By “seismic events” we understand earthquakes of any size. There exists a broad scientific literature on earthquakes and on the processing of seismologic data. We refer readers interested in a detailed description of these subjects to corresponding books (see, for example, Lay and Wallace, 1995, and Shearer, 2009). We start this book with an introductory review of the theory of linear elasticity and of the mechanics of seismic events. The aim of this chapter is to describe classical fundamentals of the working frame necessary for our consideration of induced seismicity. We conclude this chapter with a short introduction to methodical aspects of the microseismic monitoring.

Linear elasticity and seismic waves

Deformations of a solid body are motions under which its shape and (or) its size change. Formally, deformations can be described by a field of a displacement vector u(r). This vector is a function of a location r of any point of the body in an initial reference state (e.g., the so-called unstrained configuration; see, for example, Segall, 2010). Initially we accept here the so-called Lagrangian formulation, i.e. we observe motions of a given particle of the body.

However, the field of displacements describes not only deformations of the body but also its possible rigid motions without changes of its shape and its size, such as translations and/or rotations.

In contrast to rigid motions, under deformations, distances (some or any) between particles of the body change. Therefore, to describe deformations, a mathematical function of the displacement field is used that excludes rigid motions of a solid and describes changes of distances between its particles only. This function is the strain tensor ∈, which is a second-rank tensor with nine components ∈ij. Here the indices i and j can accept any of values 1, 2 and 3 denoting the coordinate directions of a Cartesian coordinate system in which the vectors u and r have been defined.