• P S Moharir

      Articles written in Journal of Earth System Science

    • Estimation of the compounding distribution in the compound Poisson process model for earthquakes

      P S Moharir

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      Compound Poisson process models have been studied earlier for earthquake occurrences, with some arbitrary compounding distributions. It is more meaningful to abstract information about the compounding distribution from the empirical observations on the earthquake sequences. The difinition of a compound distribution can be interpreted as an integral transform of the compounding distribution. The latter distribution can therefore be estimated by inverting the integral transform. Alternatively, from the moments of the observable random variablesviz. (a) the number of earthquakes per unit time or (b) the waiting times for subsequent earthquakes, the moments of the compounding distribution can be obtained. This information can be converted into a statement about the compounding distribution.

    • History syndrome or Popperian credentials of Geology

      P S Moharir

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      Earth-science is greatly concerned with history. It is argued by some that a historical discipline is not a science. This is contrary to the conclusion from the demarcation criteria of Popper, set to separate science from formal disciplines such as metaphysics, mathematics and logic. Others have spoken of the unity of all sciences. Classification of intellectual activities is based ongenus proximum anddifferentia specifica. Hence the two viewpoints can be readily reconciled. Earth-science has been criticized variously for being descriptive, inductive, explanatory, etc. Other historical and concrete sciences have also attracted similar adverse comments. These issues are discussed at length to argue that Popper’s work should be extended further to define a demarcation of science into immanent and historical. It is also argued that the rigour of cognitive and logical determinants of science is not an adequate reason to embrace sociological models of science. Further, sociological/logical models of science present a misleading dichotomy.

    • Stein estimation for SIR-predictable models of earthquake occurrence

      P S Moharir

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      It is usually accepted that a time-predictable model of earthquake occurrences is better than the so-called slip-predictable model. Here a size-interval relation (SIR)-predictable model is proposed which combines the features of the time-predictable and slip-predictable models. Unlike a constant, and hence nonpredictive, relation between the size of the next earthquake and the inter-event interval, given by the so-called slip-predictable model, the SIR-predictable model prescribes such a relation contingent upon the size of the previous earthquake. Unlike the time-predictable model, instead of predicting the time interval, it proposes a size-interval relation. Using data about a seismogenic source called Cephalonia in Greece, the superiority of the SIR-predictable model over the time-predictable model is illustrated. The SIR-predictable model can be made more efficient by employing two-stage nonlinear estimation procedures motivated by the initial work by Stein. Introducing these procedures to seismologists is an independent objective of this paper. Also, Stein estimators have a dimensionality threshold. This work discusses two techniques of threshold extension.

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