Crustal structure is characterized by large variations in topography/bathymetry of the surface and Moho, as well as by crustal velocity variations. While long period surface waves can be strongly affected by crustal structure, they lack the depth resolution necessary to constrain crustal thickness and velocity. Therefore, models of seismic velocities in the mantle depend on correcting the observed seismic waves for the effects of propagation through the crust. Typically, the effects of the crust are considered within the framework of normal mode summation and first order perturbation theory. One method, called the path average approximation (PAVA: Woodhouse and Dziewonski, 1984), assumes that the wave is only sensitive to structure along the great circle path joining the source with the receiver, and that this sensitivity is only a function of depth. Higher-order asymptotic approaches, such as non-linear asymptotic coupling theory (NACT: Li and Romanowicz, 1995), are capable of more accurately modeling the wave's actual sensitivity within the plane defined by the great circle path. However, in both approaches, the effects of crustal velocities are most often neglected, while the variations in Moho topography are considered as perturbations from an average Moho depth. On the other hand, the coupled Spectral Element Method (cSEM: Capdeville et al., 2003) is capable of fully accounting for 3D wave propagation through structure. Figure 2.59 illustrates that the differences between synthetic seismograms calculated using cSEM and NACT in a PREM mantle and realistic crustal structure can be large, especially on the transverse component. We explore the contamination of elastic models of the mantle that can result from such inadequacies in the forward modeling of crustal effects.

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