Interactions between surface processes and earthquakes at short time scale (< 1000 years) 

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Contrôle de la forme des versants sur la taille des glissements de terrain

Dans le chapitre précédent, j’ai défini un modèle mécanique simple prenant en compte la topographie et la résistance effective de la roche. A l’aide de ce modèle, j’ai clarifié la contribution respective de la friction, cohésion, propagation de la rupture et géométrie des pentes sur la distribution de taille des glissements de terrain. En particulier, j’ai démontré l’importance théorique de la longueur, de la hauteur et de la pente des versants finis sur la probabilité de grands glissements de terrain. Mais dans quelle mesure la forme du paysage contrôle-t-elle réellement la distribution de taille des glissements de terrain? Cette idée doit être comparée à des données. En utilisant le cas du bassin de la Dajia à Taiwan, j’ai souligné que la distribution de taille des glissements de terrain peut refléter la forme du paysage à l’échelle locale (au sein du même bassin versant). Dans ce chapitre, je profite de plusieurs inventaires de glissements de terrain existants pour explorer le rôle de la géométrie finie des pentes sur la distribution de la taille des glissements de terrain, en particulier pour la probabilité de grandes glissements de terrain. Ce chapitre est constitué d’un article en préparation dans lequel je compare la distribution de taille des glissements de terrain (pour plusieurs inventaires provenant de différents endroits du globe) à la géométrie du paysage, en passant par une métrique intégrant l’altitude maximale au-dessus de l’angle de friction. Je montre que cette métrique suit une distribution exponentielle, dans une région donnée, mais également à l’échelle mondiale. Cet article est suivi d’une discussion dans laquelle je propose d’approfondir mes recherches, via une approche analytique, sur le rôle de cette distribution sur la distribution de la taille des glissements de terrain.

Réponse d’une faille active à des événements érosifs extrêmes

Dans les deux chapitres précédents, j’ai étudié les contrôles potentiels sur la distribution de la taille des glissements de terrain et démontré le rôle fondamental de la géométrie du paysage. En particulier, les paysages avec d’importante hauteurs instables sont capables de produire de grands glissements de terrain sous un forçage donné. Ces zones correspondent aux zones de collision à haut risque sismique, dans lesquelles des processus érosifs et tectoniques sont susceptibles d’être couplés. Par exemple, dans un travail en préparation (Annexe A), nous soupçonnons que les nombreux glissement de terrain déclenchés par le typhon Morakot a déclenché une sismicité superficielle et modifié la b-value des séismes pendant plusieurs années après le typhon.
Ces liens potentiels doivent être approfondis à travers une approche numérique. Par conséquent, dans ce chapitre, j’ai utilisé deux modèles numériques du cycle sismique pour étudier le rôle de grands événements d’érosion sur la sismicité. Je présente d’abord les méthodes numériques utilisés. Ensuite, je présente les principaux résultats obtenus sous la forme d’un article qui sera soumis à une revue scientifique après la soutenance. Dans cet article, j’ai modélisé les effets d’un événement d’érosion sur une seule faille avec des propriétés frictionnelles hétérogènes. Ensuite, je compare les principaux résultats de cette étude avec le comportement d’une faille homogène, et je présente enfin un travail en cours dans lequel je vise à étudier le rôle d’un événement érosif sur un réseau de failles.
