The harmonic expansion approach to the retrieval of deep Earth structure

Abstract

In the study of the structure of the earth, the most effective approximation is that of spherical symmetry. One dimensional models are employed in seismology with success: the variation with depth of the variables describing the state of the earth is much more important for predicting its functionals than the changes which take place over the horizontal scale. There are, however, important reasons for departing from this simple model and considering lateral variations in the parameters describing the planet. A onedimensional, spherically-symmetric model of the medium should represent a correct global average. A problem arises in the definition of the average: data distribution is highly nonuniform. Thus, if the variations seen in the data are not the result of a random process, but, on the contrary, contain some systematic effect, then the average could be geographically biased by the areas that are more densely sampled. This is in fact the case for the earth: we have evidence, coming from different sources, that there are significant, although small, systematic geographical variations. Consequently, spherical models are weighted averages of the structure of the earth, with a weight which varies geographically. The search for three-dimensional models is then of interest also for the sake of a better knowledge of the average earth.