Research Engineer / PostDoc

17 Avril 2023

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Catégorie : Ingénieur

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Robust and fine 2D displacement computation in vicinity of discontinuities - focus on seismic faults

 

Laboratory: LaSTIG, IPGP-Tectonics

Supervision: Ewelina Rupnik (CR, LaSTIG),
Marc Pierrot Deseilligny (DR, LaSTIG)
Yann Klinger (DR, CNRS), Arthur Delorme (IR, IPGP)

Starting date: May 2023

Duration: 1 year (2nd year renewable)

Localisation: Saint-Mandé (IGN), Paris Jussieu (IPGP)

 

Keywords: photogrammetry, computer vision, 3D geometry, deformations, deep-learning, earth sciences

 

1. Context

Understanding how earthquake rupture proceeds and how it relates to ground surface deformation bear critical information for seismic hazard assessment. Fault Displacement Hazard Assessment is in fact becoming of primary importance as ground disruption could directly affect the integrity of infrastructures. In recent years, combining the tremendous increase in resolution of space imagery including sub-metric optical satellites such as Pleiades with image correlation methodology, it has become possible to identify detail of ground deformation, localised and distributed, in the fault zone. Fig. 1 shows an example of such an image of deformation where we could distinguish zones of localised deformation (sharp discontinuities) and zones where deformation seems to be more diffuse. To quantify precisely each mode of the deformation, however, we need to ensure that in the direct vicinity of the rupture, our measurement is not affected by a bias in measurement due to processing artefacts, such as averaging deformation over correlation windows that would span the rupture.

 

 

Calculating displacement with cross-correlation defined over squared windows implies that all pixels belonging to a window undergo the same displacement. This is true in regions of constant or smoothly evolving displacements, but is violated if the measurement window crosses a discontinuity, for instance a seismic fault (see Fig. 2(a)). As a consequence, measurements at discontinuities are noisy and possibly biased, as can be observed in Fig. 1 within the encircled region.

The aim of this project is to improve the robustness and accuracy of displacement computation by defining the measurement over a triangulated mesh that is geometrically coherent with the underlying fault. By doing so, we believe to be able to improve the characterization of the fault itself, and of the behaviour of the tectonic plate in its vicinity. In particular, the proposed method will be beneficial in scenarios where (1) multiple faults are closely situated to one another, (2) the fault is poorly discriminative, and (3) the surface follows a non-Lambertian reflection leading to decorrelation for different Sun and sensor positions.

 

2. Methodology

The method is meant to be applied "on top" of 2D displacements obtained with traditional methods, and it introduces two novelties with respect to the state-of-the-art: first, it proposes an adaptive measurement region, and second, it reformulates the way the displacement between two regions is computed. To achieve the first, we propose to build a triangulated mesh (e.g., constrained delaunay triangulation [2]) by leveraging displacement maps computed with the classical cross-correlation techniques [3]. To enforce the mesh consistency with the fault, the mesh can be conditioned on the points lying along the fault. In the first instance, these points will be manually inserted, however, at a later stage, a semi-automated framework can be developed. Fig. 2(b) illustrates a toy-example of the region adaptive framework. The triangulated mesh is marked in green, and the fault is in blue. Note that the mesh perfectly respects the fault's boundary, as opposed to the classical approach in Fig. 2(a).