Statistical Evaluation of Seismic Velocity Models of Permafrost
Publication: Journal of Cold Regions Engineering
Volume 38, Issue 3
Abstract
The warming climate in high-latitude permafrost regions is leading to permafrost degradation. Estimating seismic wave velocities in permafrost could help predict the geomechanical properties of permafrost and provide information to plan and design resilient civil infrastructure in cold regions. This paper evaluates the performance of seven models when predicting the seismic wave velocities of permafrost statistically; these models are the time-average, Zimmerman and King, Minshull et al., weighted equation, three-phase, Biot–Gassmann theory modified by Lee (BGTL), and Dou et al. models. The data used in the evaluation are from published laboratory and in situ data, which includes 369 data points for joint P and S wave velocities from nine publications and 943 unfrozen water content data points from 12 publications. The unfrozen water content that is used in these models is determined from a modified Dall’Amico’s model that is proposed, which is evaluated against six existing unfrozen water content models based on soil temperature. This paper finds that saturated nonsaline permafrost generally shares similar linear trends between the P and S wave velocities, regardless of soil type, porosity, grain size, and temperature. Fitting all existing data, an empirical linear relationship is derived between the P and S wave velocities. Among the seven models evaluated, the Minshull et al. and BGTL models are the most accurate when predicting the seismic velocities of permafrost.
Practical Applications
Unfrozen water content and seismic wave velocity models are valuable tools for quantitatively predicting permafrost dynamics and degradation, with practical applications in various engineering areas with permafrost environments. As permafrost thaws due to rising temperatures, these models could be used to guide the quantitative interpretation of geophysical changes in subsurface conditions, assess the potential for ground instability, and predict future permafrost degradation. Unfrozen water content models are used to predict the percentage of unfrozen water within permafrost, which links the changes with permafrost temperature. Unfrozen water content models of permafrost are essential when assessing permafrost thaw, thermal performance, heat transfer processes in permafrost, and the effect of civil infrastructure on permafrost (Chen et al.,). The seismic wave velocity models could help engineers assess the subsurface conditions in permafrost areas; this assessment is crucial for environmental and seismic monitoring, land use planning, infrastructure design and construction, and natural resources exploration.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or codes generated or used during the study are available in a repository or online in accordance with funder data retention policies. Ji, X., Liew, M., and Xiao, M. 2022. Supplementary data for “Statistical Evaluation of Seismic Wave Velocity Models of Permafrost.” Penn State Data Commons. https://doi.org/10.26208/6H4X-JC81.
Acknowledgments
This study is supported by the National Science Foundation under Grants CMMI-2034363, CMMI-2034366, and ICER-1927718. Dr. Min Liew provided advice on data collection.
Author contributions: Xiaohang Ji: Conceptualization, methodology, software, formal analysis, investigation, writing the original draft, and visualization. Ming Xiao: Conceptualization, methodology, validation, writing (review and editing), visualization, supervision, project administration, and funding acquisition. Eileen Martin: Conceptualization, writing (review and editing), project administration, and funding acquisition. Tieyuan Zhu: Conceptualization, writing (review and editing), project administration, and funding acquisition.
References
Anderson, D. M., and A. R. Tice. 1972. “Predicting unfrozen water contents in frozen soils from surface area measurements.” Highway Res. Rec. 393: 12–18.
Berryman, J. G. 1995. “Mixture theories for rock properties.” In Rock physics and phase relations: A handbook of physical constants. Vol. 3, edited by T. J. Ahrens, 205–228. Chichester, UK: Wiley.
Biot, M. A. 1956. “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range.” J. Acoust. Soc. Am. 28 (2): 179–191. https://doi.org/10.1121/1.1908241.
Carcione, J. M., and G. Seriani. 1998. “Seismic and ultrasonic velocities in permafrost.” Geophys. Prospect. 46 (4): 441–454. https://doi.org/10.1046/j.1365-2478.1998.1000333.x.
Castagna, J. P., M. L. Batzle, and R. L. Eastwood. 1985. “Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.” Geophysics 50 (4): 571–581. https://doi.org/10.1190/1.1441933.
Chen, K., M. Jin, G. Li, Y. Liu, J. Lu, Y. Zhao, and Q. Yu. 2023. “Thermal performance and heat transfer process of an expressway embankment with horizontal-thermosyphons in permafrost regions.” Cold Reg. Sci. Technol. 212: 103887. https://doi.org/10.1016/j.coldregions.2023.103887.
