P'P' (PKPPKP) are P waves that travel from a hypocenter through the Earth's core, reflect from the free surface and travel back through the core to a recording station on the surface. Here we report the observations of hitherto unobserved near-podal P'P' waves (at epicentral distance < 10{sup o}) and very prominent precursors preceding the main energy by as much as 60 s. We interpret these precursors as a back-scattered energy from previously undocumented horizontally connected small-scale heterogeneity in the upper mantle beneath the oceans in a zone between 150 and 220 km depth beneath the Earth's surface. From these observations, we identify a frequency dependence of attenuation quality factor Q in the lithosphere through forward modeling of the observed amplitude spectra of the main and back-scattered P'P' waves. In addition, we did not find that travel times corresponding to very polar paths through the centermost inner core with respect to the rotation axis of Earth are anomalously advanced, which argues for isotropic or at best --weakly-anisotropic center of Earth in the direction parallel with the rotation axis. More systematic sampling near Earth's center and characterization of anisotropy in Earth's center will be a subject of future research efforts.