Maximum Entropy Method and Seismic Frequency – Magnitude Relation

Entropy is a state function. The entropy increase principle tells us that under isolated or adiathermal conditions, the spontaneous development of a system from a state of non-equilibrium to a state of equilibrium is a process of entropy increase, in which a state of equilibrium corresponds to a state of maximum entropy. When the system is in a state of equilibrium, it is also at its most chaotic and disordered. The occurrence of earthquakes can be classified as a random event and can be described using entropy. Earthquakes occur in the most disordered way, indicating that entropy has reached its maximum value, so we can use the Maximum Entropy Method to determine the distribution of earthquakes that occur within a certain area curing a particular period of time. Results show that the formula representing the relationship between seismic frequency and magnitude (based on data and experience) is in fact a negative exponential distribution under given restraints and supposing seismic entropy is set as the maximum value. Therefore, we can theoretically explain the origin of the relationship between seismic frequency and magnitude.