Interpretation Methods for Seismic Downhole Test in Inclined Boreholes

Pedro Bautista, Zenon Aguilar


Geotechnical investigations often involve inclined boreholes, which can be used for downhole (DH) seismic surveys. However, as there is no interpretation method for downhole tests in inclined boreholes (IDH), this study proposes alternative interpretation methods based on the direct method (DM), interval method (IM), modified interval method (MIM), and refracted ray path method (RRM). We have named the proposed methods, adding an I to the original name to indicate that they are performed in an inclined well, i.e., DMI, IMI, MIMI, and RRMI. To analyze the applicability of the proposed methods, eight simple models with horizontal layers and four 2D models were used to obtain the P- and S-wave velocity profiles. Among all the proposed methods, the RRMI method showed the best fit between the calculated S-wave velocity (Vs) profile and the real models, providing good reliability. To test the equations and hypotheses, new interpretation steps were developed based on Snell's law and a modification of the numerical bisection method, which showed that the error increased slightly as the dip angle of the well decreased. The next step was to test the accuracy of the RRMI method in the field and develop downhole test processing software for vertical and inclined boreholes.


Doi: 10.28991/CEJ-2023-09-10-016

Full Text: PDF


Inclined Borehole; Seismic Downhole Test; P-S Well Logging; P And S Wave Velocity Profiles; RRMI Method.


Wang, J. S., Hwang, J. H., Lu, C. C., & Deng, Y. C. (2022). Measurement uncertainty of shear wave velocity: A case study of thirteen alluvium test sites in Taipei Basin. Soil Dynamics and Earthquake Engineering, 155, 107195. doi:10.1016/j.soildyn.2022.107195.

Miao, Y., He, H., Liu, H., & Wang, S. (2022). Reproducing ground response using in-situ soil dynamic parameters. Earthquake Engineering and Structural Dynamics, 51(10), 2449–2465. doi:10.1002/eqe.3671.

Yang, Z., Liu, X., Guo, L., Cui, Y., Liu, T., Shi, W., & Ling, X. (2022). Effect of silt/clay content on shear wave velocity in the Yellow River Delta (China), based on the cone penetration test (CPT). Bulletin of Engineering Geology and the Environment, 81(1), 28. doi:10.1007/s10064-021-02520-y.

Elbeggo, D., Ethier, Y., Dubé, J. S., & Karray, M. (2022). Critical insights in laboratory shear wave velocity correlations of clays. Canadian Geotechnical Journal, 59(6), 935–951. doi:10.1139/cgj-2020-0033.

Baziw, E. J. (2002). Derivation of seismic cone interval velocities utilizing forward modeling and the downhill simplex method. Canadian Geotechnical Journal, 39(5), 1181–1192. doi:10.1139/t02-061.

Baziw, E., & Verbeek, G. (2022). Incorporation of SH source wave parameter “SH Polarization” within DST seismic trace characterization. Cone Penetration Testing 2022, 109–114. doi:10.1201/9781003308829-8.

Kim, D. S., Bang, E. S., & Kim, W. C. (2004). Evaluation of various downhole data reduction methods for obtaining reliable VS profiles. Geotechnical Testing Journal, 27(6), 585–597. doi:10.1520/gtj11811.

Ullah, S., Younas, S. W., Asim, M., Fahad, M., & Fahim, M. (2022). Site Effects Study in the Peshawar District using Seismic Noise. Civil Engineering Journal, 8(4), 751-764. doi:10.28991/CEJ-2022-08-04-010.

Chu, J., Wu, S. F., Chen, H., Pan, X. H., & Chiam, K. (2021). New Solutions to Geotechnical Challenges for Coastal Cities. Geotechnical Engineering Journal of the SEAGS & AGSSEA, 52(1), 61-66.

Prasad, B.N.V.S., Murthy, V.M.S.R., & Naik, S.R. (2022). Challenges in Drill Equipment Selection vis-à-vis Underground Excavations – A Methodology. Proceedings of Geotechnical Challenges in Mining, Tunneling and Underground Infrastructures, ICGMTU 2021, Lecture Notes in Civil Engineering, 228. Springer, Singapore. doi:10.1007/978-981-16-9770-8_9.

Hasan, M., Shang, Y., Shao, P., Yi, X., & Meng, H. (2022). Evaluation of Engineering Rock Mass Quality via Integration Between Geophysical and Rock Mechanical Parameters. Rock Mechanics and Rock Engineering, 55(4), 2183–2203. doi:10.1007/s00603-021-02766-8.

