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Null geodesics of the metric tensor formed from the coefficients of the second-order terms in the partial differential equation for sound are interpreted as the space-time path histories of sound pulses in a geometric ray trace theory for sound propagation in moving inhomogeneous inviscid fluids.

The Greater Himalayan sequence in India and Nepal records crustal thickening processes during and following the onset of India-Asia collision (ca. 54-50 Ma), which resulted in Late 2 Eocene-Early Miocene kyanite-and sillimanite-grade regional metamorphism, and Oligocene-Miocene crustal anatexis forming migmatites and leucogranites. In the Pakistan Himalaya, these events are not recorded in the exposed rocks beneath the obducted Kohistan island arc. Instead, the kyanite-grade gneiss of the Besham Group and sillimanite-grade gneiss of the calcareous Alpurai schist record U-Pb monazite ages of 482.4 ± 7.9 Ma and 464.5 ± 4.0 Ma, respectively. These ages, together with along-strike equivalent rocks in the Lesser Himalaya of India and Nepal, record an Ordovician-age orogeny (the Bhimpedian orogeny) spanning at least from 490 to 460 Ma, following Neoproterozoic-Cambrian sedimentation, and preceding late Ordovician-Silurian post-orogenic molasse deposition and development of a stable shelf margin at 460-440 Ma. These new ages for peak metamorphism in the Pakistan Himalaya overlap with those of widespread S-type granites occurring along the Lesser Himalaya (e.g. Mansehra, Mandi, and Kathmandu granites), Greater Himalaya (e.g. Nanga Parbat, Kinnaur Kailas, and Ama Drime), and in the North Himalayan domes (e.g. the Tso Morari, Kangmar, and Kampa domes). We suggest that in Pakistan, the unexposed Tethyan and Greater Himalayan sequences have been overthust by the Kohistan arc, and the Besham-Alpurai gneisses are equivalent to Lesser Himalayan rocks to the east.

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