Matching and merging low-resolution and high-resolution seismic images

In this application, we have two seismic datasets acquired over the same area containing non-stationary spatial and temporal differences in spectral content. The high-resolution data displayed in Figure 11a has a larger frequency bandwidth and a higher dominant frequency, producing a high-resolution image of the shallow subsurface. The legacy data displayed in Figure 11b contains important low-frequency content resulting in better depth coverage. The workflow for matching and merging the two datasets developed by Greer and Fomel (2018) is summarized in the following three steps: (1) amplitude and frequency balancing by non-stationary triangle smoothing, (2) estimating and removing variable time shifts, and (3) blending the two images by least-squares inversion. Here we will perform step (1) only, showing the effectiveness of the proposed radius estimation method in balancing the spectral content between two datasets.

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Figure 11. Field data example 3. (a) High-resolution image. (b) Low-resolution legacy image.

We match the two datasets using the proposed radius estimation method substituting the high-resolution data as $\mathbf{d}_{input}$, and the low-resolution data as $\mathbf{d}_{output}$ 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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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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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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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.