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Journal articles on the topic 'Mathematical geophysics'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 March 2023

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1

Temirbekova, L. N., N. M. Temirbekov, V. L. Los, Ye I. Imangaliyev, D. R. Baigereyev, and M. B. Nurmangalieva. "A MODULE OF A GEOINFORMATION SYSTEM BASED ON NUMERICAL MODELING OF INVERSE PROBLEMS OF GEOCHEMISTRY BY REGULARIZING ALGORITHMS." Bulletin Series of Physics & Mathematical Sciences 75, no. 3 (September 15, 2021): 15–28. http://dx.doi.org/10.51889/2021-3.1728-7901.02.

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Currently, due to the rapid development of computer technology in geology, methods and approaches of scientific visualization based on additional data analysis are being intensively developed. The general concept is that the main data field on the daily surface and additional conditions are set at the input. Further, methods of mathematical geophysics are used for their analysis and processing, as a result of which new information is obtained for deep surveys. Then, in the information system, visualization tools are applied to the new information received and to the main data field. Thus, the information system is based on the synthesis of visual representation methods and methods of mathematical geophysics, computational mathematics from different branches of knowledge. This paper presents a description of the software module of the geoinformation system, based on the methods of intelligent detection of anomalies of hidden deposits, for deep predictive and search modeling of deposits. The functioning of the software module is based on the application of the theory of inverse problems of mathematical geophysics with elements of artificial intelligence using geological data on the earth's surface, geophysical measurements and geochemical analyses as input data. The program module for the inverse problem of the continuation of potential fields in the direction of disturbing masses is used for real data of a specific mineral deposit.

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Gurefe, Yusuf, Yusuf Pandir, and Tolga Akturk. "On the Nonlinear Mathematical Model Representing the Coriolis Effect." Mathematical Problems in Engineering 2022 (September 26, 2022): 1–12. http://dx.doi.org/10.1155/2022/2504907.

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In this study, the traveling wave solutions of a nonlinear partial differential equation (NPDE) called as Geophysics Korteweg-de Vries (GpKdV) equation are obtained using the modified exponential function method (MEFM). Coriolis effect is stated with the help of this model used in geophysics. The nonlinear model has a Coriolis coefficient representing this effect.

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Kogan, L. I. "EXPEDITIONS AND RESEARCHES OF MARINE GEOPHYSICS YU.P. NEPROCHNOV." Journal of Oceanological Research 48, no. 2 (August 28, 2020): 208–24. http://dx.doi.org/10.29006/1564-2291.jor-2020.48(2).16.

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This article is dedicated to the anniversary of geophysicist, doctor of physical and mathematical sciences, Professor Yuri Pavlovich Neprochnov, who would turn 90 years old this year. Prof. Neprochnov created a school of seismic marine geologists. He had numerous students, who prepared and successfully defended 12 Ph.D., and D.Sc. dissertations under his leadership. He is the author and co-author of more than 400 scientific articles and 18 monographs. Neprochnov was a Member of the Second World War, a Member of the Scientific Council of the Russian Academy of Sciences on the problems of the oceans, where he led the working group on seismic and integrated geophysics; Coordinator of International projects for scientific cooperation with India, China and Finland, a Member of the Editorial board of the Journal «Oceanology», was elected a full Member of the Russian Academy of Natural Sciences and a Member of the New York Academy of Sciences, and in 2002 for his labor successes and a great contribution to strengthening friendship and cooperation between peoples he was awarded the title of Honored Scientist of the Russian Federation. His friend and colleague in scientific geophysical research L.I. Kogan recalls years of teamwork and expresses his appreciation for professional friendships throughout his life.

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4

Moorkamp, Max. "Research resource review: Mathematical methods for geophysics and space physics." Progress in Physical Geography: Earth and Environment 41, no. 2 (April 2017): 243–44. http://dx.doi.org/10.1177/0309133317704051.

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5

Buchen, P. W. "Seismic Migration And Mathematical Mapping." Exploration Geophysics 22, no. 1 (March 1991): 55–58. http://dx.doi.org/10.1071/eg991055.

