An image-focusing semblance functional for velocity analysis

The challenge of quantifying image focusing

In this section, I introduce two simple synthetic data sets that illustrate the opportunities and challenges of measuring image focusing for velocity analysis. I start by showing how the application of a minimum entropy functional can help to determine the correct migration velocity, but also it can mislead the estimation.

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Figure 1. (a) Reflectivity function assumed to compute a synthetic prestack data set, and (b) the stacked section obtained by migrating the data set with a low velocity. [CR]

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Figure 2. (a) Reflectivity function assumed to compute a synthetic prestack data set, and (b) the stacked section obtained by migrating the data set with a low velocity. [CR]

Figure 1a and Figure 2a show the reflectivity functions assumed to generate the two data sets. The first one contains a strong diffractor and two dipping planar reflectors broken by a fault. Focusing analysis of the diffractor and the reflectors' truncations provides velocity information additional to the one available by conventional analysis of the reflections from the planar interfaces. The second model consists of a continuous sinusoidal reflector. It shows the potential pitfalls of measuring image focusing in presence of curvature in the structure. Figure 1b and Figure 2b show the result of migrating with a low velocity the modeled data corresponding to the reflectivity functions shown in Figure 1a and Figure 2a, respectively. In Figure 1b both the image of the point diffractor and the image of the reflectors' truncations show the typical signs of undermigration; that is, not fully collapsed diffracted events. In Figure 2b the bottom of the syncline shows triplication that are signs of undermigration, whereas the top of the anticline does not show any clear defocusing problems.

An image-focusing semblance functional for velocity analysis