Earthquake focus as an excitable medium: consecutive axiomatics of scalar field description

Abstract

By the logic of author's works, new potentialities to develop the classical kinematic focus models appear if the basic relations concerning a distributed displacement discontinuity vector are treated as axiomatic statements. The modulus of the discontinuity vector or slip function is seen as an abstract scalar field, invariant under the group of "quasi-Lorentz" transformations, with some arbitrary constant in the role of the limit propagation velocity of interactions. A consistent axiomatics of the field is built, similar to the Lagrangian approach of ordinary physics, in the situation where there is no "underpinning" in experimental data. The attention is drawn to the non-traditionality of a key requirement of action minimality and to the issue of compatibility with the condition of positive definiteness of the energy density for an arbitrary nonlinear field.