A new approach to the theory of leaking modes is presented. By taking both the frequency (ω) and wavenumber (k) simultaneously as complex variables, it is shown that the transient wave solution for a point source in a layered elastic half-space can be reduced exactly to a sum of single integrals to be referred to as mode integrals. Each mode integral is associated with a single root ωm(k) of the characteristic equation Δ(ω,k) = 0. Each root is analytically continuous along the entire infinite path of integration for the associated mode integral. For a certain range of k, the root corresponds to a Rayleigh mode and for the remaining range it corresponds to a leaking mode. At appropriate distances and arrival times, the mode integrals can be accurately approximated by the saddle point method.
The theory is applied in detail to the computation of theoretical seismograms for body wave arrivals between Pn and Sn for a simple continental crustal model. The results prove to be in excellent agreement with corresponding results recently published by Bouchon which, for the first time, adequately explain the essential mechanism responsible for the unbiquitous complexity of observed crustal phases.