Suitability of L- and U-Curve Methods for Calculating Reasonable Adsorption Energy Distributions from Nitrogen Adsorption Isotherms

Arnrich, Steffen; Bräuer, Peter; Klauck, Mandy; Kalies, Grit

doi:10.1260/0263-6174.32.7.521

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…The GDED method is similar to the L curve method and the U curve method in some aspects (Arnrich et al., 2014; Hansen, 1992; Hansen & O’Leary, 1993; Krawczyk‐Stańdo et al., 2007). These three methods are used to determine the relative weight ratio of the virtual observation (regularization parameter), and both consider the relationship between the data misfit and model roughness.…”

Section: Discussionmentioning

confidence: 99%

“…Based on the Tikhonov regularization method, virtual observations must be added to the smoothing constraints, and the weight ratio of these virtual observations is often called the regularization parameter. At present, existing methods for choosing the regularization parameter mainly include the ridge method (Arthur & Robert, 1970), the generalized cross‐verification method (GCV method; Allen, 1974; Golub et al., 1979; Stone, 1974), the L curve method (Hansen, 1992; Hansen & O’Leary, 1993), and the U curve method (Arnrich et al., 2014; Krawczyk‐Stando & Rudnicki, 2007; L. Y. Wang et al., 2018).…”

Section: Introductionmentioning

confidence: 99%

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A New Method Applied for the Determination of Relative Weight Ratios Under the TensorFlow Platform When Estimating Coseismic Slip Distribution

Zhao

Zhou

et al. 2022

JGR Solid Earth

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When estimating a coseismic slip distribution with multiple observation types, the relative weight ratios (the contribution ratios of all kinds of actual observations in the joint inversion, which should be positive by default) and regularization parameter critically impact the inversion accuracy. In this paper, we propose a new method for determining the relative weights of multiple observations of jointing inversion slip distributions. This method regards the observations and the relative weight ratios as the training data sets and training parameters, respectively; in addition, the constructed Loss $Loss$ function was optimized by the gradient descent method and the exponential decay learning rate method under the TensorFlow platform (GDED). We compared the GDED method with the Helmert variance component estimation method (HVCE) and Akaike's Bayesian information criterion method (ABIC) by designing eight simulation experiments. These simulations included changing the errors and resolutions of the observations, the grid size, the strike angle and the dip angle of the fault, the moment magnitudes of earthquakes, the number of observation types, and the complexity of subduction‐zone earthquakes. We analyzed and discussed the characteristics of the above three methods in determining the relative weight ratios during the joint inversion process. The results of these simulation experiments showed that the GDED method and the ABIC method perform much better than the HVCE method when negative variance occurs in the HVCE method, while the accuracies of the slip distributions produced by the three methods were similar when no negative variance occurred; the GDED method can be used to prevent the occurrence of negative variance compared to the HVCE method and is more time efficient than the ABIC method. Furthermore, we applied these methods to invert the source parameters of the 2015 Mw 8.3 Illapel earthquake (in Chile), and the inversion results showed that the slip of the Illapel earthquake was mainly distributed at depths of approximately 10–50 km. The maximum slip of the Illapel earthquake was approximately 7.9 m, distributed 50–70 km northwest of the epicenter at depths of approximately 10–20 km.

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