Dans ce chapitre, je montre que la réponse d’une faille active à un grand événement érosif peut être significative, et dépend de la durée et de l’amplitude de cet événement. Je montre également que pour un changement de contrainte suffisamment important, la magnitude des séismes change également significative-ment, et la faille produit plus de petits séismes en proportion comparée à un cas où elle n’est pas perturbée. Je montre également que ces résultats se retrouvent pour une faille homogène, mais avec une réponse moins im-portante. Ces résultats devraient être étendus à une population de failles de différentes tailles, afin d’étudier le changement de b-value engendré par un changement de contrainte du à un grand événement érosif.
Ces travaux ont permis d’améliorer les connaissances actuelles sur les processus contribuant à façonner la surface de la Terre à court terme (10-1000 ans). Notre approche, basée sur des études numériques, a conduit aux résultats principaux suivants:
1) Un modèle mécanique très simple de glissements de terrain prenant en compte la géométrie des pentes est capable de reproduire la distribution de taille des glissements de terrain. Ce modèle a mis l’accent sur l’importance de la cohésion pour la distribution des petits glissements de terrain, sur la contribution de la propagation de la rupture en 2D à la loi de puissance, et sur l’influence de la forme du paysage sur la distribution de taille des grands glissements de terrain.
2) La géométrie des pentes a une importance fondamentale dans la distribution de taille des glissements de terrain. Un critère simple mesurant la hauteur des pentes instables, hC , est reflété dans les inventaires de glissements de terrain. Cette métrique est distribuée de manière exponentielle dans de nombreuses régions du monde et contrôle la probabilité des grands glissement de terrain.
3) Les grands événements d’érosion peuvent potentiellement engendrer des séismes et modifier la distribu-tion de taille des tremblements de terre lors de l’export des sédiments. La magnitude et la durée de l’érosion sont deux paramètres fondamentaux pour évaluer la réponse des failles. Notre étude, basée sur une seule faille, doit être étendue à une population de failles afin de quantifier le changement potentiel de b-value dû à de grands événements d’érosion.
The present elevation and shape of worldwide mountain ranges result from the balance between the processes that build them and the processes that level them. A large range of deformation processes and associated time-scales contribute to landscape evolution: from an earthquake rupture propagating at meters per second over several seconds to the building of mountain ranges by accumulation of tectonic deformation over millions of years. Erosional processes are the surface processes that remove material away from mountain ranges by river sediment transport and erosion, glacial carving and ablation, landsliding and hillslope erosion, mechanical and chemical weathering, etc. These processes contribute to erode mountain ranges and interplay with tectonic uplift at all time scales. In this section, I briefly review the interactions between tectonics and erosion at geological (1 Myrs-100 Myrs) and intermediate (10 000 yrs – 1 Myrs) time scales. I then focus on those interactions at shorter time scales (< 1000 years) and their main implications for human life as well as for mountain building.

