Estimation of average shear V_sz and compressional V_pzwaves velocities using wavelength-depth relation obtained from surface waves analysis

Document Type : Research Article


1 M.Sc. Student, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran


Shear wave velocity ( ) and its average based on travel time from the surface to a depth of 30 m, is known as ( ) are often used in engineering projects to determine soil parameters, evaluate the dynamic properties of the soil and classify it. This quantity is directly related to the important property of soil and rock, i.e., their shear strength. The average shear wave velocity is used in geotechnics to assess soil liquefaction and in earthquake engineering to determine soil period, site amplification coefficient, and determination of attenuation. Usually, the average shear wave velocity is obtained from shear wave refraction survey, PS logging or from shear wave velocity profile obtained by inversion of experimental dispersion curve of surface waves. Surface wave analysis is one of the methods for estimating the profile of shear wave velocity, but inverting of dispersion curve is a time-consuming part of this process and also, the inverse problem has a non-unique solution. This becomes more evident when the goal is to determine a two- or three-dimensional shear wave velocity model.
This study provides a method to estimate directly the average shear wave velocity ( ) as well as the average compressional wave velocity ( ) from dispersion curves of surface waves without the need to invert the dispersion curves. For this purpose, we need to exploit the relation between surface wave wavelength and investigation depth. Estimating the wavelength-depth relationship requires access to a shear wave velocity model (a reference model) in the study area, which can be obtained from well data, refraction seismic profiles, or by inverting one of the experimental surface wave dispersion curves.
The  is then estimated directly from dispersion curve using the wavelength-depth relationship. In addition, due to the dependence of the value of  to Poisson's ratio and the sensitivity of the estimated wavelength-depth relationship to this ratio, we estimate the Poisson's ratio profile and average compressional velocity ( ) for the study area, from the .
For a given range of Poisson's ratio values, theoretical dispersion curves of the synthetic earth models are determined by forward modeling. Then using these dispersion curves and estimated average shear wave velocity of the model, the wavelength-depth relationship corresponding to each Poisson's ratio is determined. In the next step by comparing experimental and estimated wavelength-depth relationships, one can estimate the Poisson's ratio at each depth. Then the average compressional wave velocity ( ) is estimated using the  and the Poisson's ratios.
We evaluated the performance of the proposed method by applying on both real MASW seismic data set from USA and synthetic seismic data. The synthetic data collected over synthetic earth model and showed that the average shear and compression waves velocities are estimated with uncertainty of less than 10% in layered earth model with very large lateral variations in shear and compression waves velocities.
According to the results, the proposed method can be used to take the non-destructive advantages of the surface wave method in engineering, geotechnical, and earthquake engineering projects to get the average shear wave velocity .


