Terrain correction computation using Gaussian quadrature

A method and a program (tcq) in FORTRAN 90 based on Gaussian quadrature are developed to compute the terrain correction (TC). TCs were determined on 1010 benchmarks using the Gaussian quadrature, prism and FFT methods using a 3″×3″ elevation grid for the inner zone and a 30″×30″ elevation grid for the outer zone. In order to achieve a 0.1 mgal accuracy in TC while reducing the computing time, the best inner and outer radii for TC computation are 20 and 200 km, respectively. The Gaussian quadrature is a highly accurate numerical integrator and yields results that outperform those from the prism method and the FFT method. The singular problem of the kernel function in TC is treated by considering the innermost zone effect, which can be expressed as a complete elliptic integral of the first kind. The innermost zone effect must be taken into account if the required accuracy of TC is at a 1-mgal level.