We have developed a numerical method to convolve nonrigid effects with a nutation theory of the rigid Earth. We assume that the nonrigid effects are based on a linear response theory and that its transfer function is expressed as a rational function of the frequency. The polynomial parts of the transfer function are replaced by numerical differentiations, and the fractional parts are replaced by numerical integrations. In replacing the fractional part, our method requires the coefficients of the free oscillation. These are determined by fitting the theory that includes the nonrigid effects to the observational data. The numerical differentiations and integrations are effectively performed by means of symmetric formulae. Numerical tests show that our method is sufficiently precise, namely, the difference between the analytical and numerical convolutions is of the order of a nanoarcsecond. Since our method only requires the rigid nutation theory to be expressed as a numerical table of values versus time, it enables one to create a purely numerical nutation theory of the nonrigid Earth. By comparison with the numerically convolved results, we evaluate the errors of the current method for the analytical convolution in creating the nutation theory, which reach about 1 μas. We confirm that these errors come from an inappropriate treatment of the mixed secular terms. Even if a transfer function is real-valued, the nonrigid-Earth nutation series must contain out-of-phase terms as long as the corresponding rigid-Earth nutation series includes mixed secular terms.
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