Induced Seismicity Using Dieterich's Rate and State Theory and Comparison to the Critical Pressure Theory

A theoretical frame of seismicity evolution due to stress changes in a medium is the rate- and state-dependent theory of frictional fault motion. The evolution is expressed in the form of a differential equation, which can be used for normal stress changes on faults caused by fluid pressure changes resulting from injection. If the pressures rate is high enough the seismic activity becomes proportional to the local pressure rate in accordance with the Critical Pessure Theory. Examples including constant pressure injection, shut-in and variable injection rates lead to results comparable to the Critical Pressure Theory.