# Browsing by Author "Krishnaraj, Naveen"

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Item Implementing a New and Rigorous Technique for 1-D NMR Inversion: Slope of L-curve and Adaptive Pruning(2017-08) Krishnaraj, Naveen; Myers, Michael T.; Hathon, Lori A.; Arad, AlonShow more 1-D NMR data inversion is the process of obtaining T2 amplitude distribution from NMR spin echo trains. NMR inversion is an ill-posed problem, the noise in the data allows for many possible solutions. We solve for the amplitudes on an equally spaced logarithmic scale, representing a typical pore system distribution. If a least square method is used the solution is highly unstable, so we adopted a technique, Tikhonov-Regularization to restrict the range of possible solutions. A stable version of this algorithm was developed and a detailed parametric studies was performed. Two different L-cure parametrizations, the slope of the L-curve method and adaptive pruning was adopted. We generated forward models for the T2 echo train, using an assumption of multiply peaked amplitude distributions with varying levels of Gaussian noise. The forward models were then inverted using the developed algorithm to examine how much of the original information was lost. We conclude with a discussion of the limitations of NMR inversion and the relative merits of each L-curve parametrization.Show more Item Joint Inversion and Unsupervised Learning Applied to NMR Data Processing that Eliminates the Need for Regularization(2021-08) Krishnaraj, Naveen; Myers, Michael T.; Hathon, Lori A.; Soliman, Mohamed Y.; Qin, Guan; Arad, Alon; Ge, XinminShow more An accurate data processing algorithm is at the heart of a successful Nuclear Magnetic Resonance (NMR) log interpretation. The first step in the traditional inversion algorithm is inverting for T2 distribution from the magnetization data at a single depth. A recent innovation involves finding volume fractions of the different components (capillary bound water, clay bound water, free water, organic matter, oil, etc.) using data from multiple depths/measurements and adopting Blind Source Separation (BSS) techniques. NMR data inversion and Blind Source Separation are both ill-posed problems. These algorithms are strongly influenced by noise and have significant error bars, especially for low values of T2. This research develops an algorithm that utilizes a joint inversion and blind source separation approach using a new technique, "Kernel Incorporated Non-Negative Matrix Factorization" (KINMF). This algorithm outputs T2 distributions and the volume fractions of different components from magnetization data by incorporating multiple measurements. This single-step, hybrid approach has a de-noising effect and generates accurate results without regularization. It significantly reduces the smearing effect that arises from standard regularization techniques and leads to one-to-two orders of magnitude improvement in processing speeds (e.g., compute time for the conventional method in a clastic system is higher than 120 sec; for the KINMF it is less than 15 sec). The algorithm was validated using forward modeling and comparison with experimental datasets. We conclude that the major impact of applying KINMF is for T2 relaxation times less than 100 ms and significantly improved computational times (enhanced real-time data processing). This should lead to broader applicability and improved physical interpretation of the data.Show more