ORIGINAL ARTICLE
Anisotropic Brittleness Characterization and Analysis of VTI Media
Qiyu Yang,
Jingye Li,
Jinming Cui,
Yongping Wang,
Lei Han,
Yuning Zhang,
Qiyu Yang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorCorresponding Author
Jingye Li
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Correspondence: Jingye Li ([email protected])
Search for more papers by this authorJinming Cui
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorYongping Wang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorLei Han
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorYuning Zhang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorQiyu Yang,
Jingye Li,
Jinming Cui,
Yongping Wang,
Lei Han,
Yuning Zhang,
Qiyu Yang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorCorresponding Author
Jingye Li
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Correspondence: Jingye Li ([email protected])
Search for more papers by this authorJinming Cui
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorYongping Wang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorLei Han
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorYuning Zhang
College of Geophysics, China University of Petroleum-Beijing, Beijing, China
State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing, China
Search for more papers by this authorFirst published: 08 July 2025
Funding: This research was supported by the R&D Department of China National Petroleum Corporation (2022DQ0604-04).
ABSTRACT
The brittleness index is a crucial parameter for evaluating the brittleness of subsurface reservoirs. Accurate brittleness determination optimizes fracture design and guides oil and gas extraction, especially in shale formations. Traditionally, the brittleness index assumes isotropy, which fails to capture the anisotropic nature of shale reservoirs and often leads to prediction errors. To mitigate this challenge, this study introduces a stiffness coefficient matrix specifically designed for anisotropic media and proposes a brittleness index equation tailored for transverse isotropic (VTI) media. Experimental results show that the proposed anisotropic brittleness index provides a more accurate assessment of shale reservoir brittleness than the conventional isotropic brittleness index. Ultimately, the anisotropic brittleness index is applied to field logging data, thereby validating the effectiveness of the method in distinguishing between reservoirs of high and low brittleness.
Open Research
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
- Ameen, M., M. Elwageeh, A. Abdelaziz, S. Bonduà, and M. Elkarmoty. 2023. “Study of the Relationship Between Mode I Fracture Toughness and Rock Brittleness Indices.” Applied Sciences 13, no. 18: 10378. https://doi.org/10.3390/app131810378.
- Ba, J., P. Hu, W. Tan, T. M. Müller, and L. Y. Fu. 2021. “Brittle Mineral Prediction Based on Rock-Physics Modelling for Tight Oil Reservoir Rocks.” Journal of Geophysics and Engineering 18, no. 6: 970–983. https://doi.org/10.1093/jge/gxab062.
- Bachrach, R., K. Osypov, D. Nichols, Y. Yang, Y. Liu, and M. Woodward. 2013. “Applications of Deterministic and Stochastic Rock Physics Modeling to Anisotropic Velocity Model Building.” Geophysical Prospecting 61, no. 2: 404–415. https://doi.org/10.1111/j.1365-2478.2012.01133.x.
- Bandyopadhyay, K. 2009. “ Seismic Anisotropy: Geological Causes and Its Implications to Reservoir Geophysics.” PhD thesis, Stanford University. https://api.semanticscholar.org/CorpusID:129873813.
- Berryman, J. G. 1980. “Long-wavelength propagation in fluid-saturated propous media.” The Journal of the Acoustical Society of America 68: 1809–1831. https://doi.org/10.1121/1.385171.
10.1121/1.385171 Google Scholar
- Cai, Z., L. Zhao, T. Long, et al. 2024. “Elastic and Anisotropic Properties of Organic-Rich Lacustrine Shales: An Experimental Study.” Geophysical Prospecting 72, no. 8: 2958–2977. https://doi.org/10.1111/1365-2478.13564.
- Cao, D., J. Han, J. Xiao, Q. Liu, F. Fu, and D. Liu. 2023. “Method for Evaluating the Brittleness of Shale Minerals Under the Constraints of Elastic Characteristics.” Chinese Journal of Geophysics 66, no. 11: 4781–4791. https://doi.org/10.6038/cjg2022Q0688.