Christ, M., Y.-C. Kim, and J.-B. Park. 2009. “The influence of temperature and cycles on acoustic and mechanical properties of frozen soils.” KSCE J. Civ. Eng. 13 (3): 153–159. https://doi.org/10.1007/s12205-009-0153-1.
Dall’Amico, M., S. Endrizzi, S. Gruber, and R. Rigon. 2011. “A robust and energy-conserving model of freezing variably-saturated soil.” Cryosphere 5 (2): 469–484. https://doi.org/10.5194/tc-5-469-2011.
Dou, S., S. Nakagawa, D. Dreger, and J. Ajo-Franklin. 2016. “A rock-physics investigation of unconsolidated saline permafrost: P-wave properties from laboratory ultrasonic measurements.” Geophysics 81 (1): WA233–WA245. https://doi.org/10.1190/geo2015-0176.1.
Dou, S., S. Nakagawa, D. Dreger, and J. Ajo-Franklin. 2017. “An effective-medium model for P-wave velocities of saturated, unconsolidated saline permafrost.” Geophysics 82 (3): EN33–EN50. https://doi.org/10.1190/geo2016-0474.1.
Dvorkin, J., and A. Nur. 1998. “Time-average equation revisited.” Geophysics 63 (2): 460–464. https://doi.org/10.1190/1.1444347.
Eberhart-Phillips, D., D.-H. Han, and M. D. Zoback. 1989. “Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone.” Geophysics 54 (1): 82–89. https://doi.org/10.1190/1.1442580.
Ferrero, A. M., A. Godio, M. Migliazza, L. Sambuelli, A. Segalini, and A. Théodule. 2014. “Geotechnical and geophysical characterization of frozen granular material.” In Landslides in cold regions in the context of climate change, edited by W. Shan, Y. Guo, F. Wang, H. Marui, and A. Strom, 205–218. Cham, Switzerland: Springer.
Fu, R., J. Zhang, and Z. Hou. 1983. “Ultrasonic velocities in frozen soil.” In Proc. 4th Int. Conf. on Permafrost, 311–315. Washington, DC: The National Academies Press.
Gassmann, F. 1951. “Elastic waves through a packing of spheres.” Geophysics 16 (4): 673–685. https://doi.org/10.1190/1.1437718.
Ge, X., Z. Yang, and B. Still. 2013. “Mechanical properties of naturally frozen ice-rich silty soils.” In Mechanical properties of frozen soil, 124–139. West Conshohocken, PA: ASTM International.
Hashin, Z., and S. Shtrikman. 1963. “A variational approach to the theory of the elastic behaviour of multiphase materials.” J. Mech. Phys. Solids 11 (2): 127–140. https://doi.org/10.1016/0022-5096(63)90060-7.
Haynes, F. D., and J. A. Karalius. 1977. Effect of temperature on the strength of frozen silt (No. 77). Hanover, NH: Dept. of Defense, Dept. of the Army, Corps of Engineers, Cold Regions Research and Engineering Laboratory.
Hill, R. 1952. “The elastic behaviour of a crystalline aggregate.” Proc. Phys. Soc. London, Sect. A 65 (5): 349. https://doi.org/10.1088/0370-1298/65/5/307.
Hivon, E., and D. C. Sego. 1990. “Determination of the unfrozen water content of saline permafrost using time-domain reflectometry (TDR).” In Proc. 5th Canadian Permafrost Conf., 257–262. Quebec, Canada: University of Laval.
Hoyer, W. A., S. O. Simmons, M. M. Spann, and A. T. Watson. 1975. “Evaluation of permafrost with logs.” In Proc., SPWLA 16th Annual Logging Symp. Richardson, TX: One Petro.
Hu, G., L. Zhao, X. Zhu, X. Wu, T. Wu, R. Li, C. Xie, and J. Hao. 2020. “Review of algorithms and parameterizations to determine unfrozen water content in frozen soil.” Geoderma 368: 114277. https://doi.org/10.1016/j.geoderma.2020.114277.
Kim, Y., D. Chae, K. Kim, and W. Cho. 2016. “Physical and mechanical characteristics of frozen ground at various sub-zero temperatures.” KSCE J. Civ. Eng. 20 (6): 2365–2374. https://doi.org/10.1007/s12205-015-0542-6.
King, M. S., R. W. Zimmerman, and R. F. Corwin. 1988. “Seismic and electrical properties of unconsolidated Permafrost.” Geophys. Prospect. 36 (4): 349–364. https://doi.org/10.1111/j.1365-2478.1988.tb02168.x.
