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f2-1,f2-z1
Figure 4. Field data example 1. (a) Raw Field Data. (b) Magnified section. |
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rect50,new_rect50
Figure 5. Field data example 1. Estimated non-stationary smoothing radius using 5 iterations of (a) the line-search approach proposed by Chen and Fomel (2021) and (b) the proposed Gauss-Newton approach. |
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The locally orthogonalized signal and noise using the line-search radius are shown in Figures 6b and 6e respectively, and the locally orthogonalized signal and noise using the Gauss-Newton radius are shown in Figures 6c and 6f respectively. The local similarity is a metric that can be used to evaluate signal and noise separation (Chen and Fomel, 2015). The local similarity between the signal and noise using the f-x method, non-stationary orthogonalization using the line-search radius, and non-stationary orthogonalization using the Gauss-Newton radius is displayed in Figures 7a, 7b, and 7c respectively. The proposed method does the best job of separating coherent signals from random noise since its corresponding local similarity values are the smallest. The zoomed in results of signal and noise separation for the three methods are displayed in Figure 8. In the zoomed in signals, we point to the areas where the signal is stronger for non-stationary orthogonalization using the proposed Gauss-Newton method compared to the two other approaches. In the zoomed in noise results, these same areas correspond to locations of higher signal leakage for the two other methods compared to the proposed method. Thus, from a visual standpoint, the proposed method recovers the strongest signals and also achieves the least signal leakage in the removed noise.
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f2-fx-1,f2-orthon-1,new-f2-orthon-1,f2-fx-1-n,f2-orthon-1-n,new-f2-orthon-1-n
Figure 6. Field data example 1. De-noised data using the (a) f-x method, (b) non-stationary orthogonalization using line-search radius proposed by Chen and Fomel (2021) for regularization, and (c) non-stationary orthogonalization using proposed Gauss-Newton radius for regularization. (d-f) Removed noise corresponding to (a-c), respectively. |
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f2-s,f2-s-orthon,new-f2-s-orthon
Figure 7. Field data example 1. Local similarity of de-noised data and removed noise for (a) f-x method, (b) non-stationary orthogonalization using the line-search radius proposed by Chen and Fomel (2021), and (c) non-stationary orthogonalization using the proposed Gauss-Newton radius. |
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f2-fx-z1-0,f2-orthon-z1-0,new-f2-orthon-z1-0,f2-fx-z1-n,f2-orthon-z1-n,new-f2-orthon-z1-n
Figure 8. Field data example 1. (a-f) Magnified sections corresponding to framed boxes in Figure 6 (a-f) respectively. |
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