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Field Data Example

We apply our method to a 2D deepwater field dataset acquired to image the Nankai Trough subduction zone in Japan off the shore of Honshu in the Philipine Sea, where the Philipine Plate subducts below the Eurasian Plate. Moore et al. (1990) contains relevant data acquisition parameters and processing results associated with this dataset, which is referred to as NT62-8. Moore and Shipley (1993) performed structural interpretation on the line. Additional regional context may be found in Moore et al. (2007) and Bangs et al. (2009). This experiment examines CMPS 900-1301 from that line, previously used by Forel et al. (2005) and Decker et al. (2017a). This portion of the line highlights the transition from trench, stretching to to the south, or off to the left of our study area with lower CMP numbers, to a highly deformed accretionary wedge of sedimentary rocks featuring numerous thrust faults that overlays the subducting oceanic crust within our study area. This dataset features numerous diffractions, making it well suited for application to diffraction imaging.

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nankai-data,nankai-dif
Figure 15.
Field data from Nankai Trough: (a) complete data; (b) plane-wave destruction diffraction data.
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Data are pre-processed by correcting traces to be zero-mean, using a 10-125 Hz bandpass filter, applying surface consistent amplitude correction, and resampling to 4 ms. Data are then DMO stacked, shown in Figure 15a, and diffractions are extracted through plane-wave destruction (Fomel et al., 2007). Diffraction data are displayed in Figure 15b. OVC is performed on the diffraction data from Figure 15b, outputting a suite of slope-decomposed diffraction images for 60 different migration velocities, beginning at 1.4 km/s with a 20 m/s increment.

Slope-decomposed images are used to perform the probabilistic diffraction imaging process, illustrated in Figure 16. Stacking the slope-decomposed partial images, $ I(t,v,x,p)$ over slope $ p$ provides the partial images in the top left box plot of Figure 16. Semblance is calculated from slope-decomposed partial images according to Equation 2, and is used to generate the imaging weights shown in the bottom row of Figure 16 as well as the expectation velocity and its variance, plotted in Figures 17a and 17b respectively.

nankai-weights3a-3
nankai-weights3a-3
Figure 16.
Illustration of the probabilistic diffraction imaging process on the Nankai field dataset on a gather centered at Distance 4100 m: Top left box plot contains partial images output by the OVC process after stacking over slope. Top middle box plot contains the combined weights that the left panel will be multiplied by. Top right box plot shows the partial images on the left multiplied by the combined weights. Bottom left box plot shows $ W_1$ , the image semblance. Bottom middle box plot contains $ W_2$ , a weight normally distributed around expectation velocity, $ \bar{v}$ , using the expectation velocity's variance, $ \sigma ^2_v$ . Bottom right box plot has $ W_3$ , a weight based on the magnitude of semblance's gradient.
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nankai-v-exp nankai-v-exp-var
nankai-v-exp,nankai-v-exp-var
Figure 17.
Nankai Trough velocity attributes calculated from semblance: (a) expectation velocity; (b) velocity variance.
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Multiplying the weights together provides the combined weight in the top middle box plot of Figure 16. Multiplying those weights by the partial images in velocity in the top left box plot generates the weighted partial images in the top right box plot. We use the expectation velocity in Figure 17a to generate a deterministic complete image, shown in Figure 18a. We generate a deterministic diffraction image plotted in Figure 18b by migrating the diffraction data in Figure 15b using the expectation velocity in Figure 17a, and a equal weight diffraction image, Figure 18c by stacking the partial images in the upper left box plot of Figure 16 over velocity with equal weights. Stacking the weighted partial images in the upper right panel of Figure 16 over velocity provides the probabilistic diffraction image in Figure 18d.

nankai-full nankai-deterministic nankai-path-sum nankai-prob-dimage
nankai-full,nankai-deterministic,nankai-path-sum,nankai-prob-dimage
Figure 18.
Images of the Nankai Trough: (a) deterministic complete image generated by migrating the complete data in Figure 15a using the expectation velocity, Figure 17a; (b) deterministic diffraction image generated by migrating the diffraction data, Figure 15b, using the expectation velocity, Figure 17a; (c) diffraction image generated through the equal weight stack over velocity of the the partial images in the left box plot of Figure 16; (d) probabilistic weight diffraction image created by stacking the weighted partial images in the top right box plot of Figure 16 over velocity.
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We generate a suite of slope gathers for midpoints at 4100 m to illustrate how different wavefield components contribute to the four images. Figure 19a contains a slope gather corresponding to the Nankai Trough complete image, Figure 18a. That gather is overlaid by a fuchsia plot of image slope at that midpoint computed by warping the complete image to squared time, determining slope, and then warping that slope back to non-squared time following the same process used in the toy model example to find the slope plotted in Figure 18a. Figure 19b displays the slope gather corresponding to the deterministic diffraction image, Figure 18b, Figure 19c features the gather corresponding to the equal weight image, Figure 18c, and Figure 19d has the gather corresponding to the probabilistic diffraction image, Figure 18d.

