The effect of transition regions between continental and oceanic structures on the propagation of L_g waves from continental sources is examined. In particular, the attenuation due to variations in layer thickness in such transition regions is calculated and explained for a suite of simple models. The measured attenuation, due to the geometry of the transition regions between the oceanic and continental structures within a partially oceanic path with source and receiver in a continental structure, is at most a factor of four for frequencies from 0.01 to 1 Hz. This is inadequate to explain the observed extinction of L_g along such paths. This extinction has previously been attributed to the effects of the transition region geometry. The method used to calculate the results presented in this study is developed and its validity and accuracy are demonstrated. Propagator matrix seismograms are coupled into a Finite Element calculation to produce hybrid teleseismic SH mode sum seismograms. These hybrid synthetics can be determined for paths including any regional transition zone or other heterogeneity that exists as part of a longer, mostly plane-layered, path. Numerical results presented for a suite of transition models show distinct trends in each of the regions through which the wavefield passes. The wavefield passes through a continent-ocean transition region, then a region of oceanic structure, and finally through an ocean-continent transition region. When an L_g wavefront passes through a continent-ocean transition, the amplitude and coda duration of the L_g wave at the surface both increase. At the same time, much of the modal L_g energy previously trapped in the continental crust is able to escape from the lower crust into the subcrustal layers as body waves. The magnitude of both these effects increases as the length of the transition region increases. When the wavefront passes through the region of oceanic structure further energy escapes from the crustal layer, and produces a decrease in L_g amplitude at the surface. The rate of amplitude decrease is maximum near the transition region and decreases with distance from it. When the wavefield passes through the ocean-continent transition region a rapid decrease in the L_g amplitude at the surface of the crust results. The energy previously trapped in the oceanic crustal layer spreads throughout the thickening crustal layer. Some of the body wave phases produced when the wavefield passes through the continent-ocean transition region are incident on the continental crust in the ocean-continent transition region. These waves are predominantly transmitted back into the crust. The other body wave phases reach depths below the depth of the base of the continental crust before reaching the ocean-continent transition and, thus, escape from the system
