Velocity analysis using similarity-weighted semblance

Synthetic examples

The first synthetic example is a simple four-layer hyperbolic CMP gather. By using the traditional semblance, AB semblance and the proposed similarity-weighted semblance, the semblance spectra are shown in Figure 2. From the comparison, we can see that the resolution is clearly different for three approaches. The AB semblance suffers from the low-resolution problem as pointed out by Fomel (2009), compared with the other two approaches. For both traditional and AB semblances, there exists a fake peak between the third and fourth layer. The similarity-weighted semblance obtains a very high resolution both vertically and horizontally. In this example, the reference trace is chosen as the traditionally stacked trace.

By adding some Gaussian white noise onto the first synthetic example, we get the second example (Figure 3). The performance of the three approaches are improved a lot due to the added random noise. The fake peaks appearing in the first example disappear because of the random property of Gaussian white noise, which indicates the fact that a small level of random noise can aid the semblance calculation process to some extent. Compared with the other two approaches, the similarity-weighted semblance obtained a very high resolution. In this example, the reference trace is chosen as the traditionally stacked trace.

The third synthetic example is a CMP gather with class II AVO anomalies (Figure 4). The class II AVO anomalies cause seismic amplitudes to go through a polarity reversal (Fomel, 2009; Rutherford and Williams, 1989). In this test, the weighting function is a combination between the similarity based weight and trend based weight. We implement this by first weighting each trace using the proposed approach and then apply the trend based approach (Fomel, 2009). While the traditional semblance can not capture the information of the AVO anomalies, the AB semblance and the proposed similarity-weighted semblance can handle the AVO phenomena correctly. Because of the combination between the AB semblance and similarity-weighted semblance, the resolution of the proposed approach will decrease a little bit. This phenomenon results from the fact that taking AVO effect into consideration will decrease the resolution, as analyzed in Fomel (2009). However, the resolution using the proposed approach is still higher than that of the AB semblance and comparable to the traditional semblance. In this example, the reference trace is chosen as the traditionally stacked trace.

It's worth to be mentioned that the black strings appearing on the top of velocity maps denote the automatically picked optimum velocities using the algorithm introduced in Fomel (2009). Thus, the trends of black strings between different semblance approach do not differ too much. With manual picking, the results for both traditional semblance and AB semblance will result much larger velocity uncertainties, which will result in larger migration uncertainties (Fomel and Landa, 2014). There are also some unreasonable changes in the black strings, which result from the fact that the synthetic events are sparse and the automatically picking algorithms can not handle such problem. Figure 5 shows a comparison between the true velocity and the picked velocities from different approaches for the third synthetic example. The black solid line denotes the true velocity. The blue dash line denotes the picked velocity using the similarity-weighted semblance. The green long dash line denotes the picked velocity from the traditional semblance and the red dot dash line denotes the picked velocity from the AB semblance. It is clear that the AB semblance and similarity-weighted semblance are much similar and the similarity-weighted semblance can make the automatic picking more accurate. The velocity picked from the traditional semblance, however, deviates the true velocity a lot and is not acceptable.

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Figure 2. Comparison between semblance spectra for a clean synthetic data. Left: CMP gather. Middle left: using traditional semblance. Middle right: using AB semblance. Right: using similarity-weighted semblance.

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Figure 3. Comparison between semblance spectra for a noisy synthetic data. Left: CMP gather. Middle left: using traditional semblance. Middle right: using AB semblance. Right: using similarity-weighted semblance.

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Figure 4. Comparison between semblance spectra for a synthetic data with class II AVO anomalies. Left: CMP gather. Middle left: using traditional semblance. Middle right: using AB semblance. Right: using similarity-weighted semblance.

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Figure 5. Comparison between the true velocity and picked velocities for the third synthetic example with class II AVO anomalies. Black solid line denotes the true velocity. Green long dash line corresponds to the picked velocity by traditional semblance. Red dot dash line corresponds to the picked velocity by AB semblance. Blue dash line corresponds to the picked velocity by similarity-weighted semblance.

Velocity analysis using similarity-weighted semblance