A series approximation to the Kirchhoff integral for Gaussian and exponential roughness covariance functions

The Kirchhoff integral is a fundamental in scattering theory, appearing both the approximation and small slope approximation. In this work, functional Taylor series to presented, under condition that roughness covariance function follows either an exponential or Gaussian form—in one-dimensional two-dimensional cases. Previous approximations [Gragg, Wurmser, Gauss (2001) J. Acoust. Soc. Am. 110(6), 2878–2901; Drumheller Gragg 110(5), 2270–2275] assumed outer scale of was very large compared wavelength, whereas proposed method can treat arbitrary scales. Assuming infinite implies root mean square (rms) infinite. efficiently surfaces with finite therefore rms height. This shown converge independently acoustic parameters converges within roundoff error reasonable number terms for wide variety dimensionless parameters. quickly when height slowly it large.