Continuum mechanics and foundations of seismology

Theoretical seismology is a subject whose foundations belong to the realm of continuum mechanics. Consequently, its mathematical structure relies on formulations of such scholars as Cauchy, Voigt, Truesdell and Noll. The concepts of symmetries, invariances, etc. are intrinsic parts of this discipline. Inverse problems are the essence of the structure of
seismology; in this context, the contributions of Herglotz and Wiechert of the Göttingen Mathematical Institute should be emphasized.

In this talk, I will discuss the symmetries of a Hookean solid, which is used as a mathematical analogy for the Earth. I will show the solution
of the inverse problem of identifying the symmetry class and the orientation of such a solid in an arbitrary coordinate system. Also, I
will examine the issue of a given solid being close to a particular symmetry class, as opposed to belonging to it; an important issue in
view of both theoretical idealizations and experimental limitations.