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6

Løseth, Lars O., Hans M. Pedersen, Bjørn Ursin, Lasse Amundsen, and Svein Ellingsrud. "Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?" GEOPHYSICS 71, no. 4 (July 2006): W29—W40. http://dx.doi.org/10.1190/1.2208275.

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Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.

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7

Peng, Liangrong, and Liu Hong. "Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes." Entropy 23, no. 11 (October 31, 2021): 1447. http://dx.doi.org/10.3390/e23111447.

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The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

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8

Kubáčková, Ludmila. "Mathematical geophysics. A survey of recent developments in seismology and geodynamics." Tectonophysics 172, no. 3-4 (February 1990): 370–71. http://dx.doi.org/10.1016/0040-1951(90)90044-9.

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9

Shore, K. Alan. "Mathematical methods for geophysics and space physics, by William I. Newman." Contemporary Physics 58, no. 1 (November 23, 2016): 113–14. http://dx.doi.org/10.1080/00107514.2016.1259256.

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10

Li, Zhenhua, and Mirko van der Baan. "Tutorial on rotational seismology and its applications in exploration geophysics." GEOPHYSICS 82, no. 5 (September 1, 2017): W17—W30. http://dx.doi.org/10.1190/geo2016-0497.1.

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Traditionally, seismological interpretations are based on the measurement of only translational motions, such as particle displacement, velocity, and/or acceleration, possibly combined with pressure changes; yet theory indicates that rotational motions should also be observed for a complete description of all ground motions. The recent and ongoing development of rotational sensors renders a full analysis of the translational and rotational ground motion possible. We have developed the basic mathematical theory related to rotational motion. And we also evaluated several instruments used to directly measure the rotational ground motion, which may be applicable for exploration geophysics. Finally, we made several applications of rotational motion in exploration geophysics, namely, (1) P- and S-wavefield separation, (2) wavefield reconstruction, (3) ground-roll removal, (4) microseismic event localization and reflection seismic migration by wavefield extrapolation, and (5) moment tensor inversion. The cited research shows that in particular, the information on the spatial gradient of the wavefield obtained by rotational sensors is beneficial for many purposes. This tutorial is meant to (1) enhance familiarity with the concept of rotational seismology, (2) lead to additional applications, and (3) fast track the continued development of rotational sensors for global and exploration geophysical use.

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11

Nikitenko, M. N., V. N. Glinskikh, and D. I. Gornostalev. "Mathematical Substantiation of Pulsed Electromagnetic Soundings for New Problems of Petroleum Geophysics." Numerical Analysis and Applications 14, no. 2 (April 2021): 155–66. http://dx.doi.org/10.1134/s1995423921020051.

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12

Lanzoni, Stefano. "Mathematical modelling of bedload transport over partially dry areas." Acta Geophysica 56, no. 3 (July 2, 2008): 734–52. http://dx.doi.org/10.2478/s11600-008-0033-y.

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13

Závoti, J., J. Somogyi, J. Kalmár, and L. Battha. "Research in mathematical geodesy." Acta Geodaetica et Geophysica Hungarica 40, no. 3-4 (October 2005): 283–92. http://dx.doi.org/10.1556/ageod.40.2005.3-4.3.

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14

Tenzer, Robert, Peter Vajda, and Peter Hamayun. "A mathematical model of the bathymetry-generated external gravitational field." Contributions to Geophysics and Geodesy 40, no. 1 (January 1, 2010): 31–44. http://dx.doi.org/10.2478/v10126-010-0002-8.

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A mathematical model of the bathymetry-generated external gravitational field The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and other major known density contrasts within the Earth's crust. The currently available data of global crustal density structures have, however, a very low resolution and accuracy. The compilation of the global crust density contrast stripped gravity field is thus limited to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this study we derive the expressions used in forward modelling of the bathymetry-generated gravitational field quantities and the corresponding bathymetric stripping corrections to gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The expressions for the potential and its radial derivative are formulated for the adopted constant (average) ocean saltwater density contrast and for the spherical approximation of the geoid surface. These newly derived expressions are utilized in numerical examples to compute the gravitational potential and attraction generated by the ocean density contrast. The computation is realized globally on a 1 x 1 arc-deg geographical grid at the Earth's surface.

