Tunneling signals can be studied ideally by application of the Cagniard-de Hoop method. Here, we use this method to derive the response function for the canonical configuration of two acoustic half-spaces, excited by a line source. In order to reveal the characteristics of the tunneling signal, we expand the Cagniard response around the relevant ray parameter and evaluate the associated signal. The result is the nongeometrical arrival due to a tunneling ray. This arrival can be modeled accurately by asymptotic theory when the phase is allowed to be complex (instead of real in the case of geometrical arrivals); a few numerical results illustrate this.