MICROFACIES STUDIES OF THE JURASSIC TAKATU FORMATION, WESTERN SULAIMAN FOLD-THRUST BELT, PAKISTAN

Takatu Formation is well exposed in the western Sulaiman Fold- Thrust Belt, Pakistan. It has an unconformable upper contact with Sembar Formation which is marked by oxidized surface and lower contact with Triassic Wulgai Formation. The Takatu Formation contains a wide variety of limestones, which are fine to coarse grained, palatal, lumpy, skeletal, micritic, nodular, oolitic, and intraclastic. The Takatu Formation is mainly carbonate-litho package with minor siliciclastic content interbedded as shale and marls. The petrography of limestone allowed the differentiation and demonstrated of four major and sub microfacies types. These includes, Mudstone, Wackestone, Packstone and Grainstone microfacies, which are further sub-divided into five microfacies such as, Bioclastic wackstone, Calcispheric packstone, Peloidal packstone, Ooidal grainstone, and Lithoclastic grainstone. These microfacies were compared with standard microfacies and standard zones for their possible depositional environments. On the bases of our studies, it is interpreted that Takatu Formation was deposited in diverse environment ranging from the marginal shallow shelf, upper slope and in deeper parts of the shelf

Fractional Radon Transform and its Convolution Theorem

Fractional Radon transform which is symbolized with the notation , it is different to the classical Radon transform. The shift property of fractional Radon transform is controlled by the fractional order Rotation of the input object at angle  will rotate the fractional Radon transform at that angle thus, the fractional Radon transform is rotation invariant. The fractional Fourier transform, with respect to  of the fractional Radon transform of an object is the central slice at angle  of the -dimensional fractional Fourier transform of this object. In this paper we explain the mathematical formation of fractional Radon transform and established a convolution theorem for the fractional Radon transform