An Automated Method for Mapping Independent Spatial b Values

We present an automated method for mapping the b values. The algorithm is very simple and presents three advantages: (a) it does not requires any tuning of the parameters like, for instance, a fixed cell size or a maximum radius of the cell; (b) it implies a more appropriate use of the catalog, by using almost all the events in the catalog used (with a tolerance of 1%) with no overlap; (c) it implies the full independence of the b values, thus allowing the statistical comparison of the results using standard tests. Although the resulting b values are comparable with those obtained by applying the other methods of common use in seismology, these latter (a) leave out many earthquakes from the analysis, with loose of useful information, (b) produce diffuse cells overlapping aiming at reaching many cells of the grid in order to get the correct number of events in each cell, and (c) results in correlated b values, which do not allow the test of significance for the differences in the b values. Finally, due to the independence from any ad hoc a-priori choice, our method is suitable for automatic and operator-free procedures.Plain Language Summary The methods usually used in seismology for mapping the b value require the tuning of some parameters depending on the analyzed catalog. Here we propose a method that only implies the choice of the minimum number of earthquakes needed to obtain reliable b value estimates, which does not depend on the specific cases. Due to the mutual complete independence of the resulting b values, the proposed method allows the use of standard statistical tests to compare the results.