abstract Travel times and amplitudes of PKP, P2KP and higher multiple K phases are determined from a worldwide distribution of short-period seismograms. The sources are one explosion in Novaya-Zemlya and seven earthquakes, consisting of one intermediate focus event in the New Hebrides, and deep-focus events in Fiji, Java, Kermadec Islands, and Peru. The data are used to determine a new velocity model of the lowest mantle and the core. In the new velocity model 132, the velocity of the bottom of the mantle is 13.44 km/sec; the core mantle boundary is placed at 2892 ± 2 km. The velocity model of the core produces the PKP caustic B1 at 143° and the P2KP caustic B2 at −125°. A velocity discontinuity of 0.01 km/sec at a depth of 4550 km represents the top of the transition zone to account for the earliest forerunners of PKP. To account for the later forerunners a second discontinuity of 0.02 km/sec is placed at a depth of 4850 km. Since the forerunner data could not be resolved into branches, neither discontinuity is well defined. The top of the inner core boundary is placed at a depth of 5145 km with an uncertainty of at least 10 km and represents a discontinuity of 0.576 km/sec. Older core models have transition zone discontinuities an order of magnitude larger than those of model 132 with a discontinuity at the inner core boundary of about 1 km/sec. The smaller velocity discontinuities are a result of interpreting the amplitudes and travel times of PKP so that the turning points D and G are located at 120° and 140°, respectively, rather than at 110° and 125° as in previous interpretations. Amplitude ratios of PKP phases yield an inner core Q of about 400 and amplitude ratios of P3KP, P4KP and P5KP result in an outer core Q of about 4000.