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a b s t r a c tWe review the relative motion of India and Asia for the last 100 million years and present a revised reconstruction for the India-Antarctica-Africa-North America-Eurasia plate circuit based on published motion histories. Deformation of these continental masses during this time introduces uncertainties, as does error in oceanic isochron age and location. Neglecting these factors, the data ipso facto allow the inference that the motion of India relative to Eurasia was distinctly episodic. Although motion is likely to have varied more smoothly than these results would allow, the geological record also suggests a sequence of distinct episodes, at about the same times. Hence we suggest that no single event should be regarded as the collision of India with Asia. The deceleration of the Indian plate commencing at ∼65 Ma is matched by an equally significant prior acceleration and this aspect must be taken into account in geodynamic scenarios proposed to explain the collision of India with Asia.

Abstract-This paper is concerned with filtering of hidden Markov processes (HMPs) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMMs), namely finite output alphabet models, conditions for lumpability of all HMPs representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived.The paper also describes an approach to efficient suboptimal filtering for HMPs which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.

Background and objectives 2 Operations 8 Lithostratigraphy 18 Biostratigraphy and micropaleontology 26 Paleomagnetism 39 Petrophysics 50 Geochemistry 56 Stratigraphic correlation 58 References