Kozlowski, T. 2007. “A semi-empirical model for phase composition of water in clay-water systems.” Cold Reg. Sci. Technol. 49: 226–236. https://doi.org/10.1016/j.coldregions.2007.03.013.
Kurfurst, P. J. 1976. “Ultrasonic wave measurements on frozen soils at permafrost temperatures.” Can. J. Earth Sci. 13 (11): 1571–1576. https://doi.org/10.1139/e76-163.
Kuster, G. T., and M. N. Toksöz. 1974. “Velocity and attenuation of seismic waves in two-phase media: Part I. Theoretical formulations.” Geophysics 39 (5): 587–606. https://doi.org/10.1190/1.1440450.
Lai, Z., X. Zhao, R. Tang, and J. Yang. 2021. “Electrical conductivity-based estimation of unfrozen water content in saturated saline frozen sand.” Adv. Civ. Eng. 2021: 8881304. https://doi.org/10.1155/2021/8881304.
Leclaire, P., F. Cohen-Ténoudji, and J. Aguirre-Puente. 1994. “Extension of Biot’s theory of wave propagation to frozen porous media.” J. Acoust. Soc. Am. 96 (6): 3753–3768. https://doi.org/10.1121/1.411336.
Lee, M. W. 2002. “Biot–Gassmann theory for velocities of gas hydrate-bearing sediments.” Geophysics 67 (6): 1711–1719. https://doi.org/10.1190/1.1527072.
Lee, M. W., D. R. Hutchinson, T. S. Collett, and W. P. Dillon. 1996. “Seismic velocities for hydrate-bearing sediments using weighted equation.” J. Geophys. Res.: Solid Earth 101 (B9): 20347–20358. https://doi.org/10.1029/96JB01886.
Li, H. 2009. “Experimental and numerical study of sonic wave propagation in freezing sand and silt.” Ph.D. thesis, Dept. of Mining and Geological Engineering, Univ. of Alaska Fairbanks.
Li, X., and X. Li. 2023. “A soil freezing-thawing model based on thermodynamics.” Cold Reg. Sci. Technol. 211: 103867. https://doi.org/10.1016/j.coldregions.2023.103867.
Li, X., X. Li, and J. Liu. 2023a, In press. “A dynamic soil freezing characteristic curve model for frozen soil.” J. Rock Mech. Geotech. Eng. https://doi.org/10.1016/j.jrmge.2023.09.008.
Li, X., S.-F. Zheng, M. Wang, and A.-Q. Liu. 2023b. “The prediction of the soil freezing characteristic curve using the soil water characteristic curve.” Cold Reg. Sci. Technol. 212: 103880. https://doi.org/10.1016/j.coldregions.2023.103880.
Li, Z., J. Chen, and M. Sugimoto. 2020. “Pulsed NMR measurements of unfrozen water content in partially frozen soil.” J. Cold Reg. Eng. 34 (3): 04020013. https://doi.org/10.1061/(ASCE)CR.1943-5495.0000220.
Liew, M., X. Ji, M. Xiao, L. Farquharson, D. Nicolsky, V. Romanovsky, M. Bray, X. Zhang, and C. McComb. 2022. “Synthesis of physical processes of permafrost degradation and geophysical and geomechanical properties of permafrost.” Cold Reg. Sci. Technol. 198: 103522. https://doi.org/10.1016/j.coldregions.2022.103522.
Lu, J., W. Pei, X. Zhang, J. Bi, and T. Zhao. 2019. “Evaluation of calculation models for the unfrozen water content of freezing soils.” J. Hydrol. 575: 976–985. https://doi.org/10.1016/j.jhydrol.2019.05.031.
Lyu, C., S. A. G. Amiri, G. Grimstad, K. V. Høyland, and T. Ingeman-Nielsen. 2020. “Comparison of geoacoustic models for unfrozen water content estimation.” J. Geophys. Res.: Solid Earth 125 (10): e2020JB019766. https://doi.org/10.1029/2020JB019766.
McGaw, R. W., R. L. Berg, and J. W. Ingersoll. 1983. “An investigation of transient processes in an advancing zone of freezing.” In Proc., 4th Int. Conf. on Permafrost, 821–825. Washington, DC: The National Academies Press.
