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Field Data Example I

We test the capabilities of the proposed approach on the field dataset acquired with a high-resolution 3D (HR3D) marine seismic acquisition system (P-cable) in the Gulf of Mexico to characterize structure and stratigraphy of the shallow subsurface (Merzlikin et al., 2017b; Greer and Fomel, 2018; Meckel and Mulcahy, 2016; Klokov et al., 2017b). The acquisition geometry is defined by a `cross cable' of a catenary shape with paravans (diverters) at the ends oriented perpendicular to the inline (transit) direction that tows twelve $ 25 $   m long streamers with separation of $ 10-15 $   m . Source-receiver offsets are on order of $ 100-150 $   m , while the source sampling is $ 6.25 $   m . The target interval of interest in this paper is associated with the $ 0.222$   s time slice, which approximately corresponds to $ 160 $   m depth. Diffraction imaging is applied to the dataset stack preprocessed with the following procedures: $ 40 $   Hz low-pass filter, wavelet deconvolution, surface-consistent amplitude corrections, predictive deconvolution, missing trace interpolation and acquisition footprint elimination using F-K filtering in the image domain. More detailed description of the acquisition geometry, geology, and interpretation of diffraction images can be found in Klokov et al. (2017b) and Merzlikin et al. (2017b). Here we focus on the interval with a channel of high wavelength sinuosity (Merzlikin et al., 2017b). For simplicity, constant velocity model of $ 1.5 $   km/s is used for both migration and inversion. Higher accuracy diffraction-based velocity estimation for the same dataset is described in Merzlikin et al. (2017b).

The stacked volume is shown in Figure 6. The post-stack 3D Kirchhoff time migration image of the target slice is shown in Figure 7a. Channel delineation is hindered by stronger reflections and acquisition footprint - horizontal lines. We eliminate the footprint in inline and crossline PWD diffraction images using F-K filtering before combining them in a structure tensor (equation 2) and forming AzPWD linear combination (Merzlikin et al., 2017b). Result of AzPWD volume migration is shown in Figure 7b. Channel and other small-scale features (e.g. fault at in-lines $ 2.5-3.0 $   km and cross-lines $ 6.0-6.4 $   km ) are highlighted but the image is still noisy.

Figure 6.
High-resolution 3D marine seismic dataset from the Gulf of Mexico: stacked volume.
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We follow the proposed workflow and first generate the data to be fit by the inversion (Figure 8a) by applying AzPWD and path-summation integral migration to the stack (Figure 6). We run five outer and two inner iterations and use $ \lambda=0.008$ , $ \epsilon=20$ , $ N=30$ and $ K=1$ . Due to low signal-to-noise ratio of the dataset small number of inner iterations is used to prevent leakage of noise to the diffraction image domain. The result of the proposed approach is shown in Figure 8b. The channel appears to be highlighted and denoised. Most of the low-amplitude events are also preserved and highlighted including the fault feature (in-lines $ 2.5-3.0 $   km and cross-lines $ 6.0-6.4 $   km ). Discontinuities of edges intersecting each other at inlines $ 1.0-1.5 $   km and crosslines $ 4.0-5.0 $   km are caused by their rapidly varying orientations prohibiting smoothing from emphasizing different strikes simultaneously.

Figures 9a and 9b show the diffractivity model after thresholding and after thresholding followed by anisotropic smoothing applied correspondingly. The figures illustrate that anisotropic smoothing merges neighbor samples and thus is necessary for edge diffraction regularization. The result is consistent with the experiments shown in Figure 1.

Figure 10 shows the stack after reflection elimination, modeled diffractions from denoised diffractivity shown in Figure 8b and their difference. Denoised diffractions in Figure 10b show clear hyperbolic signatures. Reflection energy remainders after AzPWD application prominent in Figure 10a (e.g., $ 0.222$   s TWTT (two-way traveltime), inline $ 1.625 $   km and crosslines $ 5.5-6.25 $   km and $ 0.222$   s TWTT, inlines $ 2.4-2.7 $   km and crosslines $ 6.25-6.5 $   km ) are also removed. Difference in Figure 10c is predominated by noise, reflection remainders (e.g., regions mentioned above) and acquisition footprint and proves the effectiveness of the approach.

To account for amplitude differences and for higher continuity of denoised diffractions (Figure 10b) in comparison to the stack with AzPWD (Figure 10a) signal and noise orthogonolization (Chen and Fomel, 2015) has been applied. Similarity between restored signal (Figure 10b) and restored noise (Figure 10c) is measured. Then, signal energy, which leaked to the difference volume (Figure 10c) and which has high similarity with the signal events actually predicted (Figure 10b), is withdrawn from the noise volume and added to the signal estimate.

mig3-slice xspr-prec-slice
Figure 7.
$ 0.222$ s time slice: (a) 3D post-stack Kirchhoff migration of the stack shown in Figure 6; (b) 3D post-stack Kirchhoff migration of the stack after AzPWD. Subsurface discontinuities appear to be highlighted in (b) in comparison to (a), in which they are masked by specular energy. At the same time, diffraction image (b) still appears to be noisy.
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linpi-data-slice modl-wk-100
Figure 8.
$ 0.222$ s time slice: (a) observed data (Figure 6) preconditioned by AzPWD and path-summation integral migration; (b) inversion result (strong smoothing is used to highlight the continuity of edge diffractions). Significant improvement in signal-to-noise ratio of edge diffractions has been achieved (compare with Figure 7b).
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hs-modl-wk-100-thr hs-modl-wk-100
Figure 9.
Last iteration diffractivity model: (a) after thresholding; (b) after thresholding followed by anisotropic smoothing. While thresholding allows for denoising, anisotropic smoothing emphasizes edge diffraction continuity and accounts for its kinematic behavior when observed along the edge.
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xspr-notmig diffractions-ortho noise-ortho
Figure 10.
(a) Stack with reflections removed; (b) Kirchhoff modeling of diffractivity from Figure 9b; (c) difference between (a) and (b) is predominated by noise and, in particular, by reflection remainders (notice coherent events with slowly varying amplitudes, e.g., $ 0.222$   s TWTT, inline $ 1.625 $   km and crosslines $ 5.5-6.25 $   km and $ 0.222$   s TWTT, inlines $ 2.4-2.7 $   km and crosslines $ 6.25-6.5 $   km ) and acquisition footprint.
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Next: Field Data Example II Up: Merzlikin et al.: Anisotropic Previous: Synthetic Data Example