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15

Kurgansky, V. ""GEOPHYSICAL RESEARCHES OF MINING HOLES" – 50 YEARS AT TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 1 (84) (2019): 89–94. http://dx.doi.org/10.17721/1728-2713.84.13.

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Development of carotage (retrospective years 1969-2019) at Taras Shevchenko National University of Kyiv is described. Basic achievements are shown in educational and scientific directions. Carbonate rocks methodology study problems, petrophysical models which allowed building physically well-founded dependences of "core-core", "core-geophysics", "geophysics- geophysics" type are described. Petrophysical simulation, theory of probability and mathematical statistics methods allowed the author to work out a complex system of data processing and interpretation in welllogging. Current status and tendency in dataware drilling process of the deep oil and gas wells are examined. Absolutely new ideology of operative getting of the reliable directional survey data without special logging services (telesystem in the process of drilling, autonomous inclinometer and other) is proposed.

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16

Kumar Patidar, Ashok, Vikas Prajapat, and Vishal Kumar. "A theoretical study of fluid mechanics and its mathematical model with physical interpretation." Material Science Research India 7, no. 2 (February 8, 2010): 505–8. http://dx.doi.org/10.13005/msri/070224.

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In this paper we have studied of fluid Mechanics and Mathematical models for different kinds of fluids with their physical interpretation, we have analysed importance of fluid mechanics and its important role in the study of astrophysical situation, Meteorology, Osceanography, Geophysics and its numerous application in allmost all branches of engineering and technology.

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17

Muir, Jack B., and Victor C. Tsai. "Geometric and level set tomography using ensemble Kalman inversion." Geophysical Journal International 220, no. 2 (October 21, 2019): 967–80. http://dx.doi.org/10.1093/gji/ggz472.

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SUMMARY Tomography is one of the cornerstones of geophysics, enabling detailed spatial descriptions of otherwise invisible processes. However, due to the fundamental ill-posedness of tomography problems, the choice of parametrizations and regularizations for inversion significantly affect the result. Parametrizations for geophysical tomography typically reflect the mathematical structure of the inverse problem. We propose, instead, to parametrize the tomographic inverse problem using a geologically motivated approach. We build a model from explicit geological units that reflect the a priori knowledge of the problem. To solve the resulting large-scale nonlinear inverse problem, we employ the efficient Ensemble Kalman Inversion scheme, a highly parallelizable, iteratively regularizing optimizer that uses the ensemble Kalman filter to perform a derivative-free approximation of the general iteratively regularized Levenberg–Marquardt method. The combination of a model specification framework that explicitly encodes geological structure and a robust, derivative-free optimizer enables the solution of complex inverse problems involving non-differentiable forward solvers and significant a priori knowledge. We illustrate the model specification framework using synthetic and real data examples of near-surface seismic tomography using the factored eikonal fast marching method as a forward solver for first arrival traveltimes. The geometrical and level set framework allows us to describe geophysical hypotheses in concrete terms, and then optimize and test these hypotheses, helping us to answer targeted geophysical questions.

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18

Turcotte, D. L., H. Ockendon, J. R. Ockendon, and S. J. Cowley. "A mathematical model of vulcanian eruptions." Geophysical Journal International 103, no. 1 (October 1990): 211–17. http://dx.doi.org/10.1111/j.1365-246x.1990.tb01763.x.

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19

Correia, António. "Mathematical methods for geo-electromagnetic induction." Tectonophysics 244, no. 4 (April 1995): 286–87. http://dx.doi.org/10.1016/0040-1951(95)90040-3.

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20

Aniszewski, Andrzej. "Particular application of a mathematical transport model incorporating sub-surface reactive pollutants." Acta Geophysica 59, no. 1 (October 28, 2010): 110–23. http://dx.doi.org/10.2478/s11600-010-0040-7.

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21

Ouchi, Toru. "Population dynamics of earthquakes and mathematical modeling." Pure and Applied Geophysics PAGEOPH 140, no. 1 (1993): 15–28. http://dx.doi.org/10.1007/bf00876868.

