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Seismic energy partitioning and scattering in laterally heterogeneous ocean crust

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Abstract

We present finite difference forward models of elastic wave propagation through laterally heterogeneous upper oceanic crust. The finite difference formulation is a 2-D solution to the elastic wave equation for heterogeneous media and implicitly calculatesP andSV propagation, compressional to shear conversion, interference effects and interface phenomena. Random velocity perturbations with Gaussian and self-similar autocorrelation functions and different correlation lengths (a) are presented which show different characteristics of secondary scattering. Heterogeneities scatter primary energy into secondary body waves and secondary Stoneley waves along the water-solid interface. The presence of a water-solid interface in the model allows for the existence of secondary Stoneley waves which account for much of the seafloor ‘noise’ seen in the synthetic seismograms for the laterally heterogeneous models.

‘Random’ incoherent secondary scattering generally increases aska (wavenumber,k, and correlation length,a) approaches one. Deterministic secondary scattering from larger heterogeneities is the dominant effect in the models aska increases above one. Secondary scattering also shows up as incoherence in the primary traces of the seisograms when compared to the laterally homogeneous case. Cross-correlation analysis of the initialP-diving wave arrival shows that, in general, the correlation between traces decreases aska approaches one. Also, because many different wave types exist for these marine models, the correlation between traces is range dependent, even for the laterally homogeneous case.

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References

  • Aki, K. (1973),Scattering of P-waves under the Montana Lasa, J. Geophys. Res.78, 1334–1346.

    Google Scholar 

  • Aki, K. (1982),Scattering and attenuation, Bull. Seism. Soc. Am.72, 319–330.

    Google Scholar 

  • Alford, R. M., Kelly, K. R., andBoore, D. M. (1974),Accuracy of finite difference modeling of the acoustic wave equation, Geophysics39, 834–842.

    Google Scholar 

  • Alterman, Z. andLoewenthal, D.,Computer generated seismograms, inMethods in Computational Physics, v. 12 (Bolt, B. A., ed.), (Academic Press, New York, 1972).

    Google Scholar 

  • Bhasavanija, K. (1983),A finite difference model of an acoustic logging tool: The borehole in a horizontally layered geologic medium, Ph.D. thesis, Colorado School of Mines, Golden, Colorado.

    Google Scholar 

  • Brekhovskikh, L. M.,Waves in Layered Media (Academic Press, New York, 1960), 503p.

    Google Scholar 

  • Bullen, K. E. andBolt, B. A.,An Introduction to the Theory of Seismology (Cambridge University Press, New York, 1985), 498p.

    Google Scholar 

  • Cerjan, C., Kosloff, D., Kosloff, R., andReshef, M. (1985),A nonreflecting boundary condition for discrete acoustic and elastic wave equations, Geophysics50, 705–708.

    Google Scholar 

  • Cerveny, V. andRavindra, R.,Theory of Seismic Head Waves (University of Toronto Press, Toronto. 1971), pp. 235–250.

    Google Scholar 

  • Chernov, L. A.,Wave Propagation in a Random Medium (McGraw-Hill Book Co., New York, 1960), 168p.

    Google Scholar 

  • Clayton, R. andEngquist, B. (1977),Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seis. Soc. Am.67, 1529–1540.

    Google Scholar 

  • Dougherty, M. E. andStephen, R. A. (1987),Geoacoustic scattering from seafloor features in the ROSE area, J. Acoust. Soc. Am.82, 238–256.

    Google Scholar 

  • Ewing, J. I. andPurdy, G. M. (1982),Upper crustal velocity structure in the ROSE area of the East Pacific Rise, J. Geophys. Res.87, 8397–8402.

    Google Scholar 

  • Fornberg, B. (1987),The pseudospectral method: Comparisons with finite differences for the elastic wave equation, Geophysics52, 483–501.

    Google Scholar 

  • Frankel, A. andClayton, R. W. (1986),Finite difference simulations of seismic scattering: Implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity, J. Geophys. Res.91, 6465–6489.

