On Numerical Integration of Sea Bed Logging EM Models

This paper presents an alternative method to evaluate numerically the Fourier-Bessel integrals occurring in many electromagnetic field models used in the interpretation of geophysical data. In particular the interest is in the sea-bed-logging layered earth problem with a horizontal electric dipole (HED) in an anisotropic media when the lateral coordinate ρ is large (on the order of 10 km) resulting in highly oscillatory integrals that are difficult to evaluate numerically. The method replaces the real axis integration with a mathematically equivalent complex contour integration that converges exponentially when the product of the integration variable λ and the horizontal coordinate ρ is large. Example computations are made for the three components of the electric field for a standard form of the onedimensional HED layered earth model. Analytic and numerical forms are compared for the primary fields and show good agreement.