- Chen, J., G. Zhang, H. Chen, and X. Yin. 2014. “The Construction of Shale Rock Physics Effective Model and Prediction of Rock Brittleness.” In SEG Technical Program Expanded Abstracts 2014, 2861–2865. Society of Exploration Geophysicists. https://doi.org/10.1190/segam2014-0716.1.
10.1190/segam2014?0716.1 Google Scholar
- Deng, J., H. Wang, H. Zhou, Z. Liu, L. Song, and X. Wang. 2015. “Microtexture, Seismic Rock Physical Properties and Modeling of Longmaxi Formation Shale.” Chinese Journal of Geophysics 58, no. 6: 2123–2136. https://doi.org/10.6038/cjg20150626.
- Dou, L., H. Yang, Y. Xiao, H. Gao, T. Li, and H. Sun. 2021. “Probability Study of Formation Brittleness and New Quantitative Evaluation of Fracability for Shale Reservoirs.” Progress in Geophysics 36, no. 2: 576–584. https://doi.org/10.6038/pg2021EE0460.
10.6038/pg2021EE0460 Google Scholar
- Feng, C., X. Deng, W. Yin, Z. Wang, and Z. Mao. 2018. “Brittleness Index Prediction via Well Logs and Reservoir Classification Based on Brittleness.” In Proceedings of the SPE Asia Pacific Oil and Gas Conference and Exhibition. 191934, 1-11. Society of Petroleum Engineers. https://doi.org/10.2118/191934-MS.
10.2118/191934?MS Google Scholar
- Gholami, R., V. Rasouli, M. Sarmadivaleh, V. Minaeian, and N. Fakhari. 2016. “Brittleness of Gas Shale Reservoirs: A Case Study From the North Perth Basin, Australia.” Journal of Natural Gas Science and Engineering 33: 1244–1259. https://doi.org/10.1016/j.jngse.2016.03.013.
- Glinsky, M. E., A. Cortis, J. Chen, D. Sassen, and H. Rael. 2015. “Geomechanical Property Estimation of Unconventional Reservoirs Using Seismic Data and Rock Physics.” Geophysical Prospecting 63, no. 5: 1224–1245. https://doi.org/10.1111/1365-2478.12211.
- Gong, F., G. Zou, Z. Zhang, S. Peng, G. Wang, and H. Chen. 2024. “An Anisotropic Rock Physics Modeling for the Coalbed Methane Reservoirs and Its Applications in Anisotropy Parameter Prediction.” Journal of Applied Geophysics 225: 105381. https://doi.org/10.1016/j.jappgeo.2024.105381.
- Grieser, B., and J. Bray. 2007. “Identification of Production Potential in Unconventional Reservoirs.” In Proceedings of the Production and Operations Symposium, 106623, 1–6. Society of Petroleum Engineers. https://doi.org/10.2118/106623-MS.
10.2118/106623?MS Google Scholar
- Gui, J., P. Chen, and T. Ma. 2019. “The Spatial Distribution of Elastic Parameters of Orthotropic Rocks.” Journal of Southwest Petroleum University (Science & Technology Edition) 41, no. 3: 13–28. https://doi.org/10.11885/j.issn.1674-5086.2018.09.21.02.
10.11885/j.issn.1674?5086.2018.09.21.02 Google Scholar
- Guo, Z., X. Y. Li, C. Liu, X. Feng, and Y. Shen. 2013. “A Shale Rock Physics Model for Analysis of Brittleness Index, Mineralogy and Porosity in the Barnett Shale.” Journal of Geophysics and Engineering 10, no. 2: 025006. https://doi.org/10.1088/1742-2132/10/2/025006.
- Guo, Z. Q., M. Chapman, and X. Y. Li. 2012. “ A Shale Rock Physics Model and Its Application in the Prediction of Brittleness Index, Mineralogy, and Porosity of the Barnett Shale.” In SEG Technical Program Expanded Abstracts 2012, 1–5. Society of Exploration Geophysicists. https://doi.org/10.1190/segam2012-0777.1.