From geological time scales to the seismic cycle time scale

At the beginning of the XIXth century, scientists started recognizing that climate could dramatically change over geological time scales. Past continental glaciations had been recognized from their geomorphological evidence, such as the erratic blocks founded in the Alpine valleys. But how to explain such a major cooling that glaciers were extended enough to carry those blocks to the lowest parts of the valleys that are currently ice-free?
During the mid-XIXth century, the link with mountain building emerged as the most possible explana-tion. In his essay on Alpine glaciers, the German-Swiss geologist Jean de Charpentier observed the geometry of moraines and deduced that those deposits were likely to have been formed after the rise of the Alps (Charpentier, 1841). He proposed that orogenesis induced deep cracks and crevasses through which surface runoff water entered the warm depths of the Earth and vaporized, contributing to moisturize and cool the atmosphere (figure 1.1). Although the mechanism he proposed was incorrect, this was one of the first pub-lished attempts to draw a link between surface processes and the rise of mountain ranges. Then, during one century, several scientists (e.g., Dana, 1856, Lyell, 1875) took up and supported this novel idea, named the « relief hypothesis » by Ramsay (1924), that mountain ranges cool the atmosphere and cause a temperature decrease.
This theory was further investigated during the second half of the XXth century, together with the devel-opment of paleoclimatology. Extensive ocean coring programs such as the Deep Sea Drilling Project (begun in 1968) recovered a lot of Tertiary sediment cores well suited to investigate the Cenozoic evolution of global climate. The common outcome of numerous paleobotanic investigations (e.g., Wolfe, 1978) and oxygen iso-topes measurements (e.g., Savin, 1977) was that the continental glaciations inferred by Charpentier and his contemporaries was the last step of a 50 Myr global cooling that temporally correlates with the late Cenozoic rise of mountain belts such as the Himalayas or the Rocky Mountains. Further investigations have shown that mountain building can significantly change the climate at geological time-scales through several mecha-nisms. First, increasing mountain range elevation induces an increase of Earth’s albedo, by leading to longer winters, increasing the area and duration of snow cover, and leading to the expansion of glaciers (Birchfield and Wertman, 1983). Moreover, weathering rates and river fluxes can increase with increasing uplift rates. This enhanced continental weathering would trap more CO2 in the ocean and decrease greenhouse effect (Raymo et al., 1988). Mountain ranges can also dramatically change atmospheric flow, and favour cold climate (Kutzbach et al., 1989). An elevated topography enhances precipitations on the wind side of the mountain, and can induce strong monsoon in areas such as southern Asia. As mountain building enhances precipitation, it is likely to enhance erosional processes, which are strongly linked to climate (Wilson, 1973, Jansson, 1982). In climatological settings with efficient erosion, as in Taiwan (Suppe, 1981) or New Zealand (Adams, 1980), the uplift rate can be balanced by the rate of erosion, leading to a steady-state topography at geological time scales.
However, since the end of the XXth century, geologists and geophysicists progressively changed their vision of climate and erosion as passive processes responding to mountain building. Since plate tectonics theory won general acceptance in 1967, and after the wartime boom in seismology research and the development of satellite imagery, geologists dramatically improved their knowledge of the surface and crustal structure of mountain belts. Over millions of years, mountains grow (at millimetres to centimetres per year) by thrusting and thickening of the upper crust under the compressional forces due to plate motions. Under this frame, geologists and physicists start thinking of mountain as a wedge (similarly to the wedge developing in front of a bulldozer) that deforms until a critical slope is reached (Dahlen et al., 1984, Koons, 1990). In this model, surface processes cannot be ignored; if some material is removed from the top of the wedge, it changes the distribution of mass and stresses in the belt, and induces internal deformation that re-establishes the critical taper. During the 90s, the advances in numerical modelling have highlighted that erosion is expected to control the size, structure and pattern of deformation in several mountain belts (Koons, 1990, Willett, 1999, Willett et al., 1993, Beaumont et al., 1996). A striking example is the Southern Alps of New Zealand, where the asymmetry of rainfall, mainly coming from the west coast, is able to explain the asymmetric topographic profile and the pattern of uplift (Willett, 1999). Climate, erosion and uplift are now commonly considered as a series of feedbacks, and it is largely accepted that surface processes can strongly influence tectonic de-formation over geological time scales (Whipple, 2009).
The increasing amount of geodetic data, the deployment of seismometer network, mainly in the Himalayas (e.g., Pandey et al., 1999), and then the development of the Global Positioning System (GPS) during the 90s (Bilham et al., 1997, Larson et al., 1999, Jouanne et al., 1999) allowed geologists to look at mountain deformation at shorter time scales. Long-term crustal thickening is mainly accommodated by slip along major faults, but if we look at shorter time scales, faults do not slip continuously. Over periods of 100-1000 years, they accumulate tectonic stress, and then release it during sudden, large ruptures (i.e., earthquakes). The succession of loading (aseismic) and relaxation (seismic) phases are commonly known as the seismic cycles. During the late XXth century, mountain building started being studied through seismotectonics (i.e., the study of earthquakes as a tectonic component). Because erosion removes crustal material, it partly drives continental rock uplift through isostatic rebound: the gravitational equilibrium between crust and mantle is restored by land’s vertical motion. In a numerical model of long and short-term deformation of the Himalayas, Cattin and Avouac (2000) showed that erosion, through isostasy, is likely to interplay with tectonics during the interseismic period as well as during orogenic deformation. However, the role of erosion on fault slip is easier to decipher in some particular places, where long-term deformation is so low that it is hardly detected by GPS, and that yet experience seismic activity. It is the case in mountain ranges considered stable such as the Pyrenees or the Western Alps (Vernant et al., 2013) or for intraplate earthquakes such as in New Madrid (Missouri) (Calais et al., 2010). In those cases, fault slip is likely to be enhanced by the isostatic rebound of the lithosphere caused by erosion, which induces a normal stress decrease in the upper crust sufficient to unclamp pre-existing faults that are close to failure.

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Why do we care about short-term interactions between tec-tonics and erosion ?