Stephenson, W. J., Yong, A., & Martin, A. (2022). Flexible multimethod approach for seismic site characterization. Journal of Seismology, 26(4), 687–711. doi:10.1007/s10950-022-10102-y.

Moran, A. R., & Hettiarachchi, H. (2011). Geotechnical characterization of mined clay from Appalachian Ohio: Challenges and implications for the clay mining industry. International Journal of Environmental Research and Public Health, 8(7), 2640–2655. doi:10.3390/ijerph8072640.

Crice, D. (2011). Near-surface, downhole shear-wave surveys: A primer. The Leading Edge, 30(2), 164–171. doi:10.1190/1.3555327.

Martin, G. K., & Mayne, P. W. (1997). Seismic Flat Dilatometer Tests in Connecticut Valley Varved Clay. Geotechnical Testing Journal, 20(3), GTJ19970011. doi:10.1520/gtj19970011.

Campanella, R. G., & Stewart, W. P. (1992). Seismic cone analysis using digital signal processing for dynamic site characterization. Canadian Geotechnical Journal, 29(3), 477–486. doi:10.1139/t92-052.

Saad, R., & Mohamad, E. T. (2014). Dynamic soil properties study using seismic down-hole geophysical method. Electronic Journal of Geotechnical Engineering, 19(Z2), 9931–9939.

Parasie, N., Franken, T., & Peuchen, J. (2022). Assessment of seismic cone penetration testing for small strain shear modulus. Cone Penetration Testing 2022, 203–208, CRC Press, Boca Raton, United States. doi:10.1201/9781003308829-23.

Kramer, S. L. (1996). Geotechnical earthquake engineering. Pearson Education India, Noida, India.

Markvorsen, S., & Pendás-Recondo, E. (2023). Snell’s law revisited and generalized via Finsler geometry. International Journal of Geometric Methods in Modern Physics, 20(08). doi:10.1142/s0219887823501384.

Hallal, M. M., & Cox, B. R. (2019). Theoretical Evaluation of the Interval Method Commonly Used for Downhole Seismic Testing. Geo-Congress 2019. doi:10.1061/9780784482131.038.

Auld, B. (1978). Cross-hole and down-hole vs by mechanical impulse. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 15(3), 67. doi:10.1016/0148-9062(78)90209-7.

Batsila, E. (1995). Investigation of ray path assumptions on downhole velocity profiles. PhD Thesis, University of Texas at Austin, Austin, United States.

Bang, E. S., & Kim, D. S. (2007). Improvement of Data Interpretation Method for Downhole Seismic Method. 4th International Conference on Earthquake Geotechnical Engineering, 25-29, June, 2007, Thessaloniki, Greece.

Edwards, C.H. (1979). The Calculus According to Cauchy, Riemann, and Weierstrass. The Historical Development of the Calculus. Springer Study Edition. Springer, New York, United States. doi:10.1007/978-1-4612-6230-5_11.

Dixit, N. D., & Mathur, P. K. (2021). Comparision of Numerical Accuracy of Bisection, Newton Raphson, Falsi-Position and Secant Methods. Advances in Mathematics: Scientific Journal, 10. doi:10.37418/amsj.10.12.13.

Bóna, A., & Slawinski, M. A. (2003). Fermat’s principle for seismic rays in elastic media. Journal of Applied Geophysics, 54(3–4), 445–451. doi:10.1016/j.jappgeo.2003.08.019.

O’reilly, O., Yeh, T. Y., Olsen, K. B., Hu, Z., Breuer, A., Roten, D., & Goulet, C. A. (2022). A High-Order Finite-Difference Method on Staggered Curvilinear Grids for Seismic Wave Propagation Applications with Topography. Bulletin of the Seismological Society of America, 112(1), 3–22. doi:10.1785/0120210096.

Noye, J. (1984). Finite Difference Techniques for Partial Differential Equations. North-Holland Mathematics Studies, 95–354, Elsevier, Amsterdam, Netherlands. doi:10.1016/S0304-0208(08)71201-5.

Esmailzadeh, M., Najafi, H. S., & Aminikhah, H. (2021). A numerical method for solving hyperbolic partial differential equations with piecewise constant arguments and variable coefficients. Journal of Difference Equations and Applications, 27(2), 172–194. doi:10.1080/10236198.2021.1881069.

Akujuobi, C. M. (2022). Wavelets and Wavelet Transform Systems and Their Applications: A Digital Signal Processing Approach. Springer, Cham, Switzerland. doi:10.1007/978-3-030-87528-2.

Full Text: PDF

DOI: 10.28991/CEJ-2023-09-10-016


  • There are currently no refbacks.

Copyright (c) 2023 Pedro Bautista, Zenon Aguilar

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.