3D-seismic data have increasingly shifted seismic interpretation work from a horizons-based to a volume-based focus over the past decade. The size of the identification and mapping work has therefore become difficult and requires faster and better tools. Faults, for instance, are one of the most significant features of subsurface geology interpreted from seismic data. Detailed fault interpretation is very important in reservoir characterization and modeling. The conventional manual fault picking is a time-consuming and inefficient process. It becomes more challenging and error-prone when dealing with poor quality seismic data under gas chimneys. Several seismic attributes are available for faults and discontinuity detection and are applied with varying degrees of success. We present a hybrid workflow that combines a semblance-based fault likelihood attribute with a conventional ant-tracking attribute. This innovative workflow generates optimized discontinuity volumes for fault detection and automatic extraction. The data optimization and conditioning processes are applied to suppress random and coherent noise first, and then a combination of seismic attributes is generated and co-rendered to enhance the discontinuities. The result is the volume with razor sharp discontinuities which are tracked and extracted automatically. Contrary to several available fault tracking techniques that use local seismic continuity like coherency attributes, our hybrid method is based on directed semblance, which incorporates aspects of Dave Hale’s superior fault-oriented semblance algorithm. The methodology is applied on a complex faulted reservoir interval under gas chimneys in a Malaysian basin, yet the results were promising. Despite the poor data quality, the methodology led to detailed discontinuity information with several major and minor faults extracted automatically. This hybrid approach not only improved the fault tracking accuracy but also significantly reduced the fault interpretation time and associated uncertainty. It is equally helpful in detecting any seismic objects like fracture, chimneys, and stratigraphic features.

Our goal in this paper is to prove some fixed point and common fixed theorems for contractive type maps in a CMS over Banach algebra, which unify, extend and generalize most of the existing relevant fixed point theorems from Shaoyuan Xu and Stojan Radenovic [1]. We provide illustrative example to verify our results.

The main objective of the present work is to solve the non-linear inviscid Burger equation using the second-order TVD scheme with the different TVD limiters. These limiters include Non-MUSCL (monotone upwind scalar conservation laws) Harten-Yee upwind limiters, Roe-Sweby upwind limiters and Davis-Yee symmetric TVD limiters. These limiters are then used in conjunction with the explicit finite difference second order TVD scheme to model the flow in which discontinuity is present. Non-linear Burger equation was solved for this purpose to capture a one dimensional traveling discontinuity. Every limiter was individually tested for its ability to resolve the discontinuity in as few mesh point as possible. In addition, each limiter's capability to eliminate spurious oscillations associated with numerical computation of discontinuities was investigated. The results showed that all the TVD limiters were able to completely eliminate the spurious oscillations except Roe-Sweby limiter that caused the solution to diverge.

Abstract:The Fixed Point Theorem had been proved on Reciprocally Continuous Self Mapping. In this paper the fixed point theorem on reciprocally continuous self mapping is proved under Menger Space.

In this paper we prove common fixed point theorem for compatible mapping.