A complete solution for the wave propagation of an SH torque pulse in a heterogeneous sphere in which density and shear modulus vary as the power of the distance from the center of the sphere is worked out. The solution which is obtained in the form of an infinite series of Legendre polynomial, is transformed into an integral and the integral is evaluated at a saddle point. It is found that times of arrival of different reflected phases agree with those predicted by geometrical ray theory. Further, the expectations in case of a homogeneous earth are also valid in the heterogeneous case.

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