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22

Menke, W. ""A Guided Tour of Mathematical Methods for the Physical Sciences" by Roel Snieder." Seismological Research Letters 73, no. 1 (January 1, 2002): 94–95. http://dx.doi.org/10.1785/gssrl.73.1.94.

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23

Gazi, Ainal Hoque, and Mohammad Saud Afzal. "A new mathematical model to calculate the equilibrium scour depth around a pier." Acta Geophysica 68, no. 1 (November 4, 2019): 181–87. http://dx.doi.org/10.1007/s11600-019-00383-2.

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24

Li, Guang, Xiaoqiong Liu, Jingtian Tang, Jin Li, Zhengyong Ren, and Chaojian Chen. "De-noising low-frequency magnetotelluric data using mathematical morphology filtering and sparse representation." Journal of Applied Geophysics 172 (January 2020): 103919. http://dx.doi.org/10.1016/j.jappgeo.2019.103919.

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25

Li, Guang, Xiao Xiao, Jing-Tian Tang, Jin Li, Hui-Jie Zhu, Cong Zhou, and Fa-Bao Yan. "Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering." Applied Geophysics 14, no. 4 (December 2017): 581–89. http://dx.doi.org/10.1007/s11770-017-0645-6.

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26

Karinskiy, A. D., and A. A. Krasnosel’skikh. "Mathematical and physical modeling to justify a new geophysical method—electrical anisotropy logging." Russian Geology and Geophysics 59, no. 9 (September 2018): 1192–200. http://dx.doi.org/10.1016/j.rgg.2018.08.012.

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27

SEN, P. N. "A mathematical model for QPF for flood Forecasting purposes." MAUSAM 42, no. 2 (February 28, 2022): 201–4. http://dx.doi.org/10.54302/mausam.v42i2.3152.

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A mathematical, model for Quantitative Precipitation Forecasting (QPF) has been developed on the basis of physical and dynamical laws. The surface and upper air meteorological observations have been used as inputs in the model. The output is the rate of precipitation from which the amount of precipitation can be computed time integration. The model can be used operationally for rainfall forecasting.

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28

SINHA, D. K., BRATATI BANERJI, and SUTAPA CHAUDHURI. "A mathematical model on the suppression of hail growth." MAUSAM 41, no. 1 (February 22, 2022): 31–36. http://dx.doi.org/10.54302/mausam.v41i1.2272.

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This paper presents essentially a dynamic model on the suppression of hail growth in mathe matical terms. The interaction between the hygroscopic seeding and microphysical parameters are considered and their effects on the total amount of hail and rainfall available at the surface are investigated. The present model reveals some important charlatanistic features on the control of the growth of a hailstone. Correlations are observed between seeding and embryo radius as well as between seeding and the density of the hailstone. The concentration of ice is found to reduce sufficiently in the seeded case with a possibility of less availability of hail at the surface. The present model is compared with the model developed by the same group of authors (Banerji et al. loc. cit.). It is found that the hygroscopic seeding controls the growth of hailstone.

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29

Ramm, A. G. "Some inverse scattering problems of geophysics." Inverse Problems 1, no. 2 (May 1, 1985): 133–72. http://dx.doi.org/10.1088/0266-5611/1/2/005.

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30

Petrovič, Dušan. "Mathematical Elements of Orienteering Maps." Kartografija i geoinformacije 21 (January 3, 2023): 126–47. http://dx.doi.org/10.32909/kg.21.si.9.

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Mathematical elements of maps, in addition to the methods of presenting content with cartographic symbols and the criteria of cartographic generalization, are the most important elements of modern ground plan view maps. At the same time, on maps for orienteering disciplines, which are the most internationally unified maps in the world, the mathematical basis is not defined in very detailed specifications. In this paper, we describe the background and reasons for the apparent insignificance of mathematical content in orienteering maps, and on the example of the analysis of selected maps of Croatia and Slovenia, we determine in which period and to what extent mathematical elements were present on the maps.

