We use teleseismic recordings from a dense array of seismometers straddling both strands of the North Anatolian Fault Zone to determine crustal thickness, P/S velocity ratio and sedimentary layer thickness. To do this, we implement a new grid search inversion scheme based on the use of transfer functions, removing the need for deconvolution for source normalization and therefore eliminating common problems associated with crustal-scale receiver function analysis. We achieve a good fit to the data except at several stations located in Quaternary sedimentary basins, where our two-layer crustal model is likely to be inaccurate. We find two zones of thick sedimentary material: one north of the northern fault branch, and one straddling the southern branch. The crustal thickness increases sharply north of the northern strand of the North Anatolian Fault Zone (NAFZ), where the fault nearly coincides with the trace of the Intra-Pontide Suture; the velocity ratio changes across the southern fault strand, indicating a change in basement composition. We interpret these changes to indicate that both strands of the NAFZ follow preexisting geological boundaries rather than being ideally aligned with the stress field. The thick crust north of the northern NAFZ strand is associated with low topography and so is inconsistent with simple models of isostatic equilibrium, requiring a contribution from mantle density variations, such as possible loading from underthrust Black Sea oceanic lithosphere.