Due to the deep socioeconomic implications, induced seismicity is a timely and increasingly relevant topic of interest for the general public. Cases of induced seismicity have a global distribution and involve a large number of industrial operations, with many documented cases from as far back to the beginning of the twentieth century. However, the sparse and fragmented documentation available makes it difficult to have a clear picture on our understanding of the physical phenomenon and consequently in our ability to mitigate the risk associated with induced seismicity. This review presents a unified and concise summary of the still open questions related to monitoring, discrimination, and management of induced seismicity in the European context and, when possible, provides potential answers. We further discuss selected critical European cases of induced seismicity, which led to the suspension or reduction of the related industrial activities.

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Few problems in elastodynamics have a closed-form analytical solution. The others can be investigated with semianalytical methods, but in general one is not sure whether these methods give reliable solutions. The same happens with numerical techniques: for instance, finite difference methods solve, in principle, any complex problem, including those with arbitrary inhomogeneities and boundary conditions. However, there is no way to verify the quantitative correctness of the solutions. The major problems are stability with respect to material properties, numerical dispersion, and the treatment of boundary conditions. In practice, these problems may produce inaccurate solutions. In this paper, the study of complex problems with two different numerical grid techniques in order to cross-check the solutions is proposed. Interface waves, in particular, are emphasized, since they pose the major difficulties due to the need to implement boundary conditions. The first method is based on global differential operators where the solution is expanded in terms of the Fourier basis and Chebyshev polynomials, while the second is the spectral element method, an extension of the finite element method that uses Chebyshev polynomials as interpolating functions. Both methods have spectral accuracy up to approximately the Nyquist wave number of the grid. Moreover, both methods implement the boundary conditions in a natural way, particularly the spectral element algorithm. We first solve Lamb's problem and compare numerical and analytical solutions; then, the problem of dispersed Rayleigh waves, and finally, the two-quarter space problem. We show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist. The combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics.

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Differences between 3-D numerical predictions of earthquake ground motion in the Mygdonian basin near Thessaloniki, Greece, led us to define four canonical stringent models derived from the complex realistic 3-D model of the Mygdonian basin. Sediments atop an elastic bedrock are modelled in the 1D-sharp and 1D-smooth models using three homogeneous layers and smooth velocity distribution, respectively. The 2D-sharp and 2D-smooth models are extensions of the 1-D models to an asymmetric sedimentary valley. In all cases, 3-D wavefields include strongly dispersive surface waves in the sediments. We compared simulations by the Fourier pseudo-spectral method (FPSM), the Legendre spectral-element method (SEM) and two formulations of the finite-difference method (FDM-S and FDM-C) up to 4Hz. The accuracy of individual solutions and level of agreement between solutions vary with type of seismic waves and depend on the smoothness of the velocity model. The level of accuracy is high for the body waves in all solutions. However, it strongly depends on the discrete representation of the material interfaces (at which material parameters change discontinuously) for the surface waves in the sharp models. An improper discrete representation of the interfaces can cause inaccurate numerical modelling of surface waves. For all the numerical methods considered, except SEM with mesh of elements following the interfaces, a proper implementation of interfaces requires definition of an effective medium consistent with the interface boundary conditions. An orthorhombic effective medium is shown to significantly improve accuracy and preserve the computational efficiency of modelling. The conclusions drawn from the analysis of the results of the canonical cases greatly help to explain differences between numerical predictions of ground motion in realistic models of the Mygdonian basin. We recommend that any numerical method and code that is intended for numerical prediction of earthquake ground motion should be verified through stringent models that would make it possible to test the most important aspects of accuracy.