Physical laws for precursory phenomena of impending large earthquakes and their applications to predictions

Abstract. Changes in crustal stresses create an earthquake fault motion which radiates seismic waves. Their analyses quantify the properties of the earthquake with its rupture time, location, fault motion and size that are called earthquake source parameters. We may then regard the event as the emergence of a virtual particle of unit mass at a position in the property space whose coordinate axes are source parameters. At the next event, the particle takes a new position in the space. The consecutive events draw a pathway of the moving particle, which is a trace of the stress changes causing the particle motion. The pathway is zigzagged and non–derivative with respect to time. A mathematical tool named physical wavelets is applied to extracting the equations of particle motion. The extracted equations detect periodic anomalous accelerations precursory to large impending earthquakes weeks and months ahead of time. The periodic particle motions enable us to predict the fault size and motion, rupture time, and epicenter of impending large earthquakes. The mathematical tool with which to extract deterministic precursors embedded in the highly irregular time series of natural and earth systems is also concisely described for mitigating their hazards.