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We are now in a position to extend our results to the problem of many layers. Suppose that underlying the plane surface of the earth we have a series of n layers, each of which is bounded above and below by planes parallel to the surface. Beginning at the surface, the thicknesses of the beds are consecutively hI, h2, ha, … , hn , and the seismic wave velocities in these beds are denoted by VI, V2, Va, … , Vn, respectively. For the present we shall add a further restriction by requiring the velocities to increase with depth; i.e.,

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