Micropolar Modeling of Shear Wave Dispersion in Marine Sediments and Deep Earth Materials: Deriving Scaling Laws

We draw connections between eight different theories used to describe microscopic (atomic) and macroscopic (seismological) scales. In particular, we show that all these different theories belong to a particular case of a single partial differential equation, allowing us to gain new physical insights and draw connection among them. With this general understanding, we apply the micropolar theory to the description of shear-wave dispersion in marine sediments, showing how we can reproduce observations by only using two micropolar parameters in contrast to the seventeen parameters required by modifications of Biot's theory. We next establish direct connections between the micro (laboratory) and macro (seismological) scales, allowing us to predict (and confirm) the presence of post-perovskite in the lowermost mantle based on laboratory experiments and to predict the characteristic length Lc at which shear deformation becomes significant at seismological scales in the lowermost mantle.