10.1190/segam2012?0777.1 Google Scholar
- Hassan, A., S. Chan, M. Mahmoud, M. S. Aljawad, J. Humphrey, and A. Abdulraheem. 2022. “Artificial Intelligence-Based Model of Mineralogical Brittleness Index Based on Rock Elemental Compositions.” Arabian Journal for Science and Engineering 47, no. 9: 11745–11761. https://doi.org/10.1007/s13369-021-06487-6.
- Hill, R. 1952. “The Elastic Behaviour of a Crystalline Aggregate.” Proceedings of the Physical Society, Section A 65, no. 5: 349. https://doi.org/10.1088/0370-1298/65/5/307.
- Hu, Y., Z. Chen, and W. Liu. 2016. “A Novel Model of Brittleness Index for Shale Gas Reservoirs: Confining Pressure and Pore Pressure Effect.” Drilling and Production Technology 19, no. 5: 56–60. https://doi.org/10.2118/176886-MS.
10.2118/176886?MS Google Scholar
- Huang, X. R., J. P. Huang, Z. C. Li, Q. Y. Yang, Q. X. Sun, and W. Cui. 2015. “Brittleness Index and Seismic Rock Physics Model for Anisotropic Tight-Oil Sandstone Reservoirs.” Applied Geophysics 12, no. 1: 11–22. https://doi.org/10.1007/s11770-014-0478-0.
- Jamshidi, A., Y. Abdi, and R. Sarikhani. 2020. “Prediction of Brittleness Indices of Sandstones Using a Novel Physico-Mechanical Parameter.” Geotechnical and Geological Engineering 38: 4651–4659. https://doi.org/10.1007/s10706-020-01316-3.
- Jarvie, D. M., R. J. Hill, T. E. Ruble, and R. M. Pollastro. 2007. “Unconventional Shale-Gas Systems: The Mississippian Barnett Shale of North-Central Texas as One Model for Thermogenic Shale-Gas Assessment.” AAPG Bulletin 91, no. 4: 475–499. https://doi.org/10.1306/12190606068.
- Jin, X., S. N. Shah, J. C. Roegiers, and B. Zhang. 2014. “Fracability Evaluation in Shale Reservoirs—An Integrated Petrophysics and Geomechanics Approach.” In Proceedings of the SPE Hydraulic Fracturing Technology Conference, 168589, 1-14. Society of Petroleum Engineers. https://doi.org/10.2118/168589-MS.
10.2118/168589?MS Google Scholar
- Jones, L. E., and H. F. Wang. 1981. “Ultrasonic Velocities in Cretaceous Shales From the Williston Basin.” Geophysics 46, no. 3: 288–297. https://doi.org/10.1190/1.1441199.
- Kang, Y., C. Shang, H. Zhou, et al. 2020. “Mineralogical Brittleness Index as a Function of Weighting Brittle Minerals—From Laboratory Tests to Case Study.” Journal of Natural Gas Science and Engineering 77: 103278. https://doi.org/10.1016/j.jngse.2020.103278.
- Kim, T., S. Hwang, and S. Jang. 2017. “Petrophysical Approach for S-Wave Velocity Prediction Based on Brittleness Index and Total Organic Carbon of Shale Gas Reservoir: A Case Study From Horn River Basin, Canada.” Journal of Applied Geophysics 136: 513–520. https://doi.org/10.1016/j.jappgeo.2016.12.003.
- Lai, J., G. Wang, L. Huang, et al. 2015. “Brittleness Index Estimation in a Tight Shaly Sandstone Reservoir Using Well Logs.” Journal of Natural Gas Science and Engineering 27: 1536–1545. https://doi.org/10.1016/j.jngse.2015.10.020.
- Liu, Z., and Z. Sun. 2015. “New Brittleness Indexes and Their Application in Shale/Clay Gas Reservoir Prediction.” Petroleum Exploration and Development 42, no. 1: 129–137. https://doi.org/10.1016/S1876-3804(15)60016-7.
