A perturbation method and its application: elastic tidal response of a laterally heterogeneous planet

S U M M A R Y Theory has been long established for computing the elastic response of a spherically symmetric terrestrial planetary body to both body tide and surface loading forces. However, for a planet with laterally heterogeneous mantle structure, the response is usually computed using a fully numerical approach. In this paper, we develop a semi-analytic method based on perturbation theory to solve for the elastic response of a planetary body with lateral heterogeneities in its mantle. We present a derivation of the governing equations for our second-order perturbation method and use them to study the high-order tidal effects caused by mode coupling between degree-2 body tide forcing and the laterally heterogeneous elastic structure of the mantle. We test our method by applying it to the Moon in which small long-wavelength lateral heterogeneities are assumed to exist in the elastic moduli of the lunar mantle. The tidal response of the Moon is determined mode by mode, for lateral heterogeneities with different depth ranges within the mantle and different horizontal scales. Our perturbation method solutions are compared with numerical results, showing remarkable agreement between the two methods. We conclude that our perturbation method provides accurate results and can be adapted to address a variety of forward and inverse response problems.

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