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Seismic wave scattering inversion for fluid factor of heterogeneous media

Science China Earth Sciences volume 57, pages 542–549 (2014)Cite this article

Abstract

Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media. Combining inverse scattering theory, perturbation theory and stationary phase approximation, we derive the P-wave seismic scattering coefficient equation in terms of fluid factor, shear modulus and density of background homogeneous media and perturbation media. With this equation as forward solver, a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media. In this method, Cauchy distribution is utilized to the ratios of fluid factors, shear moduli and densities of perturbation media and background homogeneous media, respectively. Gaussian distribution is utilized to the likelihood function. The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters. Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.

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References

  • Beylkin G, Burridge R. 1990. Linearized inverse scattering problems in acoustics and elasticity. Wave Motion, 12: 15–52

    Article  Google Scholar 

  • Biot M. 1956. General solutions of the equations of elasticity and consolidation for a porous material. J Appl Mech, 23: 91–96

    Google Scholar 

  • Biot M. 1962. Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am, 34: 1254–1264

    Article  Google Scholar 

  • Buland A, Omre H. 2003. Bayesian linearized AVO inversion. Geophysics, 68: 185–198

    Article  Google Scholar 

  • Burns D R, Willis M E, Toksoz M N, et al. 2007. Fracture properties from seismic scattering. Lead Edge, 26: 1186–1196

    Article  Google Scholar 

  • Cervený V. 2000. Seismic Ray Theory. Cambridge: Cambridge University Press. 124

    Google Scholar 

  • Chen J J, Yin X Y. 2007. Three parameter AVO waveform inversion based on Bayesian theorem (in Chinese). Chin J Geophys, 50: 1251–1260

    Google Scholar 

  • Downton J E, Lines L R. 2004. Three term AVO waveform inversion. Seg Tech Prog Exp Abs, 23: 215–218

    Google Scholar 

  • Gassmann F. 1951. Uber die elastizitat poroser medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, 96: 1–23

    Google Scholar 

  • Hudson J. 1968. The scattering of elastic waves by granular media. Q J Mech Appl Math, 21: 487–502

    Article  Google Scholar 

  • Hudson J. 1977. Scattered waves in the coda of P. J Geophys, 43: 8

    Google Scholar 

  • Kaslilar A. 2007. Inverse scattering of surface waves: Imaging of near-surface heterogeneities. Geophys J Int, 171: 352–367

    Article  Google Scholar 

  • Liu F P, Meng X J, Wang Y M, et al. 2010. Jacobian matrix for the inversion of P- and S-wave velocities and its accurate computation method. Sci China Earth Sci, 54: 647–654

    Article  Google Scholar 

  • Liu E R, Chapman M, Zhang Z J, et al. 2006. Frequency-dependent anisotropy: Effects of multiple fracture sets on shear-wave polarizations. Wave Motion, 44: 44–57

    Article  Google Scholar 

  • Liu E R, Queen J H, Zhang Z J, et al. 2000. Simulation of multiple scattering of seismic waves by spatially distributed inclusions. Sci China E-Tech Sci, 43: 387–394

    Article  Google Scholar 

  • Liu E R, Zhang Z J. 2001. Numerical study of elastic wave scattering by cracks or inclusions using the boundary integral equation method. J Comput Acoust, 9: 1039–1054

    Article  Google Scholar 

  • Miles J W. 1960. Scattering of elastic waves by small inhomogeneities. Geophysics, 25: 642

    Article  Google Scholar 

  • Mora P, Sarwar A K M, Smith D L. 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics, 52: 1211–1228

    Article  Google Scholar 

  • Rajan S D, Frisk G V. 1989. A comparison between the Born and Rytov approximations for the inverse backscattering problem. Geophysics, 54: 864–871

    Article  Google Scholar 

  • Russell B H, Hedlin K, Hilterman F J, et al. 2003. Fluid-property discrimination with AVO: A Biot-Gassmann perspective. Geophysics, 68: 29

    Article  Google Scholar 

  • Scarpetta E, Tibullo V. 2008. On the oblique penetration of elastic waves into a finite number of equally spaced periodic arrays of obstacles. Wave Motion, 45: 518–539

    Article  Google Scholar 

  • Shaw R K, Sen M K. 2004. Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophys J Int, 158: 225–238

    Article  Google Scholar 

  • Smith G C, Gidlow P M. 1987. Weighted stacking for rock property estimation and detection of gas. Geophys Prospect, 35: 993–1014

    Article  Google Scholar 

  • Stolt R H, Weglein A B, Abd Elhadi Y E. 1985. Migration and inversion of seismic data. Geophysics, 50: 2458–2472

    Article  Google Scholar 

  • Weglein A B. 1993. Nonlinear inverse scattering for multiple attenuation. Society of Photo-Optical Instrumentation Engineers Conference Series. 158–160

    Google Scholar 

  • Wu R S, Aki K. 1985. Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics, 50: 582–595

    Article  Google Scholar 

  • Yang P J, Yin X Y. 2008. Nonlinear quadratic programming Bayesian prestack inversion (in Chinese). Chin J Geophys, 51: 1876–1882

    Google Scholar 

  • Zhang H, Weglein A B. 2009a. Direct nonlinear inversion of 1D acoustic media using inverse scattering subseries. Geophysics, 74: 29–39

    Article  Google Scholar 

  • Zhang H, Weglein A B. 2009b. Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series. Geophysics, 74: 15–27

    Google Scholar 

  • Zoeppritz K, Geiger L, 1919. Erdbebenwellen VIII B, Uber Reflexion and durchgang seismischer wellen duch unstetigkeitsflachen. Gottinger Nachr, 1: 66–84

    Google Scholar 

  • Zong Z Y, Yin X Y, Wu G C. 2012a. Elastic impedance variation with angle inversion for elastic parameters. J Geophys Eng, 9: 24

    Article  Google Scholar 

  • Zong Z Y, Yin X Y, Wu G C. 2012b. AVO inversion and poroelasticity with P- and S-wave moduli. Geophysics, 77: N29–N36

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Geosciences, China University of Petroleum (Huadong), Qingdao, 266580, China

    XingYao Yin, ZhaoYun Zong & GuoChen Wu

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  1. XingYao Yin
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  2. ZhaoYun Zong
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  3. GuoChen Wu
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Correspondence to XingYao Yin.

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Yin, X., Zong, Z. & Wu, G. Seismic wave scattering inversion for fluid factor of heterogeneous media. Sci. China Earth Sci. 57, 542–549 (2014). https://doi.org/10.1007/s11430-013-4783-2

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  • DOI: https://doi.org/10.1007/s11430-013-4783-2

Keywords

  • heterogeneous media
  • fluid factor
  • seismic wave scattering
  • pre-stack seismic inversion