- Lizcano-Hernández, E. G., R. Nicolás-López, O. C. Valdiviezo-Mijangos, and J. Meléndez-Martínez. 2018. “Estimation of Brittleness Indices for Pay Zone Determination in a Shale-Gas Reservoir by Using Elastic Properties Obtained From Micromechanics.” Journal of Geophysics and Engineering 15, no. 2: 307–314. https://doi.org/10.1088/1742-2140/aa9a5e.
- Lu, C., L. Ma, J. Guo, et al. 2022. “Novel Method and Case Study of a Deep Shale Fracability Evaluation Based on the Brittleness Index.” Energy Exploration & Exploitation 40, no. 1: 442–459. https://doi.org/10.1177/01445987211033656.
- Luan, X., B. Di, J. Wei, et al. 2014. “Laboratory Measurements of Brittleness Anisotropy in Synthetic Shale With Different Cementation.” In SEG Technical Program Expanded Abstracts 2014, 3005–3009. Society of Exploration Geophysicists. https://doi.org/10.1190/segam2014-0432.1.
10.1190/segam2014?0432.1 Google Scholar
- Lubis, F. H., and U. Fauzi. 2022. “The Effects of Physical and Geometrical Properties on Rock Brittleness Index Based on Numerical Modeling.” Journal of Physics: Conference Series 2243, no. 1: 012009. https://doi.org/10.1088/1742-6596/2243/1/012009.
10.1088/1742-6596/2243/1/012009 Google Scholar
- MacBeth, C., M. Boyd, W. Rizer, and J. Queen. 1998. “Estimation of Reservoir Fracturing From Marine VSP Using Local Shear-Wave Conversion.” Geophysical Prospecting 46, no. 1: 29–50. https://doi.org/10.1046/j.1365-2478.1998.770313.x.
- Man, C. S., and M. Huang. 2011. “A Simple Explicit Formula for the Voigt-Reuss-Hill Average of Elastic Polycrystals With Arbitrary Crystal and Texture Symmetries.” Journal of Elasticity 105: 29–48. https://doi.org/10.1007/s10659-011-9312-y.
- Mavko, G., T. Mukerji, and J. Dvorkin. 2020. The Rock Physics Handbook. 3rd ed. Cambridge University Press. https://doi.org/10.1017/9781108324263.
10.1017/9781108333016 Google Scholar
- Mews, K. S., M. M. Alhubail, and R. G. Barati. 2019. “A Review of Brittleness Index Correlations for Unconventional Tight and Ultra-Tight Reservoirs.” Geosciences 9, no. 7: 319. https://doi.org/10.3390/geosciences9070319.
- Mikhaltsevitch, V., M. Lebedev, M. Pervukhina, and B. Gurevich. 2021. “Seismic Dispersion and Attenuation in Mancos Shale–Laboratory Measurements.” Geophysical Prospecting 69, no. 3: 568–585. https://doi.org/10.1111/1365-2478.13056.
- Nhabanga, O. J., P. S. Ringrose, and R. M. Holt. 2021. “Use of Rock-Physics Analysis of Well Logs to Determine Compaction History of Cretaceous Shales in the Rovuma Basin.” Offshore Mozambique. Geophysical Prospecting 69, no. 6: 1282–1294. https://doi.org/10.1111/1365-2478.13104.
- Niazi, S., Z. Chen, and F. Bobaru. 2021. “Crack Nucleation in Brittle and Quasi-Brittle Materials: A Peridynamic Analysis.” Theoretical and Applied Fracture Mechanics 112: 102855. https://doi.org/10.1016/j.tafmec.2020.102855.
- Pan, X., Z. Liu, P. Wang, H. Lei, and J. Liu. 2024. “Bayesian Linearized Amplitude Variation With Offset and Azimuth Inversion and Uncertainty Analysis in Horizontal Transversely Isotropic Media.” Geophysical Prospecting 72, no. 7: 2666–2684.
- Pan, X., and G. Zhang. 2019a. “Amplitude Variation With Incident Angle and Azimuth Inversion for Young's Impedance, Poisson's Ratio and Fracture Weaknesses in Shale Gas Reservoirs.” Geophysical Prospecting 67, no. 7: 1898–1911. https://doi.org/10.1111/1365-2478.12783.
