The representation of the source. Kinematic and dynamic models

We saw in Chapter 15 that earthquakes are produced by fractures in the Earth's crust. In Reid's model of elastic rebound, faulting is caused by the sudden release of accumulated elastic strain when the strength of the material is overcome. In seismology the problem of the source mechanism consists in relating observed seismic waves to the parameters that describe the source. In the direct problem, theoretical seismic wave displacements are determined from source models, whereas in the inverse problem, the parameters of source models are derived from observed wave displacements. The first step in both problems is to define the seismic source in terms of a mechanical model that represents the physical fracture. These models or representations of the source are defined by parameters whose number depends on their complexity. Simple models are defined by a few parameters whereas more complex ones require a larger number of parameters (Madariaga, 1983; Udías, 1991; Koyama, 1997).

Fracturing can be approached in two different ways, kinematic and dynamic. Kinematic models of the source consider the slip of the fault without relating it to the stresses that cause it. Fracturing is described purely in terms of the slip vector as a function of the coordinates on the fault plane and time. From models of this type, it is relatively simple to determine the corresponding elastic displacement field.