In the context of climate change, the most superficial part of the subsoil, the so-called critical zone, is affected by the recurrence of sudden meteorological events, by the alternation of droughts and heavy rains. These phenomena lead to rapid variations in the levels of surface water tables and the water profiles of unsaturated zones, causing changes in the mechanical properties of the subsoil and increased vulnerability to flooding. Monitoring the state of the near surface is therefore crucial to enable the adaptation of anthropized urban areas to climate change.
Geophysical techniques allow spatial zoning of the physical parameters of the medium with depth, particularly in urban environments, which are more complex due to their heterogeneous structure, and composed of media that have been heavily reworked during the Anthropocene (Liu and Chan, 2007). Among them, direct current (DC) geoelectric techniques (e.g. Loke et al., 2013) are acknowledged for providing information on water content and on the position of the saturation level. In parallel, seismic monitoring is booming for the assessment of groundwater levels and subsoil water content at the scale of watersheds or water retention areas (Gaubert- Bastide et al., 2022). These approaches aim to identify relative time variations in subsoil parameters from measurements acquired over long periods. However, the need to estimate absolute values and to infer their spatial variations at a given time reveals the necessity for a finely resolved imaging approach. However, the reliability of the imaging processes for each of the two methods is quite limited. Different studies have shown the complementarity of seismic (propagation speeds) and geoelectric (resistivity) parameters for the characterization of geological structures, leading to joint inversion or data fusion strategies (Dezert et al., 2022). Most of these works are based, in seismics, on first arrival time tomography (body waves, e.g. Colombo and Rovetta, 2018). However, in urban environments, which are highly attenuating for body waves, surface waves (SW) are required. The few approaches combining SW seismic and DC geoelectrical data show promising potential but rely on the combination of imaging results and not on the combination of data (e.g. Coulouma et al., 2012; Coulouma et al., 2013).
In
this
context, this thesis
proposes to build a
fine imaging
methodology, based
on the inversion of
SW seismic and DC
geoelectrical
observables, to
characterize
saturation levels in
urban
environments.
The innovative
imaging tools
developed for
geoelectrical and
surface wave
inversion will be
used (Wang et al.
2021, Pageot et al.
2018) for the
reconstruction of 2D
sections of
the
subsurface. In order
to overcome the
difficulty of
directly
(physically) linking
the two parameters
to a common
petrophysical
quantity, a twofold
imaging process
(seismic velocity
and electrical
resistivity) is
considered in a
collaborative
inversion approach,
promoting a common
spatial structure
between the 2D
images. The
scientific approach
will implement a
dual numerical and
experimental
approach.
First, the 1D problem (tabular environment) will be considered in order to identify the levers from the two geophysical sources that best constrain the inversion process. In the 1D case, analytical solutions to both forward problems allow for fast and accurate computations, for robust results that can then be used in 2D.
This study will first be conducted numerically to evaluate the geophysical signatures of different plausible water profiles within simplified lithological sections. It will involve solving the forward SW seismic and DC geoelectrical problems separately, but on analogous hydrogeological models. This analysis will characterize the sensitivities of geophysical observables and their complementarity, to explore the collaborative reconstruction of spatially correlated 1D geophysical sections (seismic velocity and electrical resistivity).
In parallel, an experimental validation will be conducted on reduced-scale laboratory models (Dezert et al., 2019 ; Pageo et al., 2017). The main obstacle here will be the design of an experimental model common to both modalities, or of two separate but "analogous" models in terms of internal structure and water profile.
The thesis will then address 2D imaging, i.e., imaging media whose properties vary in a given vertical plane (section plane). The media studied, numerically simulated, will integrate specificity of urban environments (strong contrasts, alternations of high and low seismic velocities) at metric to decametric scales. The simultaneous reconstruction of seismic velocity and electrical resistivity images will be formulated as a joint optimization problem in these two quantities, which we will seek to correlate.
Unlike
the 1D
case, forward
problems no longer
admit analytical
solutions.
Numerical
resolution tools
will be considered,
specific to each
problem (spatial
resolution,
discretization
scheme, specific
complexity). A cost
function measuring
the error between
the
predictions of
forward problems and
the measurements
will be built,
exploiting the
experience acquired
on the 1D problem by
considering
the
sensitivities of the
two observables as a
function of the
environment. A
regularization term
will be introduced
in order to
couple
the problems by
favoring spatial
structures common to
both
images: "edge-
preserving" penalty
(Rudin et al., 1992)
in a
joint form, or
structure penalty
(Doetsch et al.,
2010). An
alternative will
consider the
reconstruction of
seismic velocities
guided by the prior
reconstruction of
resistivities (or
conversely),
or an
iterative process
alternately updating
the two images.
Since
forward
problems are
obtained from
numerical solvers,
the evaluation
of
the gradient of the
objective function
becomes numerically
expensive, therefore
optimization will be
performed by
derivative-free
optimization
techniques (Audet et
al., 2016). These
developments will
also be extended by
experimental work on
dedicated
reduced
models, common to
both geophysical
modalities or
analogous,
and
integrating
structural elements
representative of an
urban
environment.
Depending on the
progress of the
thesis, an
evaluation
of the
methods on data
acquired on a real
urban site will be
considered.
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