Alternate approaches to phase rotation

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	13
DOI	http://dx.doi.org/10.1190/1.9781560801610
ISBN	9781560801481
Store	SEG Online Store

The convolutional model is made up of two components: the wavelet and the reflectivity series. Wavelets usually are determined by directly recording them in the field or by estimating them in data processing, commonly by assuming something about their phase properties. For example, the wavelet autocorrelation function provides the amplitude characteristic. Because the autocorrelation does not contain phase information, the shape of the wavelet cannot be found without the phase information. Making the minimum-phase assumption usually solves this problem for impulsive sources. With this assumption, the deconvolution operator can be found.

Wavelet processing produces a seismic section, but the wavelets on the section are not quite symmetric wavelets, as desired. The practice is to rotate each trace on the processed section by a fixed amount to yield (approximately) symmetric wavelets. To this end, a visual or analytic means is used determine the optimum value of the constant-phase rotation that should be applied to each trace in the seismic section.

Figure 7.  The synthetic trace subjected to constant-phase rotations in $3^{\circ }$ increments. (From Neidell, 1991.)

Figure 8.  The wavelet-processed seismic section, except that the trace at shotpoint no. 620 is replaced by the synthetic trace rotated by $35^{\circ }$. (From Neidell, 1991.)

Neidell (1991) gave the following example: A well at shotpoint no. 620 provides a well log from which the reflectivity is calculated. In addition, a wavelet is estimated from the seismic data. The wavelet has zero phase and a smooth unimodal frequency content, with half-power at 10 and 50 Hz. A synthetic trace is computed by convolving the reflectivity with the wavelet. Figure 7 shows the sequence of traces obtained by constant-phase rotations in $3^{\circ }$ increments. Each of these rotated synthetic traces is compared with the real trace on the seismic section at shotpoint no. 620. It is determined that the synthetic trace rotated by 35° is most like the real trace.

Figure 8 shows the wavelet-processed seismic section, except that here, the trace at shotpoint no. 620 has been replaced by the synthetic trace rotated by $35^{\circ }$. The synthetic trace rotated by $35^{\circ }$ gives the best match of the small peak events both before and after the prominent trough-peak sequence, compared with the synthetic trace rotated by other amounts. Thus, a phase correction of about $-35^{\circ }$ seems best for converting the wavelets on the section to approximately zero phase.

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Also in this chapter

• Phase rotation
• Band-limiting root approximation
• Appendix N: The energy-delay theorem

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