Papers Published

1. Malin, P.E., A first-order scattering solution for modelling elastic wave codas. I. The acoustic case, Geophys. J. R. Astron. Soc. (UK), vol. 63 no. 2 (1980), pp. 361 - 80 .
   (last updated on 2007/04/09)

   Abstract:
   A corrected, first-order solution for modelling acoustic wave scattering in layered halfspaces containing random inhomogeneities is derived. Energy lost to higher order scattering and intrinsic attenuation is included in the correction, which is constructed so that energy is conserved to first order. The complex propagation effects of the layering are overcome by representing the motion as a sum of normal modes. This approach renders the kinematic description of the scattering two dimensional, with the wave vectors of incident and scattered modes lying parallel to the layering. At each level in the halfspace, the inhomogeneities are resolved into two-dimensional Fourier spectra also parallel to the layering. The root mean square (rms) motion of a scattered mode depends on the correlation between spectra at different levels and the group velocity of the mode. To simplify the solution, it is assumed that the inhomogeneity spectra are piecewise constant and that the energy of a normal model propagates only at its group velocity. The final step of the theory establishes a criterion for the source-receiver separations over which the results are accurate

   Keywords:
   seismic waves;seismology;