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31

Iren-Adelina Moldovan, Angela Petruta Constantin, Raluca Partheniu, Bogdan Grecu, and Constantin Ionescu. "Relationships between macroseismic intensity and peak ground acceleration and velocity for the Vrancea (Romania) subcrustal earthquakes." Annals of Geophysics 64, no. 4 (November 16, 2021): SE432. http://dx.doi.org/10.4401/ag-8448.

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The goal of this paper is to develop a new empirical relationship between observed macroseismic intensity and strong ground motion parameters such as peak ground acceleration (PGA) and velocity (PGV) for the Vrancea subcrustal earthquakes. The recent subcrustal earthquakes provide valuable data to examine these relationships for Vrancea seismogenic region. This region is one of the most active seismic zones in Europe and it is well-known for the strong subcrustal earthquakes. We examine the correlation between the strong ground-motion records and the observed intensities for major and moderate earthquakes with Mw ≥ 5.4 and epicentral intensity in the range VI to IX MSK degrees that occurred in Vrancea zone in the period 1977-2009. The empirical relationships between maximum intensity and ground parameters obtained and published by various authors have shown that these parameters do not always show a one-to-one correspondence, and the errors associated with the intensity estimation from PGA/PGV are sometimes +/-2 MSK degree. In the present study, the relation between macroseismic intensity and PGA/PGV will be given both as a mathematical equation, but also as corresponding ground motion intervals. Because of the intensity data spreading and errors related to mathematical approximations, it is necessary to systematically monitor not only the acceleration and velocity but also all the other ground motion parameters. The mathematical relation between these parameters might be used for the rapid assessment of ground shaking severity and potential damages in the areas affected by the Vrancea earthquakes.

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32

Peltier, W. R., D. Rothman, R. Snieder, and A. Sornette. "20th international conference on mathematical geophysics "Complex space-time geophysical structures", June 19-24, 1994, La Citadelle, Villefranche sur mer, France." Nonlinear Processes in Geophysics 2, no. 3/4 (December 31, 1995): 107–8. http://dx.doi.org/10.5194/npg-2-107-1995.

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33

Spiegelman, Marc, Daniel H. Rothman, Einat Aharonov, and Vladimir Lyakhovsky. "The 26th IUGG Conference on Mathematical Geophysics Sea of Galilee, Israel, 4-8 June 2006." Israel Journal of Earth Sciences 56, no. 1 (December 1, 2007): i—ii. http://dx.doi.org/10.1560/ijes.56.1.i.

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34

Mavroeidis, G. P. "A Mathematical Representation of Near-Fault Ground Motions." Bulletin of the Seismological Society of America 93, no. 3 (June 1, 2003): 1099–131. http://dx.doi.org/10.1785/0120020100.

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35

Heuer, Norbert, Tassilo Küpper, and Dirk Windelberg. "Mathematical model of a Hot Dry Rock system." Geophysical Journal International 105, no. 3 (June 1991): 659–64. http://dx.doi.org/10.1111/j.1365-246x.1991.tb00803.x.

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36

Arsen’yev, Sergey A., Lev V. Eppelbaum, and Tatiana B. Meirova. "Discrete Mathematical Model of Earthquake Focus: An Introduction." Pure and Applied Geophysics 177, no. 9 (April 23, 2020): 4097–118. http://dx.doi.org/10.1007/s00024-020-02485-1.

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37

Huang, Weilin, and Runqiu Wang. "Random noise attenuation by planar mathematical morphological filtering." GEOPHYSICS 83, no. 1 (January 1, 2018): V11—V25. http://dx.doi.org/10.1190/geo2017-0288.1.

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Improving the signal-to-noise ratio (S/N) of seismic data is desirable in many seismic exploration areas. The attenuation of random noise can help to improve the S/N. Geophysicists usually use the differences between signal and random noise in certain attributes, such as frequency, wavenumber, or correlation, to suppress random noise. However, in some cases, these differences are too small to be distinguished. We used the difference in planar morphological scales between signal and random noise to separate them. The planar morphological scale is the information that describes the regional shape of seismic waveforms. The attenuation of random noise is achieved by removing the energy in the smaller morphological scales. We call our method planar mathematical morphological filtering (PMMF). We analyze the relationship between the performance of PMMF and its input parameters in detail. Applications of the PMMF method to synthetic and field post/prestack seismic data demonstrate good performance compared with competing alternative techniques.

