Identify the two layers of earth where seismic s waves do not travel.

The outer core and the inner core

Explanation:

S waves are the secondary seismic waves or shear waves that can travel only in the solid but cannot travel in the liquid. It is because the outer core is liquid in nature and shear strength is absent in liquid. So this wave when reaches the outer core boundary, it gets absorbed. So it cannot travel in the outer core as well as in the inner core, thereby producing a shadow zone at 103°-103°.

the mantle

explanation:

earth is divided into three layers: the crust or the outermost layer on which we live; the underlying, middle layer - the mantle - and the core (the innermost layer of earth).