson N., Sambridge M., A practical grid-based method for tracking multiple refraction and re-flection phases in three-dimensional heterogeneous media, Geophysical Journal International, 2006, vol. 167, pp. 253-270. https://doi.org/10.1111/j.1365-246X.2006.03078.x
Denham L.R., The limits of seismic resolution, SEG Technical Program Expanded Abstracts, 2000, pp. 2401-2404. https://doi.org/10.1190/1.1815946
Han B., Gu H., Liu S., Yan Z., Tang Y., Liu C., Wavelength-dependent Fresnel beam propagator and migration in VTI media, J. Appl. Geophys., 2018, vol. 155, pp. 176-186.
Hubral P., Schleicher J., Tygel M., Hanitzsch C., Determination of Fresnel zones from traveltime measurements, Geophysics, 1993, vol. 58, pp. 703-712. https://doi.org/10.1190/1.1443454
Kondrat'ev O.K., Resolution of seismic exploration MOV-OGT, Geofizika (Geophysics), 2006, no. 2, pp. 3-12. [In Russian].
Kravtsov Yu.A., Orlov Yu.I., Limits of applicability of the method of geometric optics and related problems, Sov. Phys. Usp., 1980a, vol. 23, pp. 750-762.
Kravtsov Yu.A., Orlov Yu.I., Geometricheskaja optika neodnorodnyh sred (Geometric optics of inhomogeneous media), Moscow, Nauka, 1980b, 304 p. [In Russian].
Lazaratos S.K., Harris J.M., Rector J.W., Van Schaack M., High resolution cross well imaging of a west Texas carbonate reservoir. Part 4. Reflection imaging, Geophysics, 1995, vol. 60, pp. 702-711. https://doi.org/10.1190/1.1822130
Li V.O., Vladov M.L., Efficiency of 2D CDP during section subsurface investigations, Moscow University Geol-ogy Bulletin, 2012, vol. 67, no. 3, pp. 193-201. DOI: 10.3103/S0145875212030039
Lisin V.P., Chugaev A.V., Sanfirov I.A., Potentially dangerous zones investigation on the mine fields by methods of ground and borehole seismic, in Inzhenernaja i rudnaja geofizika 2018. Almaty, Kazahstan, 23-27 aprelja (Engineering and Ore Geophysics 2018. Almaty, Kazakhstan, April 23-27), Netherlands, EAGE Publishing BV, 2018, pp.1-12. [In Russian]. DOI: 10.3997/2214-4609.201800521
Liu Y., Dong L., Wang Y., Zhu J., Ma Z., Sensitivity kernels for seismic Fresnel volume tomography, Geophysics, 2009, vol. 74, pp. U35-U46. https://doi.org/10.1190/1.3169600
Matskovskiy A.A., Interference head wave in diffraction of waves from a point source by an inhomogeneous half-plane, Computational Mathematics and Mathematical Physics, 2015, vol. 55, pp. 1867-1883.
Matskovskiy A.A., Wave front sets of the Buldyrev head wave and whispering gallery waves, Journal of Math-ematical Sciences, 2016, vol. 214, pp. 337-343. https://doi.org/10.1007/s10958-016-2781-6
Pica A., Fast and accurate finite difference solution of the 3D eikonal equation parameterized in celerity, in 67th Annual International Meeting, SEG, Exp. Abstr., 1997, pp. 774-1777. https://doi.org/10.1190/1.1885777
Podvin P., Lecomte I., Finite difference computation of traveltimes in very contrasted velocity models: a mas-sively parallel approach and its associated tools, Geophysical Journal International, 1991, vol. 105, pp. 271-284. http://dx.doi.org/10.1111/j.1365-246X.1991.tb03461.x
Rawlinson N., Sambridge M., Wave front evolution in strongly heterogeneous layered media using the fast marching method, Geophysical Journal International, 2004, vol. 156, pp. 631-647. https://doi.org/10.1111/j.1365-246X.2004.02153.x
Sanfirov I.A., Chugaev A.V., Babkin A.I., Lisin V.P., Bobrov V.Y., Minetechnical applications of seismic in shal-low wells, Geofizika (Geophysics), 2018, no. 5, pp. 24-30. [In Russian].
