Seislet transform and seislet frame |

To show an example of 2-D data analysis with 2-D seislet frames, we use the CMP gather from Figure 7a. 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 17a). In this case, the zero-scale coefficients out of the 2-D seislet frame correspond to the slant-stack (Radon transform) gather (Figure 18a). Figure 19a 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:

The dip field is shown in Figure 17b. 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 18b). Figure 19b shows randomly selected frame functions for the 2-D seislet frame with varying dip fields defined by a range of constant velocities.

cdips,rrdips
Constant dip field (a) and time and space varying dip field (b).
Figure 17. |
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cdiplet,rrdiplet
2-D seislet frame coefficients with constant dip field (a) and with
varying dip field (b).
Figure 18. |
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cdipimps,rrdipimps
Randomly
selected representative frame functions for 2-D seislet frame with
constant dip field (a) and varying dip field (b).
Figure 19. |
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Seislet transform and seislet frame |

2013-07-26