nankai-full-slice-tpx-slope-3 nankai-slice-tpx-3 nankai-const-gath-3 nankai-wtd-gath-3
nankai-full-slice-tpx-slope-3,nankai-slice-tpx-3,nankai-const-gath-3,nankai-wtd-gath-3
Figure 19.
Slope gathers centered at 4100 m corresponding to (a) the complete image, Figure 18a; (b) the deterministic diffraction image, Figure 18b; (c) the equal weight image, Figure 18c; (d) the probabilistic diffraction image, Figure 18d.
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The probabilistic weight diffraction image better highlights diffractive features and suppresses remnant reflection signal than the deterministic or equal weight diffraction images. Diffractions delineating the seafloor between about 5.9 and 6.3 s, and likely tied to slumps, are well resolved in the probabilistic diffraction image, but less defined in the deterministic and equal weight images where they are either less focused or overwhelmed by their point spread functions and noise, making it more difficult to discern the location of the seafloor.

Diffractions highlighting thrust faults, particularly two that intersect the seafloor at 1000 km and 2300 km and extend downward to the right to a relatively flat décollement extending laterally at about 7.2 s and defining the plate boundary, are clearly visible in the probabilistic diffraction image. These faults are more difficult do distinguish in the deterministic diffraction image due to remnant reflections and in the equal weight diffraction image due to background noise.

A highly diffractive layer extending laterally at about 7.5 s marking the transition from sedimentary to crystalline rock is more localized in the probabilistic diffraction image than the deterministic or path integral diffraction images. This boundary marks the deepest diffractions observed in this data, so velocity data below this boundary corresponding to the crystalline rock is unavailable, as diffraction energy is not observed traveling through it.

In general the deterministic and equal weight diffraction images contain more background noise than the probabilistic image, although all three methods are able to isolate weak diffractions in the décollement at about 7.2 s and identify the lowest sedimentary region between the décollement and crystalline rock transition at 7.5 s as relatively free of diffraction energy.

Examining the gathers centered at 4100 m, notice that much of the energy present in the complete image slope gather, Figure 19a, surrounds the dominant slope denoted by the dashed fuchsia line. This is expected, as reflection signal is often the most powerful feature of a seismic image. The stationary reflection energy surrounding that line is not present in the other gathers, as it has been mostly removed by plane wave destruction - notice in the deterministic gather, Figure 19b, that energy around the dominant slope is significantly suppressed. Although not a central argument in this paper, this is interesting because it illustrates how the deterministic diffraction imaging workflow employed in the creation of this image, which was based on reflection removal by removing energy possessing the dominant slope in the data domain as identified by plane-wave destruction filters following Fomel (2002), has a similarity to the diffraction imaging method of Moser and How-ard (2008), which involves directly applying a mute around the dominant slope in gathers similar to these to surpress stationary reflection energy. In effect, the plane-wave destruction process has generated similarly muted data when viewed in these gathers. A key difference, is that plane-wave destruction is able to at least partially differentiate between diffraction energy underlying reflection energy rather than completely masking it. This feature is particularly apparent in the two gathers when dominant slopes are near zero, as can be seen near 6.1 s and 7.4 s where energy remains near the dominant slope value in the deterministic gather.