McKenzie, J. M., C. I. Voss, and D. I. Siegel. 2007. “Groundwater flow with energy transport and water–ice phase change: Numerical simulations, benchmarks, and application to freezing in peat bogs.” Adv. Water Resour. 30 (4): 966–983. https://doi.org/10.1016/j.advwatres.2006.08.008.
Meng, Q., D. Li, J. Chen, A. Xu, and S. Huang. 2008. “Experimental research on physical-mechanical characteristics of frozen soil based on ultrasonic technique.” In Vol. 2 of Proc., 9th Int. Conf. on Permafrost, 1179–1183. Fairbanks, Alaska: University of Alaska.
Michalowski, R. L. 1993. “A constitutive model of saturated soils for frost heave simulations.” Cold Reg. Sci. Technol. 22: 47–63. https://doi.org/10.1016/0165-232X(93)90045-A.
Mindlin, R. D. 1949. “Compliance of elastic bodies in contact.” J. Appl. Mech. 16: 259–268. https://doi.org/10.1115/1.4009973.
Minshull, T. A., S. C. Singh, and G. K. Westbrook. 1994. “Seismic velocity structure at a gas hydrate reflector, offshore western Colombia, from full waveform inversion.” J. Geophys. Res.: Solid Earth 99 (B3): 4715–4734. https://doi.org/10.1029/93JB03282.
Nakano, Y., and R. Arnold. 1973. “Acoustic properties of frozen Ottawa sand.” Water Resour. Res. 9 (1): 178–184. https://doi.org/10.1029/WR009i001p00178.
Nakano, Y., and N. H. Froula. 1973. “Sound and shock transmission in frozen soils.” In Proc., 2nd Int. Conf. on Permafrost, 359–369. Washington, DC: National Academy of Sciences.
Nakano, Y., R. J. Martin III, and M. Smith. 1972. “Ultrasonic velocities of the dilatational and shear waves in frozen soils.” Water Resour. Res. 8 (4): 1024–1030. https://doi.org/10.1029/WR008i004p01024.
Nobes, D. C., H. Villinger, E. E. Davis, and L. K. Law. 1986. “Estimation of marine sediment bulk physical properties at depth from seafloor geophysical measurements.” J. Geophys. Res.: Solid Earth 91 (B14): 14033–14043. https://doi.org/10.1029/JB091iB14p14033.
Oliphant, J. L., A. R. Tice, and Y. Nakano. 1983. “Water migration due to a temperature gradient in frozen soil.” In Proc., 4th Int. Conf. on Permafrost, 951–956. Washington, DC: The National Academies Press.
Pearson, C. F., P. M. Halleck, P. L. McGuire, R. Hermes, and M. Mathews. 1983. “Natural gas hydrate deposits: A review of in situ properties.” J. Phys. Chem. 87 (21): 4180–4185. https://doi.org/10.1021/j100244a041.
Qiu, E., X. Wan, M. Qu, L. Zheng, C. Zhong, F. Gong, and L. Liu. 2020. “Estimating unfrozen water content in frozen soils based on soil particle distribution.” J. Cold Reg. Eng. 34 (2): 04020002. https://doi.org/10.1061/(ASCE)CR.1943-5495.0000208.
Radd, F. J., and L. H. Wolfe. 1979. “Ice lens structures, compression strengths and creep behavior of some synthetic frozen silty soils.” Dev. Geotech. Eng. 26: 169–183. https://doi.org/10.1016/B978-0-444-41782-4.50020-8.
Ren, J., S. K. Vanapalli, and Z. Han. 2017. “Soil freezing process and different expressions for the soil-freezing characteristic curve.” Sci. Cold Arid Reg. 9 (3): 221–228.
Reuss, A. 1929. “Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle.” J. App. Mathemat. Mech. 9: 49–58. https://doi.org/10.1002/zamm.19290090104.
Schön, J. 2011. Vol. 8 of Physical properties of rocks: A workbook. Oxford, UK:Elsevier.
Smith, M. W., and A. R. Tice. 1988. “Measurement of the unfrozen water content of soils.” In Comparison of NMR (nuclear magnetic resonance) and TDR (time domain reflectometry) methods. Hanover, NH: Cold Regions Research and Engineering Lab.
Timur, A. 1968. “Velocity of compressional waves in porous media at permafrost temperatures.” Geophysics 33: 584–595. https://doi.org/10.1190/1.1439954.
