Multiple Forward Scattering of Surface Waves: Comparison With an Exact Solution and Born Single-Scattering Methods

Abstract

S U M M A R YWe present a 2-D reformulation of surface wave scattering theory in terms of potentials, which allows an extension of the Born single-scattering approach to include multiple forward scattering. No additional numerical effort compared to single scattering is required for a computation of the wavefield over the whole heterogeneous region. Born single scattering for elastic surface waves and both multiple and single scattering for acoustic waves are also covered by the formulation. It is valid for fully anisotropic perturbations of the reference medium. We use the flexibility of our formulation to compare the different approximations with each other and, additionally, test all of them against an exact solution for the particular case of a cylindrical inclusion in a layered waveguide.Our numerical results, obtained for shear velocity contrasts of about 6 per cent, show that the method which includes multiple scattering is superior to the single-scattering methods if the scattering region extends over more than one wavelength. If coupling to higher modes is suppressed, the multiple-scattering method still yields nearly exact results for the vertical displacement. The influence of mode coupling and type conversion leads to only small errors in vertical displacement. Moreover, as we show for a cylinder with a diameter of two wavelengths, even an acoustic treatment of surface waves including multiple forward scattering may be more accurate than single scattering within an elastic treatment. For scatterer sizes below one wavelength the single-scattering approaches are accurate enough, while elastic and acoustic treatments of surface waves may differ considerably.The proposed multiple-scattering method is numerically very efficient, because the numerical effort mainly depends on the degrees of smoothness of the wavefield and the heterogeneity, and is not directly coupled to the wavelength.

Constituents of Vertical-component Coda Waves at Long Periods

“…To understand the nature of surface wave propagation through the inhomogeneous Earth structure, there have been many theoretical developments based on the Born approximation and its extensions (SNIEDER, 1986;FRIEDERICH et al, 1993;SPETZLER et al, 2002) mainly focusing on the phase change due to scattering. However, these studies paid little attention to the amplitude of scattered surface waves, especially at long lapse time.…”

Minor-arc and major-arc global surface wave diffraction tomography

“…Ray-theory is a high frequency approximation, however, which is not justi ed in the presence of heterogeneities whose length-scale is comparable to the wavelength of the wave e.g., Woodhouse, 1974;Wang & Dahlen, 1995. For the ray approximation to be valid, the rst Fresnel zone must be smaller than the scale-length of the heterogeneity, which places limitations on the lateral resolution of seismic models based on ray-theory. The Born or Rytov approximation for surface wave scattering e.g., Woodhouse & Girnius, 1982;Yomogida & Aki, 1987;Snieder & Romanowicz, 1988;Bostock & Kennett, 1992;Friederich et al, 1993, Friederich 1999Meier et al, 1997;Spetzler et al, 2001Spetzler et al, , 2002Yoshizawa & Kennett, 2002;Snieder, 2002 models the nite width of the surface wave sensitivity zone. Ritzwoller et al 2002 discussed the use of this approximation in the context of global surface wave tomography, calling the resulting method global di raction tomography.…”

Theory and Observations: Normal Mode and Surface Wave Observations

“…Anomalies are assumed to accumulate along the great-circle arc between the source and receiver. Advances in parametric surface wave modeling have been made through Gaussian beam ray-tracing techniques (e.g., Yomogida, 1985), Born single and multiple scattering (e.g., Friederich et al, 1993;Snieder and Nolet, 1987), or diffraction tomography (e.g., Meier et al, 1997;Ritzwoller et al, 2002). For example, Woodhouse and Girnius (1982) presented surface kernels for normal modes that show a rather broad corridor of sensitivity to structure along the sourcereceiver great circle.…”