In this work we studied the formulation of the aftershock rate equation to be used for the forecasting of future sequences behavior. Basing both on correlation among parameter estimates made in previous works for New Zealand, Italy and California and on the application, to some Italian sequences, of an epidemic type model, we inferred that the sequence productivity scales with main shock magnitude with a coefficient definitely lower than the Gutenberg-Richter b-value (about 2/3b). We also found a clear correlation between the two parameters (p and c) of the Modified Omori Law (MOL) that could be the cause of a bias in their estimates, as well as in the estimate of the productivity, unless the time dependent part of the rate equation is re-normalized. Such correlation might indicate a possible inadequacy of the Omori law itself in characterizing real properties of the time decay process. Starting from these findings, we studied the role of the two MOL parameters by statistically comparing the goodness-of-fit, with Italian and Californian sequences, of different models ranging from the simple hyperbolic Omori law to the MOL, with varying starting times. For the majority of analyzed sequences, we found that the introduction of parameter c does not significantly improve the fit with data and thus is not necessary to well reproduce the observed sequence behavior. We could infer that parameter c is only an artifice to account for data incompleteness in the first times after the main shock and it is not representative of a specific physical properties of aftershock sequences.
Inferences on the best form of the aftershock rate equation from correlation between parameter estimates and the comparison of different time decay models
LOLLI, BARBARA;GASPERINI, PAOLO
2004
Abstract
In this work we studied the formulation of the aftershock rate equation to be used for the forecasting of future sequences behavior. Basing both on correlation among parameter estimates made in previous works for New Zealand, Italy and California and on the application, to some Italian sequences, of an epidemic type model, we inferred that the sequence productivity scales with main shock magnitude with a coefficient definitely lower than the Gutenberg-Richter b-value (about 2/3b). We also found a clear correlation between the two parameters (p and c) of the Modified Omori Law (MOL) that could be the cause of a bias in their estimates, as well as in the estimate of the productivity, unless the time dependent part of the rate equation is re-normalized. Such correlation might indicate a possible inadequacy of the Omori law itself in characterizing real properties of the time decay process. Starting from these findings, we studied the role of the two MOL parameters by statistically comparing the goodness-of-fit, with Italian and Californian sequences, of different models ranging from the simple hyperbolic Omori law to the MOL, with varying starting times. For the majority of analyzed sequences, we found that the introduction of parameter c does not significantly improve the fit with data and thus is not necessary to well reproduce the observed sequence behavior. We could infer that parameter c is only an artifice to account for data incompleteness in the first times after the main shock and it is not representative of a specific physical properties of aftershock sequences.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
