Earth's lowermost mantle has thermal, chemical, and mineralogical complexities that require precise seismological characterization. Stacking, migration, and modeling of over 10,000 P and S waves that traverse the deep mantle under the Cocos plate resolve structures above the core-mantle boundary. A small -0.07 +/- 0.15% decrease of P wave velocity (Vp) is accompanied by a 1.5 +/- 0.5% increase in S wave velocity (V(s)) near a depth of 2570 km. Bulk-sound velocity [Vb = (Vp2 - 4/3Vs2)1/2] decreases by -1.0 +/- 0.5% at this depth. Transition of the primary lower-mantle mineral, (Mg(1-x-y) Fe(x)Al(y))(Si,Al)O3 perovskite, to denser post-perovskite is expected to have a negligible effect on the bulk modulus while increasing the shear modulus by approximately 6%, resulting in local anticorrelation of Vb and Vs anomalies; this behavior explains the data well.