Ifsttar PhD subject

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Title : Imaging methodology combining seismic surface waves and DC geoelectrical information - Application to the urban environment in the context of climate change

Main host Laboratory - Referent Advisor GERS - GeoEND  -  LEPAROUX Donatienne      tél. : +33 240845669

Director of the main host Laboratory DEROBERT Xavier  -

PhD Speciality Géophysique

Axis of the performance contract 3 - COP2017 - Planning and protecting regions

Main location Nantes

Doctoral affiliation UNIVERSITE GUSTAVE EIFFEL

PhD school Matière, Molécules, Matériaux et Géosciences (3MG)

Planned PhD supervisor LEPAROUX Donatienne  -  Université Gustave Eiffel  -  GERS - GeoEND

Planned financing Contrat doctoral  - Université Gustave Eiffel

Abstract

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.

Audet, C, Kokkolaras, M. (2016). Blackbox and derivative-free optimization: theory, algorithms and applications. Optim Eng 17, 1–2 (2016).

Colombo, D., Rovetta, D., 2018. Coupling strategies in multiparameter geophysical joint inversion. Geophys. J. Int. 215, 1171–1184.

Coulouma, G., Samyn, K., Grandjean, G., Follain, S., & Lagacherie, P. (2012). Combining seismic and electric methods for predicting bedrock depth along a Mediterranean soil toposequence. Geoderma, 170, 39-47.

Coulouma, G., Lagacherie, P., Samyn, K., & Grandjean, G. (2013). Comparisons of dry ERT, diachronic ERT and the spectral analysis of surface waves for estimating bedrock depth in various Mediterranean landscapes. Geoderma, 199, 128-134.

Dezert, T., Palma Lopes, S., Fargier, Y., Côte, P. (2019). Combination of geophysical and geotechnical data using belief functions: Assessment with numerical and laboratory data. J. Appl. Geophys. 170, 103824.

Dezert, T., Fargier, Y., Lopes, S.P., Guihard, V. (2022). Canal dike characterization by means of electrical resistivity, shear wave velocity and particle size data fusion. J. Appl. Geophys. 204, 104749.

Doetsch, J., Linde, N., Coscia, I., Greenhalgh S.A., Green, A.G. (2010). Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data. Geophys. 75: G53-G64. https://doi.org/10.1190/1.3496476

Gaubert‐Bastide, T., Garambois, S., Bordes, C., Voisin, C., Oxarango, L., Brito, D., Roux, P. (2022). High‐Resolution Monitoring of Controlled Water Table Variations From Dense Seismic‐Noise Acquisitions. Water Resour. Res. 58, e2021WR030680.

Liu, L., Chan, L.S. (2007). Sustainable urban development and geophysics. J. Geophys. Eng. 4, 243–244.

Loke, M.H., Chambers, J.E., Rucker, D.F., Kuras, O., Wilkinson, P.B. (2013). Recent developments in the direct-current geoelectrical imaging method. J. Appl. Geophys. 95, 135–156.

Pageot, D., Leparoux, D., Le Feuvre, M., Durand, O., Côte, P., & Capdeville, Y. (2017). Improving the seismic small-scale modelling by comparison with numerical methods. Geophysical Journal International, 211(1), 637-649.

Pageot, D., Leparoux, D., Capdeville, Y., & Côte, P. (2018, September). Alternative Surface Wave Analysis Method for 2D Near-Surface maging Using Particle Swarm Optimization. In 3rd Applied Shallow Marine Geophysics Conference with EAGE NSG, Porto, Portugal.

Rudin, L.I., Osher, S., Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D. 60 (1–4): 259–268.

Wang, A., Leparoux, D., Abraham, O., & Le Feuvre, M. (2021). Frequency derivative of Rayleigh wave phase velocity for fundamental mode dispersion inversion: parametric study and experimental application. Geophysical Journal International, 224(1), 649-668.

Whiteley, J.S., Chambers, J.E., Uhlemann, S., Wilkinson, P.B., Kendall, J.M. (2019). Geophysical Monitoring of Moisture‐Induced Landslides: A Review. Rev. Geophys.