Schuster G.T., Quintus-Bosz A., Wavepath eikonal traveltime inversion: Theory, Geophysics, 1993, vol. 58, pp. 1314-1323. https://doi.org/10.1190/1.1443514
Sheriff R.E., Nomogram for Fresnel-zone calculation, Geophysics, 1980, vol. 45, pp. 968-972. https://doi.org/10.1190/1.1441101
Shishkina M.A., Fokin I.V., Tikhotskiy S.A., Resolution of cross-well travel-time tomography, Tehnologii sejsmorazvedki (Seismic exploration technologies), 2015, no.1, pp. 5-21. [In Russian]. http://dx.doi.org/10.18303/1813-4254-2015-1-5-21
Spetzler J., Snieder R., The effect of small-scale heterogeneity on the arrival time of waves, Geophysical Journal International, 2001, vol. 145, pp. 786-796. https://doi.org/10.1046/j.1365-246x.2001.01438.x
Spetzler J., Snieder R., The Fresnel volume and transmitted waves, Geophysics, 2004, vol. 69, pp. 653-663. https://doi.org/10.1190/1.1759451
Spetzler J., Šijačić D., Wolf K., Application of a linear finite-frequency theory to time-lapse crosswell tomogra-phy in ultrasonic and numerical experiments, Geophysics, 2007, vol. 72, pp. O19-O27. https://doi.org/10.1190/1.2778767
Tverdohlebov D.N., Korolev E.K., Practice of using the 1st Fresnel zone in seismic exploration, in 5th EAGE In-ternational Scientific and Practical Conference and Exhibition on Engineering and Mining Geophysics. Gelendzhik, Russia, Netherlands, EAGE Publishing BV, 2009, pp. 1-4. [In Russian]. https://doi.org/
10.3997/2214-4609.20147351
Vasco D.W., Nihei K.T., A trajectory mechanics approach for the study of wave propagation in an anisotropic elastic medium, Geophysical Journal International, 2019, vol. 219, pp. 1885-1899.
Vasco D.W., Peterson J.E., Majer E.L., Beyond ray tomography: wave paths and Fresnel volumes, Geophysics, 1995, vol. 60, pp. 1790-1804.
Vidale J., Finite-difference calculation of traveltimes in three dimensions, Geophysics, 1990, vol. 55, pp. 521-526. http://dx.doi.org/10.1190/1.1442863
Vidale J.E., Finite-difference traveltime calculation, Bull. Seis. Soc. Am., 1988, vol. 78, pp. 2062-2076. https://
doi.org/10.1785/BSSA0780062062
Vladov M.L., Struchkov V.A., Sudakova M.S., Shmurak D.V., Tomographic surveying at large cross-well dis-tances: negative factors, Inzhenernye izyskanija (Engineering Survey), 2020, vol. 14, no. 2, pp. 42-51. [In Russian]. DOI: 10.25296/1997-8650-2020-14-2-42-51
Watanabe T., Matsuoka T., Ashida Y., Seismic traveltime tomography using Fresnel volume approach, in 69th Annual International Meeting, SEG Expanded Abstracts, 1999, pp. 1402-1405. https://doi.org/10.1190/1.1820777
Xu S., Zhang Y., Huang T., Enhanced tomography resolution by a fat ray technique, in 76th Annual Interna-tional Meeting, SEG Expanded Abstracts, 2006, pp. 3354-3358. https://doi.org/10.1190/1.2370229
Zavalishin B.R., The use of first Fresnel zone radius in seismic exploration, Geofizika (Geophysics), 2008, no. 5, pp. 3-7. [In Russian].
Zhang L., Rector J.W., Hoversten G.M., Eikonal solver in the celerity domain, Geophysical Journal Internation-al, 2005, vol. 162, pp. 1-8. http://dx.doi.org/10.1111/j.1365-246X.2005.02626.x
