Asymptotic approximations are obtained for the electric field associated with a traveling wave current filament above Earth. A first-order asymptotic solution is obtained by applying the steepest descent technique to the direct and reflected fields separately. The first-order solution is used together with a recurrence relationship to obtain a second-order asymptotic approximation for the total field. Superposition of the fields due to two semi-infinite wires is used to find the field associated with a finite length traveling wave current filament above Earth. The fields which are computed using the asymptotic approximations are compared with the ''true'' fields which are obtained by numerical integration of the two-dimensional Sommerfeld integral. The second-order asymptotic approximation is found to yield accurate results for all observation points located away from the source. ¿ American Geophysical Union 1994