    Google Scholar 

  • Hudson, J. A. andHeritage, J. R. (1981),The use of the Born approximation in seismic scattering problems, Geophys. J. R. Astr. Soc.69, 649–657.

    Google Scholar 

  • Kelly, K. R., Ward, R. W., Treitel, S., andAlford, R. M. (1976),Synthetic seismograms: A finite difference approach, Geophysics41, 2–27.

    Google Scholar 

  • Levander, A. R. (1985),Use of the telegraphy equation to improve absorbing boundary efficiency for fourth-order acoustic wave finite difference schemes, Bull. Seism. Soc. Am.75, 1847–1852.

    Google Scholar 

  • Mandelbrot, B. B.,Fractals, Form, Chance, and Dimensions (W.H. Freeman and Company, 1977).

  • McLaughlin, K. L. (1983),Spatial coherency of seismic waveforms, Ph.D. thesis, Univ. of California-Berkeley, 275p.

  • McLaughlin, K. L., Anderson, L. M., andDer, Z. A. (1985),Investigation of scattering and attenuation of seismic waves using 2-dimensional finite difference calculations, presented at Symposium on scattering of waves in random media and random rough surfaces, Pennsylvania State University.

  • Morse, P. M. andFeshbach, H.,Methods of Theoretical Physics (McGraw-Hill Book Company, New York, 1953).

    Google Scholar 

  • Nafe, J. E. andDrake, C. L. (1957),Variations with depth in shallow and deep water marine sediments of porosity, density, and the velocities of compressional and shear waves, Geophysics22, 523–552.

    Google Scholar 

  • Nicoletis, L. (1981),Simulation numérique de la propagation d'ondes sismiques dans les milieux stratifiés à deux et trois dimensions: contributions à la construction et à l'interprétation des sismogrammes synthétiques, Ph.D. thesis, Université Pierre et Marie Curie, Paris, France.

    Google Scholar 

  • Purdy, G. M. (1982),The variability in seismic structure of layer 2 near the East Pacific Rise at 12 N, J. Geophys. Res.87, 8403–8416.

    Google Scholar 

  • Sato, H. (1982),Attenuation of S-waves in the lithosphere due to scattering by its random velocity structure, J. Geophys. Res.87, 7779–7786.

    Google Scholar 

  • Schirmer, F.,Experimental determination of properties of the Scholte wave in the bottom of the North Sea, inBottom-interacting Ocean Acoustics (eds. Kuperman, W. A., and Jensen, F. B.) (Plenum Press, New York, 1980) pp. 285–298.

    Google Scholar 

  • Stephen, R. A., in press,A review of finite difference methods for seismo-acoustic problems at the sea floor, Reviews of Geophysics.

  • Stephen, R. A. (1988),Lateral heterogeneity in the upper oceanic crust at DSDP Site 504, J. Geophys. Res.93, 6571–6584.

    Google Scholar 

  • Stephen, R. A., Pardo-Casas, F., andCheng, C. H. (1985),Finite difference synthetic acoustic logs, Geophysics50, 1588–1609.

    Google Scholar 

  • Stephen, R. A. andBolmer, S. T. (1985),The direct wave root in marine seismology, Bull. Seis. Soc. Am.75, 57–67.

    Google Scholar 

  • Tuthill, J. D., Lewis, B. R., andGarmany, J. D. (1981),Stoneley waves, Lopez Island noise, and deep sea noise from 1 to 5 Hz, Marine Geophysical Researches,5, 95–108.

    Google Scholar 

  • Vireux, J. (1986),P-SV wave propagation in heterogeneous media; Velocity-stress finite difference method, Geophysics51, 889–901.

    Google Scholar 

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Dougherty, M.E., Stephen, R.A. Seismic energy partitioning and scattering in laterally heterogeneous ocean crust. PAGEOPH 128, 195–229 (1988). https://doi.org/10.1007/BF01772597

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  • DOI: https://doi.org/10.1007/BF01772597

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