The three diffraction image gathers, the deterministic gather of Figure 19b, the equal weight gather of Figure 19c, and the probabilistic gather of Figure 19d, have significantly different appearance. Although energy near the complete image gather's dominant slope tends to be suppressed in all three gathers, as one would expect from diffraction images, the ranges over which energy is present differs significantly. Most energy in the equal weight gather is confined within $ \pm 0.003$ s$ ^2$ /m, while that of the other two gathers has a larger range, with at least some energy extending the width of each gather. The probabilistic weight gather has a more sparse, coherent, and clean appearance when compared to the other two, while the deterministic gather features more chaotic, less coherent features. The deterministic gather also features some interesting coherent energy isolated to slope values with magnitudes greater than 0.005 s$ ^2$ /m which is likely tied to out of plane diffractions, reflection energy that does not have the dominant slope at a location, or migration artifacts. An example of such an feature occurs in the deterministic gather between 6.2 and 6.4 s, which corresponds to events in the deterministic diffraction image, Figure 18b, sloping steeply downward to the right at 4100 m between 6.2 and 6.4 s. In this case they appear to be related to reflections off of a dipping fault interface cutting through the strata which define dominant slope. Although these features are interesting and can be useful for identifying faults, they are not diffractions. Also notice that within the three diffraction gathers, coherent energy is not present between $ 6.5$ and $ 6.7$ s. Indeed, in the probabilistic gather very little energy at all is present in that interval, and thus the probabilistic diffraction image, Figure 18d is mostly blank in that interval at 4100 m. However, in both the deterministic diffraction image, Figure 18b, and the equal weight diffraction image, Figure 18c, that area contains noisy, chaotic energy, which based on its appearance in the corresponding gathers is not related to diffraction.

A final noteworthy feature is visible between $ 6.7$ and $ 6.85$ in three gathers. Here we see a polarity reversal in flat flat diffraction energy for slope values near $ 0.001$ s$ ^2$ /m. This polarity reversal is an excellent example of diffractions caused by an edge rather than a point (Klem-Musatov et al., 2008). In this case, the diffraction is likely caused by a fault fault which has created a material discontinuity. This illustrates a situation where the assumption that diffractions are laterally coherent across all slopes, which is valid for point diffractions and justifies the use of gather semblance as a measure of diffraction, may not hold. Fortunately, in this case these edge diffractions are successfully resolved by the probabilistic process, the corresponding event can be seen at 4100 m beginning around 6.7 s in Figure 18d.

The probabilistic diffraction imaging process outputs a plausible RMS expectation velocity, Figure 17a using velocity analysis on data already stacked to zero offset. Because the calculated velocity field is relatively stable, we are able to calculate Dix velocity and transform our images from time to the depth domain in the manner of Sripanich and Fomel (2018).

Figures 20b and 20a contain the probabilistic diffraction image of Figure 18d and complete image of Figure 20a transformed to the depth domain and plotted with a true aspect ratio relating their horizontal and vertical components. Features, including the décollement near 5.6 km depth, the crystalline rock transition near 6 km depth, the seafloor, and thrust faults are visible in the diffraction and complete images. Reflections corresponding to highly deformed strata in an accretionary prism undergoing shortening and thickening and extending from the décollement to the seafloor are visible in the reflection image. In this image, the overriding Eurasian plate has relative motion to the left, towards the Philippine Sea and the subducting Philippine Plate has relative motion to the right, towards the Japanese island of Honshu.

nankai-vc-full-slice-depth nankai-prob-dimage-depth nankai-overlay-dix
nankai-vc-full-slice-depth,nankai-prob-dimage-depth,nankai-overlay-dix
Figure 20.
Nankai Trough images and velocities transformed from the time to depth domains: (a) complete image; (b) probabilistic diffraction image; (c) Dix velocity overlaid with complete image.
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We calculate Dix, or interval, velocity using the RMS velocity field, and transform it to the depth domain. Depth domain Dix velocity is overlaid by the depth stretched complete image, and shown in Figure 20c to provide context for the velocity field. Velocities calculated in the probabilistic imaging process are reasonable when compared to seismic velocity measurements in the region performed by the Integrated Ocean Drilling Program using core data and bore holes in the area (Moore et al., 2009). Examining the Dix velocity, we see a general trend of increasing velocity with depth until the area of the décollement near 5.7 km depth, were velocity begins decreasing. Additionally, areas where the décollement is intersected by faults tend to have higher Dix velocities than surrounding areas. This is related to the fact that thrust faults extending from the décollement to the seafloor act as conduits facilitating the dewatering and compaction of sediments overlaying the décollement. The thrust faults do not extend below the décollement, so water has more difficulty escaping, hindering compaction and leading to lower velocities as well as a low velocity anomaly below the feature. This anomalous low corresponds to the deepest reliable velocity information from this study. Because we do not observe diffractions below the layer of strong diffractions at approximately 6 km marking the transition to crystalline rock, our study does not provide information about the presumably higher velocities underlying that transition.


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Next: Conclusions Up: Decker & Fomel: Probabilistic Previous: Synthetic Example

2022-04-29