Thimus, J. F., J. Aguirre-Puente, and F. Cohen-Tenoudji. 1991. “Determination of unfrozen water content of an overconsolidated clay down to −160°C by sonic approaches-comparison with classical methods.” Ground Freezing 91: 83–88.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Voigt, W. 1928. Lerrbuch der Kristallphysik. Leipzig, Germany: Teubner.
Wang, D.-Y., Y.-L. Zhu, W. Ma, and Y.-H. Niu. 2006. “Application of ultrasonic technology for physical–mechanical properties of frozen soils.” Cold Reg. Sci. Technol. 44 (1): 12–19. https://doi.org/10.1016/j.coldregions.2005.06.003.
Watanabe, K., and Y. Osada. 2017. “Simultaneous measurement of unfrozen water content and hydraulic conductivity of partially frozen soil near 0°C.” Cold Reg. Sci. Technol. 142: 79–84. https://doi.org/10.1016/j.coldregions.2017.08.002.
Watanabe, K., and T. Wake. 2009. “Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR.” Cold Reg. Sci. Technol. 59 (1): 34–41. https://doi.org/10.1016/j.coldregions.2009.05.011.
Wen, Z., W. Ma, W. Feng, Y. Deng, D. Wang, Z. Fan, and C. Zhou. 2012. “Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay.” Environ. Earth Sci. 66 (5): 1467–1476. https://doi.org/10.1007/s12665-011-1386-0.
Wood, A. B. 1941. A textbook of sound. London: G. Bell and Sons.
Wyllie, M. R. J., A. R. Gregory, and G. H. F. Gardner. 1958. “An experimental investigation of factors affecting elastic wave velocities in porous media.” Geophysics 23 (3): 459–493. https://doi.org/10.1190/1.1438493.
Yang, Z. J., B. Still, and X. Ge. 2015. “Mechanical properties of seasonally frozen and permafrost soils at high strain rate.” Cold Reg. Sci. Technol. 113: 12–19. https://doi.org/10.1016/j.coldregions.2015.02.008.
Zhang, F., Z. J. Yang, B. Still, J. Wang, H. Yu, H. Zubeck, T. Petersen, and L. Aleshire. 2018. “Elastic properties of saline permafrost during thawing by bender elements and bending disks.” Cold Reg. Sci. Technol. 146: 60–71. https://doi.org/10.1016/j.coldregions.2017.11.014.
Zhang, M., W. Pei, S. Li, J. Lu, and L. Jin. 2017. “Experimental and numerical analyses of the thermo-mechanical stability of an embankment with shady and sunny slopes in a permafrost region.” Appl. Therm. Eng. 127: 1478–1487. https://doi.org/10.1016/j.applthermaleng.2017.08.074.
Zhang, M., X. Zhang, Y. Lai, J. Lu, and C. Wang. 2020. “Variations of the temperatures and volumetric unfrozen water contents of fine-grained soils during a freezing–thawing process.” Acta Geotech. 15: 595–601. https://doi.org/10.1007/s11440-018-0720-z.
Zhang, M., X. Zhang, J. Lu, W. Pei, and C. Wang. 2019. “Analysis of volumetric unfrozen water contents in freezing soils.” Exp. Heat Transfer 32 (5): 426–438. https://doi.org/10.1080/08916152.2018.1535528.
Zhu, Y., and D. L. Carbee. 1984. “Uniaxial compressive strength of frozen silt under constant deformation rates.” Cold Reg. Sci. Technol. 9 (1): 3–15. https://doi.org/10.1016/0165-232X(84)90043-0.
Zimmerman, R. W., and M. S. King. 1986. “The effect of the extent of freezing on seismic velocities in unconsolidated permafrost.” Geophysics 51: 1285–1290. https://doi.org/10.1190/1.1442181.
Information & Authors
Information
Published In
Journal of Cold Regions Engineering
Volume 38 • Issue 3 • September 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 22, 2023
Accepted: Jan 10, 2024
Published online: Jun 11, 2024
Published in print: Sep 1, 2024
Discussion open until: Nov 11, 2024
ASCE Technical Topics:
- Cold regions engineering
- Continuum mechanics
- Dynamics (solid mechanics)
- Earthquake engineering
- Engineering fundamentals
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fluid velocity
- Frost
- Geotechnical engineering
- Hydrologic engineering
- Hydrologic properties
- Hydrology
- Mathematics
- Permafrost
- Seismic effects
- Seismic tests
- Seismic waves
- Solid mechanics
- Statistics
- Tests (by type)
- Water and water resources
- Water content
- Wave velocity
- Waves (mechanics)
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.