Estimation from incomplete data files based on magnitude-frequency relation for earthquakes

The problem of incorporating the available seismological information provided by the major events of the historical catalog with those for the short period of instrumental data is investigated. Assuming that the frequency-magnitude law of Gutenberg and Richter is valid for both periods, an estimation procedure for the main parameter of this law and the rate of earthquake occurrence for historical period is presented. Application of the proposed method is demonstrated, using both real and simulated data. An extension to allow for variable quality of complete data with different magnitude values is also included.