- Pan, X., and G. Zhang. 2019b. “Amplitude Variation With Incident Angle and Azimuth Inversion for Young's Impedance, Poisson's Ratio and Fracture Weaknesses in Shale Gas Reservoirs.” Geophysical Prospecting 67, no. 7: 1898–1911. https://doi.org/10.1111/1365-2478.12783.
- Qian, K. R., T. Liu, J. Z. Liu, et al. 2020. “Construction of a Novel Brittleness Index Equation and Analysis of Anisotropic Brittleness Characteristics for Unconventional Shale Formations.” Petroleum Science 17: 70–85. https://doi.org/10.1007/s12182-019-00372-6.
- Reuss, A. 1929. “Berechnung der Fließgrenze von Mischkristallen auf Grund Der Plastizitätsbedingung für Einkristalle.” ZAMM—Journal of Applied Mathematics and Mechanics /Zeitschrift Für Angewandte Mathematik Und Mechanik 9, no. 1: 49–58. https://doi.org/10.1002/zamm.19290090104.
- Rickman, R., M. Mullen, E. Petre, B. Grieser, and D. Kundert. 2008. “A Practical Use of Shale Petrophysics for Stimulation Design Optimization: All Shale Plays Are Not Clones of the Barnett Shale.” In Proceedings of the SPE Annual Technical Conference and Exhibition, 115258, 1-11. Society of Petroleum Engineers. https://doi.org/10.2118/115258-MS.
10.2118/115258?MS Google Scholar
- Tan, W., J. Ba, T. Müller, G. Fang, and H. Zhao. 2020. “Rock Physics Model of Tight Oil Siltstone for Seismic Prediction of Brittleness.” Geophysical Prospecting 68, no. 5: 1554–1574. https://doi.org/10.3997/2214-4609.201901027.
- Tang, X., S. Xu, C. Zhuang, Y. Su, and X. Chen. 2016. “Assessing Rock Brittleness and Fracability From Radial Variation of Elastic Wave Velocities From Borehole Acoustic Logging.” Geophysical Prospecting 64, no. 4: 958–966. https://doi.org/10.1111/1365-2478.12377.
- Tarasov, B., and Y. Potvin. 2013. “Universal Criteria for Rock Brittleness Estimation Under Triaxial Compression.” International Journal of Rock Mechanics and Mining Sciences 59: 57–69. https://doi.org/10.1016/j.ijrmms.2012.12.011.
- Thomsen, L. 1986. “Weak Elastic Anisotropy.” Geophysics 51, no. 10: 1954–1966. https://doi.org/10.1190/1.1442051.
- Voigt, W. 1928. Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). Teubner Verlag.
- Wang, F. P., and J. F. Gale. 2009. “Screening Criteria for Shale-Gas Systems.” Gulf Coast Association of Geological Societies Transactions 59: 779–793.
- Wang, Q., Y. Wang, S. G. Guo, Z. T. Xing, and Z. W. Liu. 2015. “The Effect of Shale Properties on the Anisotropic Brittleness Criterion Index From Laboratory Study.” Journal of Geophysics and Engineering 12, no. 5: 866–874. https://doi.org/10.1088/1742-2132/12/5/866.
- Wang, Z., T. Sun, C. Feng, W. Wang, and C. Han. 2018. “An Improved Method for Predicting Brittleness of Rocks via Well Logs in Tight Oil Reservoirs.” Journal of Geophysics and Engineering 15, no. 3: 1042–1049. https://doi.org/10.1088/1742-2140/aaa935.
- Wu, H., J. Guo, G. Ji, Y. Huang, H. Ding, and P. Lin. 2024. “Estimating the Anisotropy of the Vertical Transverse Isotropy Coal Seam by Rock Physics Model–Based Inversion.” Geophysical Prospecting 72, no. 5: 2064–2075. https://doi.org/10.1111/1365-2478.13470.