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38

Kirchner, Helmut. "Book Review A Mathematical Approach by F. Cap." Pure and Applied Geophysics 166, no. 4 (April 2009): 723–24. http://dx.doi.org/10.1007/s00024-009-0467-4.

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39

Xiong Liang-Ping, Zhang Ju-Ming, and Sun Hui-wen. "Mathematical simulation of geotemperature and heat flow patterns." Journal of Geodynamics 4, no. 1-4 (December 1985): 45–61. http://dx.doi.org/10.1016/0264-3707(85)90051-1.

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40

Waltham, David. "Mathematical modelling of sedimentary basin processes." Marine and Petroleum Geology 9, no. 3 (June 1992): 265–73. http://dx.doi.org/10.1016/0264-8172(92)90075-p.

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41

Perrone, Francesco, and Niels Grobbe. "Introduction to this special section: Full-waveform inversion." Leading Edge 42, no. 3 (March 2023): 152–54. http://dx.doi.org/10.1190/tle42030152.1.

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The estimation of the parameters of a mathematical model by data-fitting procedures goes back more than 200 years. Mathematics historians seem to agree to credit C. F. Gauss for the introduction of this idea ( Gauss, 2011 ). In the field of exploration geophysics, Lailly (1983) and Tarantola (1984) were the first to propose the use of data-fitting techniques to estimate model parameters that control the propagation of waves in the subsurface. The concept of full-waveform inversion (FWI) was born.

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42

Russell, Brian. "Machine learning and geophysical inversion — A numerical study." Leading Edge 38, no. 7 (July 2019): 512–19. http://dx.doi.org/10.1190/tle38070512.1.

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As geophysicists, we are trained to conceptualize geophysical problems in detail. However, machine learning algorithms are more difficult to understand and are often thought of as simply “black boxes.” A numerical example is used here to illustrate the difference between geophysical inversion and inversion by machine learning. In doing so, an attempt is made to demystify machine learning algorithms and show that, like inverse problems, they have a definite mathematical structure that can be written down and understood. The example used is the extraction of the underlying reflection coefficients from a synthetic seismic response that was created by convolving a reflection coefficient dipole with a symmetric wavelet. Because the dipole is below the seismic tuning frequency, the overlapping wavelets create both an amplitude increase and extra nonphysical reflection coefficients in the synthetic seismic data. This is a common problem in real seismic data. In discussing the solution to this problem, the topics of deconvolution, recursive inversion, linear regression, and nonlinear regression using a feedforward neural network are covered. It is shown that if the inputs to the deconvolution problem are fully understood, this is the optimal way to extract the true reflection coefficients. However, if the geophysics is not fully understood and large amounts of data are available, machine learning can provide a viable alternative to geophysical inversion.

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Tsyfra, Ivan, and Tomasz Czyżycki. "Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/724238.

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We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.

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Aniszewski, Andrzej. "Mathematical modeling and practical verification of groundwater and contaminant transport in a chosen natural aquifer." Acta Geophysica 57, no. 2 (February 23, 2009): 435–53. http://dx.doi.org/10.2478/s11600-008-0080-4.

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Ageenkov, E. V., A. A. Sitnikov, and E. N. Vodneva. "Results of Mathematical Simulation of Transient Processes for the Sea Shelf Conditions." Russian Geology and Geophysics 63, no. 7 (July 1, 2022): 802–15. http://dx.doi.org/10.2113/rgg20204260.

