Theoretical Maximum and Cumulative Seismic Moment Relationships Confirm that Injection Volume Controls the Occurrence Rate, But Not the Magnitude, of Induced Earthquakes

Abstract Classical relationships between cumulative and maximum seismic moment, based on the Gutenberg‐Richter law, shows a non‐physical anomaly for low b ‐values. We here derive new relationships, including a low and a high b ‐value approximation. We apply these theoretical relationships to a comprehensive set of 17 induced seismic sequences, by examining the growth of the released seismicity with the injected volume. While the event number is found to be directly proportional to the volume, the cumulative and maximum seismic moment depends on the volume with an exponent that depends at first order on the b ‐value. This is confirmed by the theoretical relationships we derived, and shows that the injected volume primarily controls seismic nucleation and therefore the seismic rate of occurrence. The magnitude dependence on b ‐value, which is not considered in most moment‐volume relationships, may have a significant impact on earthquake magnitude forecasting for monitoring purposes.