Whether the earthquake occurrences follow a Poisson process model is a widely debated issue. The Poisson process model has great conceptual appeal and those who rejected it under pressure of empirical evidence have tried to restore it by trying to identify main events and suppressing foreshocks and aftershocks. The approach here is to estimate the density functions for the waiting times of the future earthquakes. For this purpose, the notion of Gram-Charlier series which is a standard method for the estimation of density functions has been extended based on the orthogonality properties of certain polynomials such as Laguerre and Legendre. It is argued that it is best to estimate density functions in the context of a particular null hypothesis. Using the results of estimation a simple test has been designed to establish that earthquakes do not occur as independent events, thus violating one of the postulates of a Poisson process model. Both methodological and utilitarian aspects are dealt with.

The paper describes an algorithm for estimating the hypocentral coordinates and origin time of local earthquakes when the wave speed model to be employed is a layered one with dipping interfaces. A constrained least-squared error problem has been solved using the penalty function approach, in conjunction with the sequential unconstrained optimization technique of Fiacco and McCormick. Joint confidence intervals for the computed parameters are estimated using the approach of Bard for nonlinear problems. These results show that when a hypocentre lies outside the array of recording stations and head waves from a dipping interface are involved, then its inclination must be taken into account for dip angles exceeding 5°.

Long-term conditional probabilities of occurrence of great earthquakes along the Himalaya plate boundary seismic zone have been estimated. The chance of occurrence of at least one great earthquake along this seismic zone over a period of 100 years (beginning the year 1999) is estimated to be about 0.89. The 100-year probability of such an earthquake occurring in the Kashmir seismic gap is about 0.27, in the central seismic gap about 0.52 and in the Assam gap about 0.21. The 25-year probabilities of their occurrence in these gaps are 0.07, 0.17, and 0.05 respectively. These probability estimates may be used profitably to assess the seismic hazard in the Himalaya and the adjoining Ganga plains.

The aftershock sequence of the September 30th, 1993 Killari earthquake in the Latur district of Maharashtra state, India, recorded by 41 temporary seismograph stations are used for estimating 3-D velocity structure in the epicentral area. The local earthquake tomography (LET) method of Thurber (1983) is used. About 1500P and 1200S wave travel-times are inverted. TheP andS wave velocities as well asV_P/V_Sratio vary more rapidly in the vertical as well as in the horizontal directions in the source region compared to the adjacent areas. The main shock hypocentre is located at the junction of a high velocity and a low velocity zone, representing a fault zone at 6–7 km depth. The estimated average errors ofP velocity andV_P/V_Sratio are ±0.07 km/s and ±0.016, respectively. The best resolution ofP and S-wave velocities is obtained in the aftershock zone. The 3-D velocity structure and precise locations of the aftershocks suggest a ‘stationary concept’ of the Killari earthquake sequence.