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hires,legacy
Figure 11. Field data example 3. (a) High-resolution image. (b) Low-resolution legacy image. |
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We match the two datasets using the proposed radius estimation method substituting the high-resolution data as
, and the low-resolution data as
in equation 15.
The starting model for the radius is chosen carefully to preserve stability. The initial guess for the radius displayed in Figure 12a is a smooth version of the theoretical radius proposed by Greer and Fomel (2018). The radius estimated after 5 iterations is displayed in Figure 12b.
The spectral content of the two datasets before and after non-stationary smoothing is displayed in Figure 13, and the differences in local frequency between the two datasets before and after non-stationary smoothing is displayed in Figure 14.
The results indicate that the frequency content between the two datasets is better balanced after smoothing with the newly estimated radius.
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rect00,rectn50
Figure 12. Field data example 3. (a) The initial guess for the smoothing radius, a smoothed version of the theoretical radius proposed by Greer and Fomel (2018). (b) Estimated smoothing radius using 5 iterations of the proposed Gauss-Newton method matching the high-resolution data and the 18 Hz high-pass filtered low-resolution data. |
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nspectra,hires-smooth50-spec
Figure 13. Field data example 3. Normalized spectra of low-resolution legacy data (red) and high-resolution data (blue) (a) before and (b) after 18 Hz high-pass filtering of low-resolution legacy data and non-stationary smoothing of high-resolution data. |
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freqdif,locfreqdif50
Figure 14. Field data example 3. (a) Initial difference in local frequency between low-resolution legacy data and high-resolution data. (b) Difference in local frequency between 18 Hz high-pass filtered low-resolution legacy data and non-stationary triangle-smoothed high-resolution data. |
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