Main Subjects

آئین‌نامه طراحی ساختمان‌ها در برابر زلزله استاندارد 2800 ایران ، 1384، کمیته دائمی بازنگری آیین نامه طراحی ساختمان‌ها در برابر زلزله، ویرایش سوم، مرکز تحقیقات ساختمان و مسکن.
Aki, K. and Richards, P. G., 2002, Quantitative seismology, Second Edition, University Science Books.
Ampuero, J. P., 2012, A Spectral Element Method tool for 2D wave propagation and earthquake source dynamics. California Institute of Technology Seismological Laboratory.
Bard, P.-Y., 1994, Effects of surface geology on ground motion: recent results and remaining issues, In Proc. of the 10th European Conf. on Earthquake Engineering, Vienna, 305-323.
Bergamo, P. and Socco, L. V., 2016, P- and S-wave velocity models of shallow dry sand formations from surface wave multimodal inversion: Geophysics, 81, no. 4, R197–R209, doi: 10.1190/geo2015-0542.1.
Brown, L. T., Diehl, J. G. and Nigbor, R. L., 2000, A simplified procedure to measure average shear-wave velocity to a depth of 30 meters (VS;30): Presented at the 12th World Conference on Earthquake Engineering.
BSSC, 1994, NEHRP Recommended provisions for the development of seismic regulations for new buildings, part I: Provisions, Building Seismic Safety Council, Federal Emergency Management Agency, Washington D.C.
Comina, C., Foti, S., Boiero, D. and Socco, L. V., 2011, Reliability of VS;30 evaluation from surface waves tests: Journal of Geotechnical and Geoenvironmental Engineering, 137, 579–586, doi: 10.1061/(ASCE)GT.1943- 5606.0000452.
Dobry, R., 2000, New site coefficients and site classification system used in recent building seismic code provisions, earthquake spectra, 16(1), 41-67.
Ernst, F., 2008, Multi-mode inversion for P-wave velocity and thick nearsurface layers: 14th European Meeting of Environmental and Engineering Geophysics, EAGE, Extended Abstracts, A13, doi: 10.3997/2214-4609 .20146236.
Foti, S. and Strobbia, C., 2002, Some notes on model parameters for surface wave data inversion: Symposium on the Application of Geophysics to Engineering and Environmental Problems SAGEEP, SEI6, doi: 10 .4133/1.2927179.
Gouveia, F., Gomes, R. C. and Lopes, I., 2019, Shallow and in depth seismic testing in urban environment: A case study in Lisbon Miocene stiff soils using joint inversion of active and passive Rayleigh wave measurements. Journal of Applied Geophysics, 169, 199-213.
Haney, M. M. and Tsai, V. C., 2015, Non perturbational surface-wave inversion: A Dix-type relation for surface waves: Geophysics, 80, no. 6, EN167–EN177, doi: 10.1190/geo2014-0612.1.
Hayashi, K., Craig, M., Kita, T. and Inazaki, T., 2015, CMP spatial autocorrelation analysis of multichannel passive surface-wave data. In SEG Technical Program Expanded Abstracts 2015 (pp. 2200-2204). Society of Exploration Geophysicists.
Ikeda, T., Tsuji, T., Konishi, C. and Saito, H., 2020, Extracting surface wave dispersion curves from two-station microtremor analysis in heterogeneous ambient noise wavefield. In SEG Technical Program Expanded Abstracts 2020. Society of Exploration Geophysicists, 3442-3446.
Konno, K. and Kataoka, S., 2000, New method for estimating the average s-wave velocity of the ground, Proceedings of the 6th International Conference on Seismic Zonation, Palm Springs, California, November, 2000.
Kramer, S.L., 1996, Geotechnical earthquake engineering, Pearson Education India.
Leong, E. C. and Aung, A. M.W., 2012, Weighted average velocity forward modelling of Rayleigh surface waves: Soil Dynamics and Earthquake Engineering, 43, 218–228, doi: 10.1016/j.soildyn.2012.07.030.
Li, P., Zhang, K., Zhang, Y. and Yan, Z., 2016, Near-surface shear-wave velocity estimation based on surface-wave inversion. The Leading Edge, 35(11), 940-945.
Mulargia, F., Castellaro, S., 2009, Experimental uncertainty on the Vs(z) profile and seismic soil classification. Seismol. Res. Lett. 80 (6), 985-988.
Murphy, J. R. and Shah H. K., 1988, An analysis of the effects of site geology on the characteristics of near-field Rayleigh waves, Bull. Seism. Soc. Am. 78, 64-82.
Nazarian, S. and Stokoe, K. H., 1984, In-situ shear wave velocity from spectral analysis of surface waves. In: Eighth World Conference on Earthquake Engineering, 3, 31-38.
Oda, Y., Hauser, E. C. and Gilliland, S., 2019, S-wave velocity structure using microtremor array measurements: a case study at Huffman Dam, OH, US. In The 13th SEGJ International Symposium, Tokyo, Japan, 12-14 November 2018. Society of Exploration Geophysicists and Society of Exploration Geophysicists of Japan, 347-350.
Okada, H., 2003, The Microtremor Survay Method. Society of Exploration Geophysicists, USA.
Olafsdottir, E. A., Erlingsson, S. and Bessason, B, 2018, Tool for analysis of multichannel analysis of surface waves (MASW) field data and evaluation of shear wave velocity profiles of soils. Canadian Geotechnical Journal, 55(2), 217-233.
Park, C. B., Miller, R. D., Xia, J., 1999, Multichannel analysis of surface waves. Geophysics, 63 (3), 800-808.
Power, M., Chiou, B. S. J., Abrahamson, N. A., Bozorgnia, Y., Shantz, T., and Roblee, C, 2008, An overview of the NGA project, Earthquake Spectra, 24, 3–21.
Sambridge, M., 1999, Geophysical inversion with a neighbourhood algorithm—I. Searching 833 a parameter space: Geophysical Journal International, 138, 479–494
Scherrer, E. F., 1999, Static corrections for seismic reflection surveys. ISBN 1-56080-080-1.
Serdyukov, A. S., Yablokov, A. V., Duchkov, A. A., Azarov, A. A. and Baranov, V. D., 2019, Slant f-k transform of multichannel seismic surface wave data. Geophysics, 84(1), A19-A24.
Socco, L. V., Foti, S. and Boiero, D., 2010, Surface wave analysis for building near surface velocitymodels: Established approaches and new perspectives: Geophysics, 75, no. 5, 75A83–75A102, doi: 10.1190/1.3479491.
Socco, L. V. and C. Comina, 2015, Approximate direct estimate of S-wave velocity model from surface wave dispersion curves: 21st Annual International Conference and Exhibition, EAGE, Extended Abstracts, A09.
Socco, L. V., Mabyalaht, G. and Comina, C., 2015, Robust static estimation from surface wave data. In SEG Technical Program Expanded Abstracts 2015. Society of Exploration Geophysicists, 5222-5227.
Strobbia, C., 2003, Surface wave methods: acquisition, processing and inversion.
Wathelet, M., Jongmans D. and Ohrnberger, M., 2004, Surface wave inversion using a direct search algorithm and its application to ambient vibration measurements, Near Surface Geophysics 2, 211-221.
Xia, J., Miller, R. D., Park, C. B. and Tian, G., 2003, Inversion of high frequency surface waves with fundamental and higher modes: Journal of Applied Geophysics, 52, 45–57, doi: 10.1016/S0926-9851(02)00239-2.
Yamanaka, H., Cimoto, K., Miyake, H., Korenaga, M., Tsuno, S. and Senna, S., 2019, Estimation of S-wave velocity structure around Fujikawa fault zone, Japan, from microtremor and earthquake records for seismic hazard assessment. In The 13th SEGJ International Symposium, Tokyo, Japan, 12-14 November 2018. Society of Exploration Geophysicists and Society of Exploration Geophysicists of Japan, 463-466.