The autofrequencies of an elastic layer of soil of finite depth and of linearly varying modulus of rigidity are found theoretically in the case (i) when the rigidity of the material increases, or (ii) decreases with depth. Also, it is shown that an approximate expression for the autofrequencies based on the mean of the limiting values of the rigidities holds within a few per cent of the true autofrequencies for small values of the rigidity ratio. The response equations for the overburden are also found in terms of the velocity spectrum of the region, or else in terms of a generalized disturbing function go(t).

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