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APPLIED GEOPHYSICS  2018, Vol. 15 Issue (2): 290-298    DOI: 10.1007/s11770-018-0687-4
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Active-source Rayleigh wave dispersion by the Aki spectral formulation
Li Xin-Xin1 and Li Qing-Chun2
1. College of Earth Sciences and Engineering, Xi'an Shiyou University, Xi'an 710065, China.
2. College of Geology Engineering and Geomatics, Chang'an University, Xi'an 710054, China.
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Abstract Rayleigh wave imaging is efficient in estimating the shear- (S) wave velocity in near-surface exploration. The key is to accurately extract the dispersion of Rayleigh wave. We propose a method to calculate the dispersion of the active-source Rayleigh wavefield by using the Aki formulation. The spectrum after the cross correlation of two-channel records in the frequency domain is expressed by the Bessel function. Using the corresponding relation between the zero point of the spectrum real part and the Bessel function root, the phase velocity at the discrete frequency point is obtained and the dispersion curve is extracted. First, the theoretical basis and calculation method used in the active-source Rayleigh wave data are introduced. Then, three sets of theoretical models are calculated by this method and the results are consistent with the theoretical dispersion. Finally, we process a group of real Rayleigh wave data and obtain the phase velocity profiles and compared them with the results obtained by the multichannel surface wave analysis method. The effectiveness and applicability of the Aki method in active-source data processing are verified. Compared with multichannel wave processing, the advantage of the Aki method lies in the use of two-channel data in a single-shot record. When the number of acquisition channels in a shot gathers is insufficient or there is a bad channel, the quality of the extracted dispersion is guaranteed.
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Key wordsRayleigh wave   dispersion   Aki spectral formulation     
Received: 2016-07-30;

This research was jointly supported by the National Natural Science Foundation of China (No.s 41374145 and 41004043) and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JM4003).

Cite this article:   
. Active-source Rayleigh wave dispersion by the Aki spectral formulation[J]. APPLIED GEOPHYSICS, 2018, 15(2): 290-298.
[1] Aki, K., 1957, Space and time spectra of stationary stochastic wave, with special reference to microtremors: Bulletin of the Earthquake Research Institute, 35, 415−456.
[2] Asten, M. W., 2006, On bias and noise in passive seismic data from finite circular array data processed using spac methods: Geophysics, 71(6), V153−V162.
[3] Buchen, P. W., and Ben-Hedor, R., 1996, Free-mode surface-wave computations: Geophysical Journal International, 124, 869−887.
[4] Chávez-García, F. J., and Luzón, F., 2005, On the correlation of seismic microtremors: Journal of Geophysical Research, 110, B11313.
[5] Cox, H., 1973, Spatial correlation in arbitrary noise fields with application to ambient sea noise: Journal of the Acoustical Society of America, 54(5), 1289−1301.
[6] Dal, G., Pipan, M., and Forte, E., et al., 2003, Determination of Rayleigh wave dispersion curves for near surface applications in unconsolidated sediments: 73th Annual International Meeting, SEG Expanded Abstracts, 1247−1250.
[7] Dorman, J., and Ewing, M., 1962, Numerical inversion of seismic surface wave dispersion data and crust-mantle structure in the New York-Pennsylvania area: Journal of Geophysical Research, 67(13), 5227-5241.
[8] Ekström, G., Abers, G. A., and Webb, S. C., 2009, Determination of surface-wave phase velocities across Usarray from noise and Aki’s spectral formulation:
[9] Geophysical Research Letters,2009,36(18), 64−66.
[10] Herrmann, R. B., 2013, Computer programs in seismology, an evolving tool for instruction and research, Seismological Research Letters,84(6), 1081−1088.
[11] Lee, W. B., and Solomon, S. C., 1979, Simultaneous inversion of surface wave phase velocity and attenuation, Rayleigh and Love waves over continental and oceanic paths: Bulletin of the Seismological Society of America, 69, 65−95.
[12] Lin, F., Ritzwoller, M. H., and Snieder, R., 2009, Eikonal tomography, surface wave tomography by phase front tracking across a regional broad-band seismic array: Geophysical Journal International, 177(3), 1091−1110.
[13] Lobkis, O. I., and Weaver, R. L., 2001, On The emergence of the green’s function in the correlations of a diffuse field: Journal of the Acoustical Society of America, 110(6), 3011−3017.
