Seislet transform and seislet frame

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## 2-D data analysis with 2-D seislet frame

To show an example of 2-D data analysis with 2-D seislet frames, we use the CMP gather from Figure 7(a). We try two different choices for selecting a set of dip fields for the frame construction.

First, we define dip fields by scanning different constant dips (Figure 17(a)). In this case, the zero-scale coefficients out of the 2-D seislet frame correspond to the slant-stack (Radon transform) gather (Figure 18(a)). Figure 19(a) shows randomly selected example frame functions for the 2-D seislet frame using constant dips

Our second choice is a set of dip fields defined by the hyperbolic shape of seismic events on the CMP gather:

 (17)

where is traveltime for reflection at offset , is the zero-offset traveltime, and is the root-mean-square velocity. For a range of constant velocities, the direct relationship between dip and velocity is given by
 (18)

The dip field is shown in Figure 17(b). Analogously to the case of constant dips, the frame coefficients at the zero scale correspond to the hyperbolic Radon transform (Thorson and Claerbout, 1985), with the primary and multiple reflections distributed in different velocity ranges (Figure 18(b)). Figure 19(b) shows randomly selected frame functions for the 2-D seislet frame with varying dip fields defined by a range of constant velocities.

cdips,rrdips
Figure 17.
Constant dip field (a) and time and space varying dip field (b).

cdiplet,rrdiplet
Figure 18.
2-D seislet frame coefficients with constant dip field (a) and with varying dip field (b).

cdipimps,rrdipimps
Figure 19.
Randomly selected representative frame functions for 2-D seislet frame with constant dip field (a) and varying dip field (b).

 Seislet transform and seislet frame

Next: Discussion Up: From transform to frame Previous: 2-D data analysis with

2013-03-02