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

Abstract

Summary We 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.