Summary Nuclear magnetic resonance (NMR) measurements are extremely valuable in the assessment of fluid-flow properties of rocks. However, inverted NMR transverse-relaxation time (T2) distributions are often biased by positivity constraints and the implementation of regularization (stabilization) methods. In some cases, it is difficult to determine whether the estimated pore-size distributions are reliable or byproducts of the inversion. On-site quality control of NMR inversion results is thus essential to avoid erroneous analyses based on nonphysical interpretations across conventional or unconventional rocks. It is also important to adjust the measurement acquisition process in real time in response to variable signal/noise conditions in the borehole environment. We introduce and compare three quality-control approaches; two of them are based on two different signal processing practices, namely the semilogarithmic derivative and the Hilbert transform, while the third is based on a nonlinear optimization technique. Validation of the inverted T2 distribution is performed by applying either method to the echo train decay of proton magnetization to estimate a pseudo-T2 distribution that is not affected by inversion artifacts. These three methods are data-driven processes for on-site, continuous quality control of borehole NMR measurements. In the first method, a pseudo-T2 distribution is constructed by taking the derivative of the echo train decay with respect to the natural logarithm of the relaxation time. For the second method, the Hilbert transform is applied to the raw proton magnetization decay to approximate the T2 distribution. The latter method consists of an approximation of the derivative of the time decay of magnetization using least-squares minimization. NMR laboratory measurements were performed on a wide variety of rocks, the associated T2 distributions were estimated using linear inversion, and the three quality-control methods were applied for comparison. The reliability of our quality-control procedures was verified by benchmarking them against the inverted T2 distributions. Furthermore, these quality-control methods, when applied continuously to borehole NMR measurements, enable the optimization of the measurements in real time to mitigate the effects of biasing noise. By verifying the location of the dominant mode of the T2 distribution during NMR measurement acquisition, the operator can determine whether (a) more stacking of proton magnetization decays is needed, or (b) longer- or shorter-time sampling is needed to attain a high-quality estimation of the pore-size distribution before performing the T2 inversion. Our work provides the basis of effective quality-control methods for NMR measurements for the petrophysical interpretation of rocks with complex pore-size distributions, especially in unconventional rocks, where noise present in the measurements (notably at early acquisition times), can mask the useful signal originating from pore-size distributions and fluids. The fast and reliable quality control of estimated T2 distributions is not affected by inversion artifacts, relying only on unfiltered, raw data.

中文翻译：

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使用伪 T2 分布的核磁共振测量的质量控制

总结 核磁共振 (NMR) 测量在评估岩石的流体流动特性方面非常有价值。然而，倒置 NMR 横向弛豫时间 (T2) 分布通常会受到正性约束和正则化（稳定）方法的实施的影响。在某些情况下，很难确定估计的孔径分布是可靠的还是反演的副产品。因此，核磁共振反演结果的现场质量控制对于避免基于常规或非常规岩石的非物理解释的错误分析至关重要。响应井眼环境中的可变信号/噪声条件，实时调整测量采集过程也很重要。我们介绍并比较了三种质量控制方法；其中两种基于两种不同的信号处理实践，即半对数导数和希尔伯特变换，而第三种基于非线性优化技术。通过将任一方法应用于质子磁化的回波序列衰减以估计不受反演伪影影响的伪 T2 分布，来验证反演 T2 分布。这三种方法是数据驱动的过程，用于对钻孔 NMR 测量进行现场连续质量控制。在第一种方法中，通过对回波序列衰减相对于弛豫时间的自然对数求导来构造伪 T2 分布。对于第二种方法，希尔伯特变换应用于原始质子磁化衰减以近似 T2 分布。后一种方法包括使用最小二乘法最小化磁化时间衰减的导数的近似值。对多种岩石进行了 NMR 实验室测量，使用线性反演估计了相关的 T2 分布，并应用了三种质量控制方法进行比较。我们的质量控制程序的可靠性通过将它们与反向 T2 分布进行基准比较来验证。此外，当这些质量控制方法连续应用于钻孔 NMR 测量时，可以实时优化测量以减轻偏置噪声的影响。通过在 NMR 测量采集期间验证 T2 分布的主要模式的位置，操作员可以确定 (a) 是否需要更多堆叠质子磁化衰减，或者 (b) 需要更长或更短时间的采样来获得在进行 T2 反演之前对孔径分布进行高质量估计。我们的工作为 NMR 测量提供了有效质量控制方法的基础，用于对具有复杂孔径分布的岩石进行岩石物理解释，特别是在非常规岩石中，其中测量中存在的噪声（特别是在早期采集时间）可以掩盖有用的来自孔径分布和流体的信号。估计的 T2 分布的快速可靠的质量控制不受反演伪影的影响，