A formula is developed to relate observed apparent complex frequencies of a multiplet to the interaction coefficients of the splitting matrix. This formula is then incorporated into a inversion scheme: estimating the interaction coefficients from the observed apparent complex frequencies. The numerical experiments demonstrated an excellent predictability of our method both in data (apparent complex frequencies) space and in model (aspherical structure of elasticity and anelasticity) space. ¿American Geophysical Union 1991