Hi. I'm Ioannis Stefanou, professor at Ecole Centrale de Nantes, Principal Investigator of the ERC Project: Controlling Earthquakes. Today, I will talk to you about the possibility of controlling the earthquake instability. Earthquakes are lethal and costly. A photo is enough to show the extent of disaster earthquakes may cause. This happened in Nepal. It was 2015 after an earthquake of magnitude 7.8. Nine thousand people were killed and 22,000 were injured. Moreover, the last decade, we discovered that earthquakes can be man-made too. Humans, we do cause earthquakes for many reasons. Following 2009, an exponential increase of seismic events was monitored in the US due to fluid injections in the Earth's crust. This phenomenon is called induced or triggered seismicity. Oil production and wastewater disposal, enhanced oil recovery, hydraulic fracturing, but also more environmentally friendly techniques like CO_2 sequestration and deep geothermal energy are some examples of applications that have a side effect, the triggering of several, but important unintentional seismic events. All these activities involve the reactivation of seismic faults due to the ejection of fluids under pressure at some kilometers in the Earth's crust. In fact, the number and the importance of induced seismicity due to these activities were such that the United States Geological Survey incorporated them in the 2014 United States national seismic hazard model. This is why we need to understand the earthquakes in depth. When we talk about understanding them in depth, we mean understanding how they are created at several kilometers deep down the Earth. How an earthquake happens. Well, an earthquake is a dynamic instability. Earth is a non-linear dynamical system which evolves toward critical states. In these states, minor defects or perturbations can become very important and cause a cascade of energetically rich dynamic events. In other words, a series of earthquakes. More than a century ago, Aleksandr Lyapunov, a famous Russian mathematician, defined in a rigorous mathematical way the stability of dynamical systems. Nowadays, his theory is the hardcore of the study of any dynamical nonlinear system. According to Lyapunov, a dynamical system is in a stable equilibrium, if for any small perturbation, it stays close or returns back to its equilibrium. If it moves away from its equilibrium, then we say that the equilibrium is unstable. Let's take a simple example. In this example, there are one, two, and three equilibrium positions. However, any tiny perturbation of equilibrium number 2 leads the ball to move far away from its initial equilibrium position. This is not the case for equilibrium number 1 and number 3, which are stable equilibrium. Due to the far field movement of the tectonic plates, huge amounts of energy are stored in the Earth's crust. During this phase, Earth is in equilibrium, but slowly energies accumulate in the rocks due to the far field tectonic movement. If some conditions are met, then faults suddenly slip, releasing huge amounts of energy. The system is unstable, an earthquake happens. You saw in your previous courses the spring slider idealization for earthquakes. Studying mathematically this system, we can find the conditions for which the system becomes unstable. We can see that the condition is simply the following. More specifically, the system is unstable if the friction drop with slip is stronger than the negative stiffness of the elastic spring. For real faults, similar but mathematically more complicated conditions are found. The interplay between elasticity and friction drop and weakening determines if an earthquake will happen or not. That means that if this inequality is not satisfied, the system will move, slide, but very slowly in a quasistatic way. In this case, no dynamic event will take place, the system will be stable. Earthquakes happen when faults do not satisfy the stability condition. But let's focus on friction. Friction depends on the normal force N that's applied to the block. By injecting or pumping fluids to a fault results in decreasing or increasing the fluid pressure. Indeed, in blue, we see this fluid pressure term and how it alters Coulomb friction according to the Terzaghi's effective stress principle. Fluid injections in some kilometers depth play exactly the same role and can cause earthquakes. But maybe we could adjust the fluid pressure in a way that the instability condition is never satisfied. In this way, the block would slide but smoothly in a stable manner. In order to illustrate this mechanism, we did analog experiments with kitchen paper. This device simulates the spring slider experiment you saw in the previous sequence, but with kitchen paper, which allow us to simulate a fluid injection. The springs represent the surrounding rocks while the paper, the resistance of the fault to friction. We simulate fluid injections by wetting the paper. You see how violent the rupture is when no injections are made and how smooth the rupture becomes when we inject fluids. In real faults, something similar could happen, but, of course, the situation is much more complicated. A real fault system can be simplified as an array of blocks as shown in the figure. If we simulate the system in the computer and monitor the amount of slip with time, we have this kind of evolution, which is also called the devil staircase. Jumps in the displacement correspond to earthquakes. As you can see, we can have big events or smaller ones in a random-like manner. The statistical distribution of these unstable earthquake events follows the Gutenberg-Richter law as you saw in your previous courses. Nevertheless, in a recent work, we have proved mathematically that by injecting fluids in a specific way, we can make the system slide in the desired, slow, aseismic way. This was accomplished using the mathematical theory of control for non-linear systems. Stabilizing for systems and make them slide smoothly is our ongoing research, the results can be fascinating. Laboratory experiments, numerical simulations, and mathematics can show us up to what extent the earthquake phenomenon could be controlled or not. This is important for current and future industrial projects involving unwanted anthropogenic seismicity, but also maybe one day for minimizing natural earthquakes as well.