- Wu, H., R. Wu, P. Zhang, Y. Huang, Y. Huang, and S. Dong. 2022. “Combined Fluid Factor and Brittleness Index Inversion for Coal-Measure Gas Reservoirs.” Geophysical Prospecting 70, no. 4: 751–764. https://doi.org/10.1111/1365-2478.13172.
- Wu, X., M. Chapman, X. Li, and H. Dai. 2012. “Anisotropic Elastic Modeling for Organic Shales.” In 74th Annual International Conference and Exhibition, EAGE, Extended Abstracts, 314. European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.20148651.
10.3997/2214?4609.20148651 Google Scholar
- Wu, Z., E. Zhao, H. Xiang, X. F. Hao, X. J. Liu, and J. Meng. 2007. “Crystal Structures and Elastic Properties of Superhard IrN2 and IrN3 From First Principles.” Physical Review B 76, no. 5: 054115. https://doi.org/10.1103/PhysRevB.76.054115.
- Xiao, W., D. Zhang, H. Yang, B. Yu, and S. Li. 2022. “Evaluation and Analysis of Sandstone Brittleness Under the Influence of Temperature.” Geomechanics and Geophysics for Geo-Energy and Geo-Resources 8: 1–19. https://doi.org/10.1007/s40948-021-00324-8.
- Yang, Q., J. Li, F. Wu, W. Li, and J. Cui. 2024. “A Petrophysical Model of Shales Considering Soft-Mineral Aspect Ratios and Its Application.” Geophysical and Geochemical Exploration 48, no. 1: 98–104. https://doi.org/10.11720/wtyht.2024.2567.
10.11720/wtyht.2024.2567 Google Scholar
- Yasin, Q., G. M. Sohail, K. Y. Liu, Q. Z. Du, and C. D. Boateng. 2021. “Study on Brittleness Templates for Shale Gas Reservoirs—A Case Study of Longmaxi Shale in Sichuan Basin, Southern China.” Petroleum Science 18, no. 5: 1370–1389. https://doi.org/10.1016/j.petsci.2021.09.030.
- Yin, S., D. Lv, L. Jin, and W. Ding. 2018. “Experimental Analysis and Application of the Effect of Stress on Continental Shale Reservoir Brittleness.” Journal of Geophysics and Engineering 15, no. 2: 478–494. https://doi.org/10.1088/1742-2140/aaa5d2.
- Yu, T., J. Ba, W. Qian, et al. 2019. “Research Progress on Evaluation Methods of Rock Brittleness in Unconventional Oil/Gas Reservoirs.” Progress in Geophysics 34, no. 1: 236–243. https://doi.org/10.6038/pg2019BB0590.
10.6038/pg2019BB0590 Google Scholar
- Zhang, F., X. Li, and K. Qian. 2017. “Estimation of Anisotropy Parameters for Shale Based on an Improved Rock Physics Model, Part 1: Theory.” Journal of Geophysics and Engineering 14, no. 1: 143–158. https://doi.org/10.1088/1742-2140/aa5afa.
- Zhang, H., W. Zhou, R. Xie, and H. Xu. 2019. “Logging Interpretation of Brittle-Plasticity Parameters Based on Stress-Strain Curves for Continental Shale Reservoirs in Xinchang Field, Western Sichuan Basin, China.” Journal of Geophysics and Engineering 16, no. 3: 571–584. https://doi.org/10.1093/jge/gxz028.
- Zhou, L., J. Li, X. Chen, X. Liu, and L. Chen. 2017. “Prestack Amplitude Versus Angle Inversion for Young's Modulus and Poisson's Ratio Based on the Exact Zoeppritz Equations.” Geophysical Prospecting 65, no. 6: 1462–1476. https://doi.org/10.1111/1365-2478.12493.
- Zhou, X., J. Ba, L. Fu, L. Zhang, Q. Cao, and C. Yu. 2020. “Rock Physics Model for Shale Brittleness Evaluation and Seismic Prediction.” Progress in Geophysics 35, no. 5: 1736–1744. https://doi.org/10.6038/pg2020DD0445.
