Processing sequence for AVO analysis

**Seismic Data Analysis**
Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

There are three important aspects of a processing sequence tailored for AVO analysis.

The relative amplitudes of the seismic data must be preserved throughout the analysis so as to recognize amplitude variation with offset. This requirement often leads to an application of a parsimonious sequence of signal processing to avoid distortion of amplitudes by undesirable effects of some processing algorithms.
The processing sequence must retain the broadest possible signal band in the data with a flat spectrum within the passband.
Prestack amplitude inversion to derive the AVO attributes must be applied to common-reflection-point (CRP) gathers (migration velocity analysis), not to common-midpoint (CMP) gathers. This is because all the AVO equations described in this section are based on a locally flat earth model that can be related to CRP raypaths but not to CMP raypaths. Specifically, the CRP gathers are associated with events in their migrated positions, whereas the CMP gathers are associated with events in their unmigrated positions. The AVO equations described in this section are all based on a horizontally layered earth model that can be related to CRP raypaths but not to CMP raypaths. Prestack time migration compensates for the effect of reflector curvature (equation 13b) on amplitude variation with offset so that the reflection amplitudes in each of the resulting CRP gathers can be associated with a locally flat earth model.

CE(\theta )={\frac {1}{\sqrt {1+A^{-1}z/\cos ^{2}\theta }}},

(13b)

We shall consider a marine 2-D seismic data set from the North Sea recorded over a producing gas field. Data specifications for the line are listed in Table 11-3.

The prestack signal processing that complies with the above requirements includes the following steps:

If a reliable source signature is available, perform signature processing (field data examples) to convert the source waveform to its minimum-phase equivalent. In the present study, no source signature was available. Apply a mute to shot records to remove the guided waves associated with the dispersive, normal-mode propagation within the water layer (Section F.1).
Apply t²-scaling to correct for geometric spreading. A gain function for geometric spreading correction that depends on primary velocities will overcorrect the amplitudes of multiples. Figure 11.2-23 shows a recorded shot record and 11.2-24 shows the same record after guided-wave muting geometric spreading correction.
Apply time-invariant spiking deconvolution with a sufficiently long operator length (Figure 11.2-25). For land data, it may be necessary to apply surface-consistent amplitude corrections and surface-consistent deconvolution to account for the near-surface effects on amplitudes (Section B.8).
When it is required, apply time-variant spectral whitening to account for the nonstationarity of the waveform.

Figure 11.2-26 shows the amplitude spectrum of the shot record in Figure 11.2-25 computed after each of the steps in the sequence prescribed above. To begin with, note that much of the energy in the raw shot record is confined to the shallow portion and is mostly associated with the guided waves. The t²-scaling restores the amplitudes in the deeper portion of the record. Spiking deconvolution followed by a wide-bandpass filter gives the desired shape to the spectrum with a flat, broadband character. Figure 11.2-27 shows the autocorrelograms of the shot record in Figure 11.2-25, again, computed after each of the steps in the sequence prescribed above. Note that the autocorrelogram of the raw shot record is dominated by the guided-wave energy at far offsets on the left and the energy associated with short period multiples and reverberations at near offsets on the right. The guided-wave muting followed by t²-scaling exposes the energy associated with multiples that range from a short- to a moderate-period. Note that spiking deconvolution with an operator length of 480 ms (about one-tenth of the total length of the shot record) has removed a significant amount of the multiple energy from the record. Both the amplitude spectrum (Figure 11.2-26c) and the autocorrelogram (Figure 11.2-27c) of the deconvolved shot record indicate that time-variant spectral whitening does not have to be included in the sequence.

**Table 11-3.** Data specifications for the line used in AVO analysis.
Line Length	23.5 km
Shot Spacing	37.5 m
Receiver Spacing	18.75 m
CMP Spacing	9.375 m
Minimum Offset	150 m
Maximum Offset	3050 m
Number of Receivers	156
Fold of Coverage	78
Sampling interval	2 ms

The prestack data after signal processing are ready now for prestack time migration to generate the CRP gathers (prestack time migration).

