Modelling of seismic phenomena
Robert Hooke as seen by Roberto Lauciello (2017)
Broadly speaking and depending on a chosen emphasis, our research can be classified within mathematical physics, continuum mechanics and seismology.
The intent of our work is to enhance theoretical aspects of seismology to render subtleties within empirical data accessible as physical information. In this process, a theory can either precede or follow observations. An experiment can be set up to support a theoretical prediction or a theory can be formulated to retrodict an observation.
We focus on the foundations of seismic theory not on the case studies of its applications. Nevertheless, interactions with such studies are important as motivations for our work and as support for our predictions. As a consequence, our work is published in mathematical journals rather than in geophysical ones.
Our novel formulations are exemplified by the following:
“This one-of-a-kind book is both refreshing and refined. It is refreshing in its presentation of an amazing blend of fundamental scientific and philosophical questions with their practical implications to concrete examples in Seismology. It is refined in its
style, in the sophistication of its quotes, in the breadth of its sources and in the many details that reveal a labour of love. It makes Seismology and natural science in general appear exciting and worthy of a lifelong pursuit. As an additional bonus, the book is also extremely useful. It presents the underlying theory of the relevant aspects of Continuum Mechanics in a clear and sufficiently rigorous way, while challenging the reader’s intellect at every step
of the way. Each chapter is followed by a set of highly nontrivial exercises, whose detailed and reasoned solution is provided. [...] Particularly welcome are the two chapters on material symmetries, regardless of their application to wave propagation. The appendices, extending over more than a hundred pages, can be considered as an independent introduction to solid mechanics. This inspiring book is highly recommended.”
University Professor of Rational Mechanics,
University of Calgary
In each case, the subject, in a broad sense, had been familiar to many geophysicists for several decades. Also, not uncommonly, the subject grew though an empirical approach rather than a theoretical one. This explains the fact that among hundreds of case studies, in which an orientation of a symmetry plane is assumed or in which Backus averaging is applied, there is hardly any mention about relaxation of restrictive assumptions or any attempt of a foundational examination of validity of approximations.
Generalization of Snell's law
Extension of proofs of Fermat’s principle
Proofs of only eight symmetry classes of a Hookean solid
Coordinate-free characterization of elasticity tensors
Fréchet-derivative approach as a ray-theory concept
Extension of wavefronts and rays
Effective elasticity tensors and distance in the 21D space
Mathematical constraints of Backus averaging