At geological time scales, rock uplift and river incision contribute to steepening hillslopes until their mechan-ical stability threshold is reached (Burbank et al., 1996, Mitchell and Montgomery, 2006), and the landscape responds by landsliding (Korup et al., 2007, Larsen and Montgomery, 2012). However, the landsliding rate in a mountain belt is not steady; the energy released during large earthquakes by seismic waves can cause strong ground motion that induces almost instantaneously a large amount of slope failures, especially in mountainous areas with steep topography. As recent examples of earthquakes that triggered tens of thou-sands of landslides, we can mention the 2015 Gorkha earthquake in Nepal (Roback et al., 2017), the 2016 Kaikoura earthquake in New-Zealand, or the recent 2018 Hokkaido earthquake (Japan). Those catastrophic landsliding events represent a major hazard for the populations living in seismically active settings. They also have strong geomorphological implications, because they instantaneously convert a large volume of rock to sediment that can be delivered to the rivers, and then mobilized (Yanites et al., 2010, Croissant et al., 2017). Those large erosional events could also modify the regional seismicity, because of the sudden stress change they induce in the shallow crust (Steer et al., 2014). In the next sections, I will look at all of those three points.

Co-seismic landslides represent a major hazard for populations

Landslides triggered by earthquakes are a major hazard in seismically active regions. They can destroy villages and cause hundred of injuries and fatalities (Marano et al., 2010, Petley, 2012, Catlos et al., 2016). For example, between 20.000 and 100.000 fatalities due to the 2008 Wenchuan earthquake in China have been attributed directly to landsliding (Huang and Fan, 2013). Coseismic landslides can also block roads and railways, which is especially problematic in isolated, narrow and inhabitated valleys with limited accessibility. They also deliver large volumes of sediments to rivers, modifying their dynamics, causing hydro-sedimentary hazards such as river aggradation or landslide dams (Collins and Jibson (2015), figure 1.2 a). Landslides can be the primary source of co-seismic damage to infrastructure (figure 1.2 b) and can prevent the functioning of transportation. Therefore, they induce economic losses that can be even more important than those caused by direct ground shaking (Bird and Bommer, 2004).

Table of contents :

1 Preamble 
1.1 From geological time scales to the seismic cycle time scale
1.2 Why do we care about short-term interactions between tectonics and erosion ?
1.2.1 Co-seismic landslides represent a major hazard for populations
1.2.2 Earthquakes and coseismic erosion shape the landscape
1.2.3 Surface processes can trigger seismicity at human-life time scales
2 Introduction 
2.1 Earthquake and landslide mechanics
2.1.1 Rock strength and brittle failure
2.1.2 Earthquake mechanics
2.1.3 Landslide mechanics
2.2 Interactions between surface processes and earthquakes at short time scale (< 1000 years)
2.2.1 Landscape response to earthquakes
2.2.2 Seismic cycle response to surface processes
2.3 Earthquake and landslide sizes
2.3.1 Observations
2.3.2 Physical meaning of power-law distribution and b-value variations
2.3.3 Upper and lower limits to rupture size
3 Modelling landslide size distribution 
3.1 Overview
3.2 Coulomb mechanics and relief constraints explains landslide size distribution
3.2.1 Introduction
3.2.2 Methods
3.2.3 Results
3.2.4 Discussion and concluding remarks
3.3 Supplementary material
3.4 General discussion
3.4.1 What is landscape strength ?
3.4.2 Consequences for landsliding volumes
4 How hillslope shape controls landslide size 
4.1 Overview
4.2 Impact of finite hillslope geometry on large landslide probability
4.2.1 Introduction
4.2.2 Methods
4.2.3 Results
4.2.4 Discussion and concluding remarks
4.3 Supplementary material
4.4 General discussion
4.4.1 Linking model and landslide data
4.4.2 Implications for large landslide hazard in seismically active regions
5 Modelling the response of active faults to large erosional events 
5.1 Overview
5.2 General presentation of the methods
5.2.1 Presentation of the two numerical models
5.2.2 How to model earthquakes of different sizes ?
5.3 Modelling fault response to large erosional events
5.3.1 Introduction
5.3.2 Methods
5.3.3 Discussion and concluding remarks
5.4 Supplementary material
5.5 Comparison of homogeneous and heterogeneous fault response
5.6 Perspective – modelling a fault network under normal stress change
6 Discussion 
6.1 Main results
6.2 Rupture processes during the seismic cycle
6.2.1 Size of rupture events
6.2.2 Implications for interaction between landslides and earthquakes at short time-scales
Bibliography

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