  In [AIP Advances 6, 121707 (2016)], a soil structured with concrete columns
distributed within two specially designed seismic cloaks thanks to a
combination of transformational elastodynamics and effective medium theory was
shown to detour Rayleigh waves of frequencies lower than 10 Hz around a
cylindrical region. The aforementioned studies motivate our exploration of
interactions of surface elastic waves propagating in a thick plate (with soil
parameters) structured with concrete pillars above it. Pillars are 40 m in
height and the plate is 100 m in thickness, so that typical frequencies under
study are below 1 Hz, a frequency range of particular interest in earthquake
engineering. We demonstrate that three seismic cloaks allow for an
unprecedented flow of elastodynamic energy. These designs are achieved by first
computing ideal cloaks' parameters deduced from a geometric transform in the
Navier equations that leads to almost isotropic and symmetric elasticity (4th
order) and density (2nd order) tensors. To do this we extend the theory of
Non-Euclidean cloaking for light as proposed by the theoretical physicists
Leonhardt and Tyc. In a second step, ideal heterogeneous nearly isotropic
cloak's parameters are approximated by averaging elastic properties of sets of
pillars placed at the nodes of a bipolar coordinate grid, which is an essential
ingredient in our Non-Euclidean cloaking theory for elastodynamic waves.
Cloaking effects are studied for a clamped obstacle (reduction of the
disturbance of the wave wavefront and its amplitude behind a clamped obstacle).
Protection is achieved through reduction of the wave amplitude within the
center of the cloak.These results represent a first step towards designs of
Non-Euclidean seismic cloaks for surface (Rayleigh and Love) waves propagating
in semi-infinite elastic media structured with pillars.
