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Structure of the inner core is often measured through traveltime differences between waves that enter the inner core (PKPdf) and waves that travel through the outer core only (PKPab and PKPbc). Here we extend the method to converted waves PKSdf and SKPdf and compare results to PKP wave measurements. PKSdf and SKPdf have a very similar path to PKPdf and if velocity variations are present in the inner core, all three wave types should experience them equally. Since traveltime deviations can be due to velocity changes (either isotropic or anisotropy) as well as wave path deviations born from heterogeneity, we simultaneously investigate wave path directions and traveltimes of PKP, SKP and PKS waves for several source-array combinations. One of the path geometries is the anomalous polar corridor from South Sandwich to Alaska, which has strong traveltimes anomalies for PKPdf relative to more normal equatorial path geometries. Here we use array methods and determine slowness, traveltime and backazimuth deviations and compare them to synthetic data. We find that path deviations from theoretical values are present in all wave types and paths, but also that large scatter exists. Although some of the path deviations can be explained by mislocation vectors and crustal variations, our measurements argue that mantle structure has to be considered when investigating inner core anisotropy. Our polar path data show similar traveltime residuals as previously published, but we also find slowness residuals for this path. Interestingly, SKPdf and PKSdf for the South Sandwich to Alaska path show traveltime residuals that are partly opposite to those for PKPdf, possibly due to an interaction with a localized ultra-low velocity zone where waves enter the core. [ABSTRACT FROM AUTHOR]