A new method for NMR data inversion based on double-parameter regularization

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. JM39-JM49 ◽  
Author(s):  
Jiangfeng Guo ◽  
Ranhong Xie ◽  
Youlong Zou ◽  
Guowen Jin ◽  
Lun Gao ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Regularization Parameter ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Entropy Method ◽  
Petroleum Exploration ◽  
Tight Sandstone ◽  
Nmr Data ◽  
Parameter Regularization

Nuclear magnetic resonance (NMR) technology plays a significant role in petroleum exploration. NMR data can be processed using inversion methods to reflect the relaxation information of all the components. We have developed a new double-parameter regularization (DPR) method for the inversion of NMR data, whose regularization terms consist of Tikhonov regularization and maximum entropy regularization. The objective function for the DPR method was solved using the Levenberg-Marquardt method, the proportional coefficient of the regularization parameter was obtained using an iteration procedure, and the optimum regularization parameter of the DPR method was selected using an S-curve. The relationship between the optimum regularization parameter and the signal-to-noise ratio (S/N) of the data was evaluated. Moreover, we compared the results of the NMR inversion obtained from the norm smooth method, the maximum entropy method, and the DPR method for simulated data. We evaluated how the proportional coefficient of the regularization parameter affected the inverted [Formula: see text] distributions and processed field NMR log data for a tight sandstone reservoir using the DPR method. The results indicated that the optimum regularization parameter for the DPR method gradually decreases with increasing data S/N. The accuracy is higher for the DPR method than for the norm smooth method and the maximum entropy method under low-S/N conditions. It is of great importance to select the proportional coefficient for the DPR method. The inverted [Formula: see text] distributions are similar for the DPR method and the norm smooth method when the proportional coefficient is small, and this is similar for the DPR method and the maximum entropy method when the proportional coefficient is large.

Fine-scale mapping of fish distribution from commercial catch and effort data using maximum entropy tomography

1998 ◽  
Vol 55 (5) ◽  
pp. 1220-1227 ◽  
Author(s):  
M Vignaux ◽  
G A Vignaux ◽  
S Lizamore ◽  
D Gresham
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Simulated Data ◽  
Real Data ◽  
Entropy Method ◽  
Fish Distribution ◽  
Bayesian Maximum Entropy ◽  
Commercial Catch ◽  
Trawl Fishery ◽  
Distribution Of Fish

We present a technique for mapping the spatial distribution of fish using commercial catch and effort data. The relative fish density can be estimated at scales smaller than the length of the unit of effort, such as a tow, by using a Bayesian maximum entropy method. This can take advantage of the fact that the tows cross to give information about the density in those areas. This is a novel application of a well-tested technique that has been used in other fields such as astronomical imaging. Its utility and robustness is demonstrated both on simulated data and on real data from the trawl fishery on spawning hoki off the west coast of the South Island of New Zealand.

Nonlinearity of the maximum entropy method in resolution enhancement

1992 ◽  
Vol 70 (12) ◽  
pp. 2887-2894 ◽  
Author(s):  
J. K. Kauppinen ◽  
D. J. Moffatt ◽  
H. H. Mantsch
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Linear Prediction ◽  
Signal To Noise Ratio ◽  
Resolution Enhancement ◽  
Nonlinear Behavior ◽  
Entropy Method ◽  
Spectral Lines ◽  
High Signal ◽  
Intensity Pattern

The nonlinear behavior of the filter-type Maximum Entropy Method (MEM) was investigated from a theoretical and a practical point of view. The integrated intensity of the output spectral lines of MEM was probed as a function of the input intensity pattern, the filter length, and the S/N ratio of the input spectrum. The nonlinear behavior of MEM has been explained and the results compared with those derived by another method, LOMEP (Lineshape Optimized Maximum Entropy linear Prediction). The study was carried out with the aim of resolution enhancement of spectra that have high signal-to-noise ratio.

Advanced Inference in the Real World

2017 ◽  
Author(s):  
Amos Golan
Keyword(s):  
Brain Tumor ◽  
Maximum Entropy ◽  
Real World ◽  
Maximum Entropy Method ◽  
Simulated Data ◽  
Entropy Method ◽  
Weather Data ◽  
Conditional Probabilities ◽  
Conditional Information

In this chapter I continue the voyage into info-metrics in action, with an emphasis on more advanced info-metric inference in real-world environments. I develop a sequence of increasingly complex applications. In the first example, the maximum entropy method is extended for inferring interval information, with an application to weather data. The next example introduces additional conditional information into the constraints. It is a laboratory example, complemented with simulated data matched to observed population frequencies. The last example is the most complex, using surprisal analysis and Bayes’s rule to infer conditional probabilities from brain tumor data. In each problem the quantities whose entropy is maximized are identified and motivated. These examples demonstrate the power and generality of the info-metrics framework by showing that it allows inference in a variety of realistic settings.

Enhanced Information Recovery in 2D On-and Off-Resonance Nutation NQR using the Maximum Entropy Method

1996 ◽  
Vol 51 (5-6) ◽  
pp. 337-347 ◽  
Author(s):  
Mariusz Maćkowiak ◽  
Piotr Kątowski
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Theoretical Description ◽  
Entropy Method ◽  
Zero Field ◽  
Resonance Effects ◽  
Information Recovery ◽  
Truncation Errors ◽  
Enhanced Resolution ◽  
2D Data

Abstract Two-dimensional zero-field nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin - 3/2 nuclei in serveral molecular crystals containing the 3 5 Cl and 7 5 As nuclei. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. It is shown that the replacement of conventional Fourier transform by an alternative data processing by MEM in 2D NQR spectroscopy leads to sensitivity improvement, reduction of instrumental artefacts and truncation errors, shortened data acquisition times and suppression of noise, while at the same time increasing the resolution. The effects of off-resonance irradiation in nutation experiments are demonstrated both experimentally and theoretically. It is shown that off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments, thus facilitating the determination of asymmetry parameters in multiple spectrum. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. In off-resonance conditions, the resolution of the nutation NQR spectrum decreases with the spectrometer offset. However, an enhanced resolution can be achieved by using the maximum entropy method in 2D-data reconstruction.

Estimating the distribution of primary reflection coefficients

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1417-1422 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Reflection Coefficients ◽  
Log Data ◽  
Neuquen Basin ◽  
Neuquén Basin ◽  
Skewness And Kurtosis

The distribution of primary reflection coefficients can be estimated by means of the maximum entropy method, giving rise to smooth nonparametric functions which are consistent with the data. Instead of using classical moments (e.g. skewness and kurtosis) to constraint the maximization, nonconventional sample statistics help to improve the quality of the estimates. Results using real log data from various wells located in the Neuquen Basin (Argentina) show the effectiveness of the method to estimate both robust and consistent distributions that may be used to simulate realistic sequences.

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