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Assessment of correctness conditionsin kinematic seismic tomography: uncertainty calculation and grid size approximation

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Category: Content №6 2025

Last Updated on 25 December 2025

Published on 30 November -0001

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Authors:

L. Shumlianska*, orcid.org/0000-0003-0234-7916, Global Change Research Group (GCRG), IMEDEA, CSIC-UIB, Esporles, Kingdom of Spain; Institute of geophysics by S. I. Subbotin name, National Academy of Sciences of Ukraine, Kyiv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

O. Kozionova, orcid.org/0000-0002-2563-8719, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

O.Topoliuk, orcid.org/0009-0007-5290-4692, Institute of geophysics by S. I. Subbotin name, National Academy of Sciences of Ukraine, Kyiv, Ukraine

V. Vilarrasa, orcid.org/0000-0003-1169-4469, Global Change Research Group (GCRG), IMEDEA, CSIC-UIB, Esporles, Kingdom of Spain

O. Tripil`ska, orcid.org/0009-0002-2457-2671, Institute of geophysics by S. I. Subbotin name, National Academy of Sciences of Ukraine, Kyiv, Ukraine

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2025, (6): 013 - 022

https://doi.org/10.33271/nvngu/2025-6/013

Abstract:

Purpose. To justify and quantitatively evaluate the characteristic dimensions of regions L within which the linearization of the eikonal equation has a correct solution in the context of kinematic ray tomography based on the principles of geometrical optics.

Methodology. The authors use the theoretical foundations for determining the correctness of solving the seismic problem of the kinematic ray tomography method based on Taylor approximation combined with regularization (the Geyko’s method). To assess the characteristic dimensions of the regions, model seismic profiles, including PANCAKE, as well as global mantle tomography data, are applied. The analysis was carried out using models of the velocity structure of the Earth’s crust and mantle in the Carpathian region, taking into account the main tectonic units.

Findings. The characteristic dimensions of the linearization region, which determine the resolution of the method, vary significantly ‒ from  0.2 km in the crust to ≈100 km in the mantle. It was determined that these sizes mainly depend on the geometry of seismic rays and the velocity structure of the medium. The main factor influencing the size of region L was found to be the size of the time spline window selected when forming one-dimensional travel-time curves in the common midpoint format. It was established that the errors of the kinematic tomography method are errors in estimating the depth of penetration of refracted rays. The paper shows how to calculate these errors and use them to assess the accuracy of the kinematic tomography method in the format of seismic velocities.

Originality. Quantitative criteria are proposed for the applicability of the linearized approach to solving the eikonal equation in heterogeneous media within the framework of the kinematic method using Taylor approximation. For the first time, a survey design network for regional tomography by the kinematic method with the possibility of setting the resolution was calculated. The effect of errors on the method’s results is demonstrated.

Practical value. The study results have important applied significance for optimizing the configurations of seismic observation networks. They allow for a more substantiated parameterization when constructing kinematic models, ensuring a balance between resolution and stability of solutions. The methodology makes it possible to design kinematic tomography surveys using natural sources of seismic waves with predictability of results at a level comparable to deep seismic sounding methods, despite the uneven distribution of sources and receivers.

Keywords: kinematic method, seismic tomography, seismic profiles

References.

1. Wang, Ya. (2017). Seismic Inversion: Theory and Applications. John Wiley & Sons, Ltd. https://doi.org/10.1002/9781119258032

2. Pratt, R. (1999). Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model. Geophysics, 64(3). https://doi.org/10.1190/1.1444598

3. Tsvetkova, T. A. (2015). Two approaches to the problem of ray tomography. Geophysical Journal, 1(37), 121-133. https://doi.org/10.24028/gzh.0203-3100.v37i1.2015.111330

4. Nolet, G., Montelli, R., & Virieux, J. (1999). Explicit, approximate expressions for the resolution and covariance of massive tomographic systems. Geophysical Journal International, 138, 36-44. https://doi.org/10.1046/j.1365-246x.1999.00858.x

5. Nolet, G. (2008). A Breviary of seismic tomography: Imaging the Interior of the Earth and Sun. Cambridge University Press. https://doi.org/10.1121/1.3203995

6. Rawlinson, N., Fichtner, A., Sambridge, M., & Youngjj, M.K. (2014). Chapter One. Seismic Tomography and the Assessment of Uncertainty. Advances in Geophysics, 55, 1-76. https://doi.org/10.1016/bs.agph.2014.08.001

7. Spakman, W., & Nolet, G. (1988). Imaging algorithms, accuracy and resolution in delay time tomography. In Vlaar, N. J., Nolet, G., Wortel, M. J. R., & Cloetingh, S. A. P. L. (Eds.) Mathematical Geophysics. Modern Approaches in Geophysics, 3, (pp. 155-187). Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2857-2_8

8. Geyko, V. S. (2004). A general theory of the seismic traveltime tomography. Geophysical Journal, 26(2), 3-32. Retrieved from http://www.igph.kiev.ua/eng/journal/2004/n2/1.html

9. Burmin, V. Yu. (2012). Inverse kinematic problems of seismology: New approaches and results. Saarbrücken, Germany: Palmar. Acad. Publ. https://doi.org/10.13140/RG.2.1.4421.3364

10.      Solimeno, S., Crosignani, B., & Di Porto, P. (1986). Guiding, Diffraction and Confinement of Optical Radiation. New York: Academic Press. Retrieved from https://www.scirp.org/reference/referencespapers?referenceid=70612

11.      Starostenko, V., Janik, T., Kolomiyets, K., Czuba, W., Środa, P., Grad, M., Kovács, I., …, & Tolkunov, A. (2013). Seismic velocity model of the crust and upper mantle along profile PANCAKE across the Carpathians between the Pannonian Basin and the East European Craton. Tectonophysics, 608, 1049-1072.

12.      Starostenko, V. I., & Gintov, O. B. (Eds.) (2018). Essays of Ukraine’s geodynamics. Kyiv.

13.      Kovács, I., Falus, Gy., Stuart, G., Hidas, K., Szabó, Cs., Flower, M. F. J., Hegedűs, E., Posgay, K., & Zilahi-Sebess, L. (2012). Seismic anisotropy and deformation patterns in upper mantle xenoliths from the central Carpathian–Pannonian region: Asthenospheric flow as a driving force for Cenozoic extension and extrusion? Tectonophysics, 514-517, 168-179. Retrieved from https://www.researchgate.net/publication/255718389_Seismic_velocity_model_of_the_crust_and_upper_mantle_along_profile_PANCAKE_across_the_Carpathians_between_the_Pannonian_Basin_and_the_East_European_Craton

14.      Geyko, V. S., Shumlianska, L. O., Bugaienko, I. V., Zaets, L. N., & Tsvetkova, T. A. (2006). Three-dimensional model of the upper mantle of Ukraine by the terms of P-waves arrival. Geophysical Journal, 28(1), 3-16. https://doi.org/10.24028/gzh.0203-3100.v34i1.2012.116573

15.      Kissling, E. (1988). Geotomography with local earthquake data. Reviews of Geophysics, 26(4), 659-698. https://doi.org/10.1029/RG026i004p00659

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