journal article·2023-09-14Open access

New Empirical Laws in Geosciences: A Successful Proposal

Jesús Díaz-Curiel, Bárbara Biosca, Lucía Arévalo-Lomas, David Paredes-Palacios, María Jesús Miguel

Applied Sciences· Volume 13· Issue 18

Abstract

The importance of empirical versus theoretical laws is a controversial issue in many scientific fields, the latter being generally accepted and the relevance of which is not discussed here. As in other areas, there are well-known theoretical and empirical formulas in geosciences that do not adequately represent the reality of a given phenomenon. Quantitative comparison of geophysical and petrophysical results with data from the other multiple fields that comprise the geosciences compels a high exigency to avoid discontinuities in existing relationships. However, the proposal of new empirical laws that more accurately reflect a given phenomenon is often considered insufficient to contradict existing formulas. The aim of this work is to defend the development of new empirical laws by showing that they constitute a true model of analysed behaviour if certain criteria are followed. This defence is especially needed when non-linearisable functions are required to fit the empirical data. To achieve this aim, this study shows the established algebraic function as a function of a single variable, whose main advantage is its application to phenomena of a geological nature that show two differentiated behaviours as the variable x is increased. A series of five examples of different phenomena related to geosciences is selected to demonstrate the level of accuracy that new empirical laws can reach in contrast to the widely accepted historical relationships.
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Research context

OpenAlex topics: Geophysical and Geoelectrical Methods · Seismic Imaging and Inversion Techniques · NMR spectroscopy and applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Energy and Fuels, School of Mines and Energy, Universidad Politécnica de Madrid, C/Ríos Rosas 21, 28003 Madrid, Spain

Department of Geological and Mining Engineering, School of Mines and Energy, Universidad Politécnica de Madrid, C/Ríos Rosas 21, 28003 Madrid, Spain

Spanish Ministry of Science and Innovation, Paseo de la Castellana 162, 28046 Madrid, Spain

Funding

“Comunidad de Madrid” Regional Government of Madrid, Spain

References (35)

Show source-provided references
1. Ensemble smoother with multiple data assimilation as a tool for curve fitting and parameter uncertainty characterization: Example applications to fit nonlinear sorption isotherms10.1007/s11004-021-09981-7 ↗
2. Nigmatullin, R., Dorokhin, S., and Ivchenko, A. (2021). Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems. Math, 9.10.3390/math9040381 ↗
3. Geophysical Estimation of Permeability in Sedimentary Media with Porosities from 0 to 50%
4. Improving some Basic Relationships of Pipe Hydraulics. Application for Processing Flowmeter Logs in Water Wells10.1016/j.flowmeasinst.2020.101698 ↗
5. Advance in the penetrometer test formulation to estimate allowable pressure in granular soils10.1007/s11440-017-0565-x ↗
6. Estimation of hydraulic transmissivity from MRS by varying the porosity exponent, in detrital aquifers of the Iberian Peninsula10.1002/nsg.12003 ↗
7. Environmental correction of gamma ray logs by geometrical/empirical factors10.1016/j.petrol.2018.10.056 ↗
8. Dalmont, V. (1856). Détermination des Lois D’écoulement de l’eau a Travers le Sable. Les Fontaines Publiques de la Ville de Dijon, Appendis, Note D.
9. Introduction to petrophysics of reservoir rocks
10. Poiseuille, J.L. (1844). Recherches Expérimentales sur le Mouvement des Liquides dans les Tubes de Très-Petits Diamètres, Imprimerie Royale.
11. Effect of impregnating waters on electrical conductivity of soils and rocks
12. Díaz-Curiel, J. (2000). Theory and Practice of Geophysical Prospecting.
13. Failure of the Conventional Expression of Tortuosity in Granular Porous Solids10.1007/s10712-021-09645-5 ↗
14. Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws10.1680/ijoti.1939.13150 ↗
15. Water storage mapping of pyroclastic covers through electrical resistivity measurements10.1016/j.jappgeo.2011.07.009 ↗
16. A combined use of Archie and van Genuchten models for predicting hydraulic conductivity of unsaturated pyroclastic soils10.1016/j.jappgeo.2014.12.002 ↗
17. Energy dissipation-based method for strength determination of rock under uniaxial compression
18. Attenuation of seismic waves in partially saturated Berea sandstone as a function of frequency and confining pressure10.3389/feart.2021.641177 ↗
19. Quality control of the initial magnetotelluric data: Analysis of calibration curves using a fitting function represented by the ratio of 4th-order polynomials10.1016/j.measurement.2023.112914 ↗
20. Yu, Y., and Loskot, P. (2023). Polynomial Distributions and Transformations. Measurement, 11.10.3390/math11040985 ↗
21. Uber die kapillare leitung des wassers im boden-aufstieg versickerung und anwendung auf die bewässerung, Sitzungsberichte der Wiener Akademie der Wissenschaften
22. New granulometric expressions for estimating permeability of granular drainages10.1007/s10064-022-02897-4 ↗
23. Transverse relaxation processes in porous sedimentary rock10.1016/0022-2364(90)90104-H ↗
24. On the Validity of the Relationship 1/T= 1/TB+ 1/TS+ 1/TD in NMR Techniques with Regards to Permeability Estimation of Natural Porous Media10.3389/feart.2021.688686 ↗
25. Díaz-Curiel, J. (1995). Interpretación y correlación automáticas de diagrafías geofísicas. Aplicación a la hidrogeología en el sur de la Cuenca del Duero. [Ph.D. Thesis, Universidad Politécnica de Madrid].
26. Bowles, J.E. (1997). Foundation Analysis and Design, McGraw-Hill. [5th ed.].
27. Terzaghi, K., and Peck, R.B. (1967). Soil Mechanics in Engineering Practice, Wiley. [2nd ed.].
28. Seevers, D.O. (1966, January 9–13). A nuclear magnetic method for determining the permeability of sandstones. Proceedings of the Transactions on SPWLA 7th Annual Logging Symposium, Houston, TX, USA.
29. A three-part study of NMR longitudinal relaxation properties of water-saturated sandstones10.2118/15643-PA ↗
30. Gesetzmässigkeiten der Turbulenten Strömung in Glatten Rohren
31. Über Die Bewegung des Wassers in engen zylindrischen Röhren [About the Movement of Water in Narrow Cylindrical Pipes]10.1002/andp.18391220304 ↗
32. Blasius, H. (1913). Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens: Insbesondere aus den Laboratorien der Technischen Hochschulen, Springer.
33. Gamma Ray Logging10.1190/1.1441436 ↗
34. Electrical conductivities in oil bearing shaly sands10.2118/1863-A ↗
35. Preface LIDAR and DEM techniques for landslides monitoring and characterization10.5194/nhess-10-1877-2010 ↗