مولانا بشیر احمد خاں
افسوس ہے پچھلے دنوں دارالعلوم دیوبند کے نہایت لائق وفائق اورمشہور استاذ مولانا بشیر احمدخاں صاحب کااچانک انتقال ہوگیا۔ مولانا ریاضیات اور ہیئت میں برِصغیر ہندوپاک کے علماء میں اپنا جواب نہیں رکھتے تھے۔ اس کے علاوہ فقہ اورحدیث میں بھی اُن کی نظر وسیع تھی، چنانچہ دارالعلوم دیوبند میں ان فنون کی اونچی کتابیں اُن کے زیر ِ درس رہتی تھیں اور کبھی کسی طالب علم نے اپنی بے اطمینانی کااظہار نہیں کیا۔ علوم وفنون میں اس درجہ مہارت اور اُن میں شغف کے ساتھ مولانا میں نظم و نسق اور دنیوی معاملات و مسائل کو سمجھنے اور ان کے حل کرنے کی صلاحیت بھی بدرجہ ٔ اتم تھی۔ اسی بناء پر چندماہ ہوئے اُن کا انتخاب نائب مہتمم کے عہدہ کے لیے ہواتھا۔ عمر اگر چہ ستّر( ۷۰) کے لگ بھگ تھی، لیکن قویٰ مضبوط اور عام تندرستی بہت اچھی تھی۔ ۱ ۲؍ اگست کومجلسِ عاملہ کی میٹنگ میں وہ شروع سے آخرتک شریک رہے اوراُس کاکبھی وہم بھی نہیں ہوسکتا تھاکہ دو دن کے بعد ہی مولانا یک بیک راہی عالم ِبقا ہوجائیں گے۔یوں بھی عابد مرتاض اور خندہ جبین وخوش اخلاق تھے۔ اﷲ تعالیٰ مغفرت وبخشش کی نوازشوں سے نوازے اور اُن کے درجات اونچے کرے آمین۔ [اکتوبر۱۹۶۶ء]
Loans or credits offered by Kopdit credit unions are a potential source of funds that need to be developed, to help accelerate the home industry and the micro and small economies. Therefore, we want to see the impact of several conditions such as the loan interest rate, GDP per capita growth, inflation rate and economic growth. Quite a number of studies have looked at the impact of interest rates, GDP growth, inflation rates and economic growth on loans or credits to banks or banking institutions. We do not look at credit or loans from banks, but on Kopdit credit unions (CU). The results of our research show that simultaneously the loan interest rate, GDP growth, inflation rate and economic growth have a strong enough influence on loans at Credit Union Credit Unions, namely 79.2454%. Partially the variable of loan interest rate, GDP growth per capita, inflation rate affects outstanding loans, while economic growth partially has no effect on outstanding loans.
Conventionally, AVO/AVA method is widely being used for reservoir characterization process on the assumption of isotropic (earth) medium. Seismic anisotropy is considered to produce first order effect upon the amplitudes of seismic wave, but this effect is often ignored during AVA studies for ease of processing, which may give unrealistic reservoir characterization results. The principal objective in this research work is to estimate the seismic anisotropy of a composite sand shale reservoir and incorporate it into AVA studies for accurate and improved reservoir charterization. A further aim of this work is to give complete workflow for the charaterziation of such reservoirs and its application to the real data from a gas prone field in Pakistan. The main elements of AVA based reservoir characterization of composite sand shale anisotropic medium include forward (rock physics and seismic modelling) and inverse modelling (recovering the spatial distribution of crucial reservoir properties). An anistropic composite sand shale medium can be characterized by five independent elastic constants either in the form of stiffness constants or two vertical velocities and three anisotropy coefficients. These five elastic constants for dry porous media has been estimated using anistropic effective medium theory in the contaxt of rock physics modelling. The input to rock physics modelling is obtained via petrophysical analysis of available wireline log data. The effective elastic constants obtained from rock physics modelling for composite sand shale medium is used for seismic AVA modelling of composite sand shale anisotropic medium in the form of angle-dependent refelection coefficients and/or seismic AVA data by using approximate and exact PP- reflection coefficients solution. During seismic inversion phase of reservoir characterization process, Bayesian inversion approach has been adapted to recover/invert the important reservoir parameters (porosity, volume of shale and water saturation) from AVA data and to carry out uncertainty analysis associated with these estimates. Our AVA modelling and analysis results on Sawan area under isotropic conditions show that seismic AVA modelling provides a strong relationship between porosity and reflection amplitude for all offset (or incident angle) ranges. From fluid saturation variation modelling it is evident that changes in water saturation do not change the AVA effect significantly which is further substantiated by investigation of CDP gathers. The seismic AVA modelling for different porosity/saturation values suggest that AVA analysis is prone to find porous sands rather than gas saturated sands. The same is shown by AVA crossplot between intercept and gradient which point out high porosity zones rather than high gas saturations. The results from our complete workflow applied on composite sand shale medium (in which shale is present in the form of lenses creating anisotropy) suggest that one can recover Vshale even at higher amount of uncertainty in AVA data, as the peak for marginal distribution lies mostly around the true value. For small amount of uncertainty in AVA data, our workflow gives reliable estimates for Sw, but as the noise increases in AVA data, it becomes difficult to recover Sw. The results from application of our workflow on C-sand reservoir of Sawan area (shale is present in the form of layers creating anisotropy) show that anisotropy effects are more pronounced in stratigraphic intervals where interbedded shales are relatively thick within reservoir sand (Sawan-06 well).The exact solution for VTI media provided by Daley and Horn’s (1977) is one with the highest potential for performing AVA inversion in sand shale composite medium with weak to strong anisotropy. We have demonstrated this fact by completing a numerical synthetic experiment for recovering porosity distributions through the Lower Goru C-sand reservoir.