Model-based deconvolution

**Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing**
Series	Geophysical References Series
Title	Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Author	Enders A. Robinson and Sven Treitel
Chapter	11
DOI	http://dx.doi.org/10.1190/1.9781560801610
ISBN	9781560801481
Store	SEG Online Store

<translate> Exploration over a large area usually involves different conditions, each of which demands its own procedures. In such circumstances, it is necessary to tie different lines together at line intersections. For example, stacked sections should tie at intersections prior to migration. Because recording features give rise to phase differences, phase matching two lines can be difficult. Phase mismatches can be attributed to differences in source characteristics, instrumentation, and processing.

To make two lines tie, shape one line into the other. The general assumption is that the reflectivity response at any intersection point is the same for both intersecting traces. The difference between the two traces often results from the fact that each trace has its own characteristic wavelet. Thus, by shaping one trace into the other, we are in effect shaping one wavelet into the other.

One way to accomplish that goal is to use least-squares shaping filters (see Chapter 9). In other words, we replace the wavelet on a trace on one line with the wavelet from the corresponding trace on the other line. An alternate name for a shaping filter is match filter, which should not be confused with the better-known matched filter (or correlation filter) that is used, for example, in vibroseis correlation. Figure 14 demonstrates the match filter for the case in which a lower-frequency trace 2 is shaped into a higher-frequency trace 1.

The match or shaping filter can be used to minimize the differences between correlated vibroseis records on one hand and impulsive source records on the other. Figure 15 shows a match-filtering example. Here, trace 2 is a correlated vibroseis trace containing a nonminimum-phase symmetric Klauder wavelet. On the other hand, trace 1 contains a minimum-phase wavelet. The objective is to match trace 2 to trace 1. Although it is not perfect, the result is quite satisfactory.