[14] Luo, Y., Xia, J., and Miller, R. D., et al., 2008, Rayleigh-wave Dispersive energy imaging using a high-resolution linear radon transform: Pure and Applied Geophysics, 165(5), 903−922.
[15] Luo, Y., Xia, J., and Miller, R. D., et al., 2009a, Rayleigh-wave mode separation by high-resolution linear radon transform: Geophysical Journal International, 179(1), 254−264.
[16] Luo, Y., Xia, J., and Xu, Y., et al., 2009b, Dipping-interface mapping using mode-separated Rayleigh waves: Pure and Applied Geophysics, 166(3), 353−347.
[17] Mcmechan, G. A., and Yedlin, M. J., 1981, Analysis of dispersive waves by wave field transformation: Geophysics, 46, 101−113.
[18] Nakahara, H., 2006, A systematic study of theoretical relations between spatial correlation and Green’s function in one-, two- and three-dimensional random scalar wavefields: Geophysical Journal International, 167(3), 1097−1105.
[19] Pan, Y., Xia, J., and Zeng, C., 2013, Verification of correctness of using real part of complex root as rayleigh-wave phase velocity with synthetic data, Journal of Applied Geophysics, 88(1), 94−100.
[20] Park, C. B., Miller, R. D., and Xia, J., 1998, Imaging dispersion curves of surface waves on multi-channel record: 68th Annual International Meeting, SEG Expanded Abstracts, 1377−1380.
[21] Sanchez-sesma, F., and Campillo, M., 2006, Retrieval of the Green’s function from cross-correlation, the canonical elastic problem: Bulletin of the Seismological Society of America, 96(3), 1182−1191.
[22] Song, Y., Castagna, J. P., and Black, R. A., et al., 1989, Sensitivity of near-surface shear-wave velocity determination from Rayleigh and Love waves: 59th Annual International Meeting, SEG Expanded Abstracts 1989, 509−512.
[23] Stephenson, W. J., Louie, J. N., and Pullammanappallil, S., et al., 2006, Blind shear-wave velocity comparison of Remi and MASW results with boreholes to 200 m in Santa Clara valley, implications for earthquake ground-motion assessment: Bulletin of the Seismological Society of America, 95(6), 2506−2516.
[24] Sun, C. Y., Wang, Y. Y., and Wu, D. S., et al., 2017, Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm: Applied Geophysics, 14(4), 551−558.
[25] Tsai, V. C., and Moschetti, M. P., 2010, An explicit relationship between time-domain noise correlation and spatial autocorrelation (SPAC) results: Geophysical Journal International, 182(1), 454−460.
[26] Wapenaar, K., Slob, E., and Snieder, R., 2006, Unified Green’s function retrieval by cross-correlation: Physical Review Letters, 97(23), 234−301.
[27] Xia, J., Miller, R. D., and Park, C. B., 1999, Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves: Geophysics, 64(3), 691−700.
[28] Xia, J., Miller, R. D., and Park, C. B., et al., 2002, Determining Q of near-surface materials from Rayleigh waves. Journal of Applied Geophysics, 51(2-4), 121-129.
[29] Xia, J., Xu, Y., and Miller, R. D., 2007, Generating an image of dispersive energy by frequency decomposition and slant stacking: Pure and Applied Geophysics, 164(5), 941−956.
[30] Xu, C., and Butt, S. D., 2006, Evaluation of masw techniques to image steeply dipping cavities in laterally inhomogeneous terrain: Journal of Applied Geophysics, 59(2), 106−116.
[31] Yao, H., Campman, X., and Hoop, M. V. D., et al., 2009, Estimation of surface wave green’s functions from correlation of direct waves, coda waves, and ambient noise in SE Tibet:Physics of the Earth & Planetary Interiors,77(1−2), 1−11.
[32] Yilmaz, Ö., 1987, Seismic data processing, society of exploration geo- physicists, Tulsa, OK.
[33] Yilmaz, Ö., Eser, M., and Berilgen, M., 2006, A case study of seismic zonation in municipal areas: The Leading Edge, 25(3), 319−330.
[34] Zhou, T. F., Peng, G. X., and Hu, T. Y., et al., 2014, Rayleigh wave nonlinear inversion based on the firefly algorithm: Applied Geophysics, 11(2), 167−178.
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