Keywords : Geophysical Imaging, Surface Wave Seismics, DC-Electrical Resistivity, Collaborative Inversion, Urban Environment

Main host Laboratory - Referent Advisor	GERS - GeoEND - LEPAROUX Donatienne tél. : +33 240845669
Director of the main host Laboratory	DEROBERT Xavier -
PhD Speciality	Géophysique
Axis of the performance contract	3 - COP2017 - Planning and protecting regions
Main location	Nantes
Doctoral affiliation	UNIVERSITE GUSTAVE EIFFEL
PhD school	Matière, Molécules, Matériaux et Géosciences (3MG)
Planned PhD supervisor	LEPAROUX Donatienne - Université Gustave Eiffel - GERS - GeoEND
Planned financing	Contrat doctoral - Université Gustave Eiffel
Abstract 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. Audet, C, Kokkolaras, M. (2016). Blackbox and derivative-free optimization: theory, algorithms and applications. Optim Eng 17, 1–2 (2016). Colombo, D., Rovetta, D., 2018. Coupling strategies in multiparameter geophysical joint inversion. Geophys. J. Int. 215, 1171–1184. Coulouma, G., Samyn, K., Grandjean, G., Follain, S., & Lagacherie, P. (2012). Combining seismic and electric methods for predicting bedrock depth along a Mediterranean soil toposequence. Geoderma, 170, 39-47. Coulouma, G., Lagacherie, P., Samyn, K., & Grandjean, G. (2013). Comparisons of dry ERT, diachronic ERT and the spectral analysis of surface waves for estimating bedrock depth in various Mediterranean landscapes. Geoderma, 199, 128-134. Dezert, T., Palma Lopes, S., Fargier, Y., Côte, P. (2019). Combination of geophysical and geotechnical data using belief functions: Assessment with numerical and laboratory data. J. Appl. Geophys. 170, 103824. Dezert, T., Fargier, Y., Lopes, S.P., Guihard, V. (2022). Canal dike characterization by means of electrical resistivity, shear wave velocity and particle size data fusion. J. Appl. Geophys. 204, 104749. Doetsch, J., Linde, N., Coscia, I., Greenhalgh S.A., Green, A.G. (2010). Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data. Geophys. 75: G53-G64. https://doi.org/10.1190/1.3496476 Gaubert‐Bastide, T., Garambois, S., Bordes, C., Voisin, C., Oxarango, L., Brito, D., Roux, P. (2022). High‐Resolution Monitoring of Controlled Water Table Variations From Dense Seismic‐Noise Acquisitions. Water Resour. Res. 58, e2021WR030680. Liu, L., Chan, L.S. (2007). Sustainable urban development and geophysics. J. Geophys. Eng. 4, 243–244. Loke, M.H., Chambers, J.E., Rucker, D.F., Kuras, O., Wilkinson, P.B. (2013). Recent developments in the direct-current geoelectrical imaging method. J. Appl. Geophys. 95, 135–156. Pageot, D., Leparoux, D., Le Feuvre, M., Durand, O., Côte, P., & Capdeville, Y. (2017). Improving the seismic small-scale modelling by comparison with numerical methods. Geophysical Journal International, 211(1), 637-649. Pageot, D., Leparoux, D., Capdeville, Y., & Côte, P. (2018, September). Alternative Surface Wave Analysis Method for 2D Near-Surface maging Using Particle Swarm Optimization. In 3rd Applied Shallow Marine Geophysics Conference with EAGE NSG, Porto, Portugal. Rudin, L.I., Osher, S., Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D. 60 (1–4): 259–268. Wang, A., Leparoux, D., Abraham, O., & Le Feuvre, M. (2021). Frequency derivative of Rayleigh wave phase velocity for fundamental mode dispersion inversion: parametric study and experimental application. Geophysical Journal International, 224(1), 649-668. Whiteley, J.S., Chambers, J.E., Uhlemann, S., Wilkinson, P.B., Kendall, J.M. (2019). Geophysical Monitoring of Moisture‐Induced Landslides: A Review. Rev. Geophys.
Keywords :	Geophysical Imaging, Surface Wave Seismics, DC-Electrical Resistivity, Collaborative Inversion, Urban Environment

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