Fluid-saturated rocks are multiphase media. Elastic stresses are supported there by the solid phase of rocks. Pore pressure is supported by saturating fluids. In such media the elastic stresses and the pore pressure are coupled.

The mechanics of poroelastic media was developed by Maurice Biot in a series of his seminal publications in the 1940s–1970s (see, for example, Biot 1956, 1962). This theory was further developed and reformulated by several scientists. A very incomplete list of corresponding works includes the publications of Gassmann (1951), Brown and Korringa (1975), Rice and Cleary (1976), Chandler and Johnson (1981), Rudnicki (1986), Zimmerman et al. (1986), Detournay and Cheng (1993) and Cheng (1997).

We consider induced microseismicity as a poromechanical phenomenon. Coussy stated in the preface to his book Poromechanics (2004): “We define Poromechanics as the study of porous materials whose mechanical behavior is significantly influenced by the pore fluid.” In this book we use several approximations derived from the theory of poroelasticity, which is part of poromechanics.

We start our introduction to poroelasticity by considering elastic compliances of porous rocks. Here we follow and correspondingly modify the approach of Zimmerman et al. (1986) and Brown and Korringa (1975). Following Detournay and Cheng (1993) we consider a very small elementary sample of a porous fluid-saturated rock with a characteristic length dl, which is assumed to be more than ten times larger than the typical size of pores and grains. Such a sample can be also considered as a representative volume of a statistically homogeneous porous medium. Both solid and fluid phases are assumed to be connected in a 3D rock structure. The pore space of a rock sample is defined as the total space occupied by all connected voids (including fractures and pores) in the sample. Let us denote by Vp the volume of the pore space of a sample of volume V.