Phd manuscript of Shoaib Ayjaz MOHAMMED
Phd defense scheduled on Sept. 26th, 2024

Abstract

It is well established that the presence of the urban agglomerate significantly modifies
the free-field ground motion at the city scale. Each building can behave as
a resonator, trapping a small fraction of seismic surface waves that is reradiated
into the ground. But when tall buildings are densely clustered, like in a city, can
we anticipate surface waves to interact with them in unusual ways? Perhaps yes.
Evidence suggests resonance coupling between vibrating structures like trees can
lead to anomalous dispersion of surface waves causing them to become evanescent
in certain frequency bands. Such media are called ‘locally-resonant’ seismic metamaterials,
and the collective behavior when several structures are present inside one
seismic wavelength corresponds to the physics observed at the lab-scale for elastic
waves in a plate with a set of rods attached to it.

This doctoral thesis focuses on metamaterial physics at the geophysics scale (a
few meters to a few kilometers) in the urban seismology context. Starting with a
relatively well understood problem of elastic wave scattering due to shallow surface
obstacles, we explain how buried columns called ‘piles’ can resonate when clamped
to a stiffer half-space. We selectively excite the dominant fundamental Rayleigh
wave mode using time-reversal and phased source array. This allows us to quantify
the scattering due to a clamped pile, which shows resonance peaks in the Mie regime.
We analyze ambient noise recordings inside a forest of pine trees and inside wind
farms, which act as proxies for a city with tall buildings. First, we revisit the dataset
acquired from dense arrays deployed in the Landes forest characterized by a dense
pine tree configuration. We observe an evanescent field radiated by the longitudinal
resonances of trees, as expected in an elastic metasurface. On the contrary, flexural
resonances in the 1-10 Hz regime, appear to have a weak coupling with the surface
waves. Plane-wave beamforming analysis of a 9-day ambient noise recording reveals
a strong cos 2θ Rayleigh wave azimuthal anisotropy (> 10%) in the forest. However,
identifying the precise source of the anisotropy with the available field data proves
challenging and numerical simulations seem necessary.

We then extend the hypothesis of coupled resonators to a forest of wind turbines.
We initially acquire data from a relatively sparse array cutting across the San Gorgonio
Pass wind farm in California. However, the spectral ratio analysis and noise
correlation of geophone pairs do not suggest any metamaterial effect, which could
be due to the spatial configuration of the turbines. We perform a field experiment
in the Nauen wind farm in Brandenburg, which hosts much larger turbines. The
dense spatial sampling from the DAS fiber-optic sensors gives us interesting insights
into the near-field radiation of the turbines. The surface field strongly attenuates
in distinct frequency bands, suggesting a metamaterial-like effect inside the wind farm.

Finally, we conduct a field experiment that aims to understand the interaction
between the ground and a simple resonator. Both active and passive data is acquired
by designing three suitable array configurations for the different phases of the experiment,
which we use to evaluate the dynamic response of the structure and the
soil. Through this effort, we generate a quality dataset in a controlled environment
for future investigation of soil-structure interaction.

The experimental and numerical studies in this thesis directly contribute to the
understanding of how seismic surface waves interact with specific features of the
urban landscape from the novel perspective of metamaterial physics. The results
might have implications for seismic hazard in urban areas.

Updated on 11 September 2024