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Abstract —Electrical exploration measurements in water areas and on land are carried out to study the electromagnetic (EM) properties of geological formations. A distinctive feature of aquatic electrical exploration is associated with the specific influence of a water column. Numerical calculations of the EM signal of the transient process for electrical lines in the axial region of the source under the conditions of marine waters with a depth of 50 to 250 m are presented in order to demonstrate how an induced polarization (IP) signal manifests itself in a transient process signal on different setups, to identify differences in the manifestation of galvanic induced polarization (GIP) and induction-induced polarization (IIP) in a transient process signal, and to substantiate these differences. The influence of the setup dimensions on the manifestation of IP during a transient process is studied by analyzing a change in the transient signal (ΔU(t)), the final difference of the transient process signal (Δ2U(t)) and transform P1(t) (ratio of these values) for a horizontal electrical setup with a source (AB) 50 to 2000 m in length, a three-electrode measuring line (M1M2M3) 50 to 2000 m in length, a distance between the source centers and the measuring line M1M3 (spacing, r) from 100 to 4000 m. Some of these parameters are used in differential-normalized electrical prospecting (DNME). The comparison of ΔU(t) and Δ2U(t) and their transforms in conducting and conducting-polarizable models under the same conditions is performed. The setup is placed on the surface and inside a conducting medium (a sea shelf water column) with a conducting polarizable base (geologic medium (ground) covered with a water layer). The polarizability of the base is taken into account by introducing a frequency-dependent resistivity using the Cole—Cole equation. It is shown by the calculations performed that the transient process components associated with the formation of an EM field and with GIP and IIP manifest themselves in dissimilar ways on differently sized setups at various depths. In a water area, IP manifests itself in two ways, being associated with both galvanic and eddy currents. In previous practical measurements, IIP was considered to be associated with interference, but this signal is simulated and can be regarded as information about IP. The factor influencing the IP manifestation in a transient process signal is a reduced setup height (hΔ), i.e., a distance between a setup and a sea bottom (polarizable base of the model) attributed to the AB line. Depending on the reduced setup height, the IP signal in transform P1(t) can manifest itself as an ascending branch at later times or appear as a descending branch passing into the negative values of P1. The pulse impact duration and the transient process measurements affect the contrasting manifestation of the polarizable base in the signal, but the measurements performed when the setup is being towed impose certain restrictions. The optimal parameters of the EM survey for IP studies should ensure a sufficient polarization range and the proper quality of measurements. The software used in the calculations was developed by OOO Sibirskaya Geofizicheskaya Nauchno-Proizvodstvennaya Kompaniya.

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Green, William R., Edward S. Krebes, and William A. Sandham. "Reviews." Leading Edge 39, no. 4 (April 2020): 286–87. http://dx.doi.org/10.1190/tle39040286.1.

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The Fossil Fuel Revolution: Shale Gas and Tight Oil, by Daniel Soeder and Scyller Borglum, ISBN 978-0-128-15397-0, 2019, Elsevier, 354 p. Mathematical Methods in the Earth and Environmental Sciences, by Adrian Burd, ISBN 978-1-107-11748-8, 2019, Cambridge University Press, 596 p. Geophysics: A Very Short Introduction, by William Lowrie, ISBN 978-0-198-79295-6, 2018, Oxford University Press, 160 p.

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Fowler, A. C., and C. G. Noon. "Mathematical models of compaction, consolidation and regional groundwater flow." Geophysical Journal International 136, no. 1 (January 1, 1999): 251–60. http://dx.doi.org/10.1046/j.1365-246x.1999.00717.x.

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DASGUPTA, S. P. "MATHEMATICAL ANALYSIS OF D.C. RESISTIVITY SOUNDING OVER A PARABOLOID*." Geophysical Prospecting 35, no. 8 (October 1987): 924–31. http://dx.doi.org/10.1111/j.1365-2478.1987.tb00851.x.

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FURNESS, PETER. "A RECONCILIATION OF MATHEMATICAL MODELS FOR SPONTANEOUS MINERALIZATION POTENTIALS1." Geophysical Prospecting 41, no. 6 (August 1993): 779–90. http://dx.doi.org/10.1111/j.1365-2478.1993.tb00884.x.

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Gouédard, P., L. Stehly, F. Brenguier, M. Campillo, Y. Colin de Verdière, E. Larose, L. Margerin, et al. "Cross-correlation of random fields: mathematical approach and applications." Geophysical Prospecting 56, no. 3 (May 2008): 375–93. http://dx.doi.org/10.1111/j.1365-2478.2007.00684.x.

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