Sort the signal-processed shot records to CMP gathers and perform velocity analysis at sparse intervals along the line. To increase the accuracy of prestack amplitude inversion and thus increase the confidence level for the AVO attributes, the fold of coverage and the offset range of the recorded data must not be reduced during the processing for any reason.
Apply NMO correction using the flat-event velocities. In this case, only three velocity functions were used in creating the velocity field for NMO correction.
When required, attenuate those multiples that have not been handled by deconvolution during the signal processing stage described above. Data suitable for AVO analysis are often associated with near-horizontal earth models or low-relief structures. Hence, techniques based on the discrete Radon transform (the radon transform) often are best suited for amplitude-preserving multiple attenuation.
Sort the data to common-offset sections and apply DMO correction.
Perform zero-offset, frequency-wavenumber time-migration on each of the common-offset sections after NMO and DMO corrections using a single, vertically varying velocity function. Again, data suitable for AVO analysis are generally associated with near-horizontal earth models or low-relief structures. Hence, use of a single, vertically varying velocity function and a zero-offset phase-shift algorithm for common-offset migration often is appropriate.
Sort the data to CRP gathers and apply inverse NMO correction using the velocity field from step (b).
Perform velocity analysis at frequent intervals along the line, and create a velocity field associated with the migrated data.
Apply NMO correction using the velocity field from step (g) and, when required, as it was in the present case study, perform residual moveout velocity analysis to remove any residual moveout errors that may be present in the CRP gathers. The residual moveout analysis actually is a good practice whatever the degree of residual moveout errors in the data, since prestack amplitude inversion is extremely sensitive to how flat the events are in the CRP gathers. Figure 11.2-28 shows selected CRP gathers that exhibit mostly flat events. A close-up view of the CRP gather (Figure 11.2-29) at the well location (CRP 1134) shows the reservoir zone highlighted by the rectangle situated between 3.1-3.3 s.
Stack the CRP gathers to obtain the image section from prestack time migration. Multiples that may have remained in the data will exhibit some residual moveout that can be exploited to further attenuate them during stacking.
For completeness of the prestack time migration sequence, unmigrate the CRP stack from step (i) using the same vertically varying velocity function as in step (e) and a phase-shift zero-offset wavefield modeling algorithm (Figure 11.2-30).
Next, apply poststack spiking deconvolution, often using the same parameters as for prestack deconvolution (Figure 11.2-31).
Remigrate the modeled zero-offset section from step (k) using the migration velocity field derived from the CRP gathers in step (g) (Figure 11.2-32). In this instance, any lateral velocity variations implied by the migration velocity field need to be accounted for by the migration algorithm of choice. Poststack amplitude inversion to derive the acoustic impedance attribute (acoustic impedance estimation) may then be applied to the final product from prestack time migration (Figure 11.2-32). Figure 11.2-33 shows the amplitude spectrum of the CRP stack after each step of the poststack processing. The amplitude spectrum of the CRP stack from step (i) shows the attenuation of high frequencies (Figure 11.2-33a), which are restored by deconvolution (Figure 11.2-33b), but are slightly shifted to lower frequencies by migration (Figure 11.2-33c). The autocorrelogram of the CRP stack from step (i) exhibits remnants of the water-bottom multiples (Figure 11.2-34a), which are largely attenuated by poststack deconvolution (Figure 11.2-34b).

Figure 11.2-28 Selected CRP gathers from prestack time migration of the data as in Figure 11.2-25.
Figure 11.2-29 The CRP gather at well location CRP 1134. The reservoir zone coincides with the time window indicated by the area within the rectangle.
Figure 11.2-30 The unmigrated stack associated with the prestack time-migrated data as in Figure 11.2-28.
Figure 11.2-31 The same stack as in Figure 11.2-30 after poststack deconvolution.
Figure 11.2-32 Migration of the stack in Figure 11.2-31 using the rms velocity field derived from the velocity analysis of the CRP gathers as in Figure 11.2-28. The area within the rectangle corresponds approximately to the sections in Figures 11.2-41 and 11.2-42.
Figure 11.2-33 Amplitude spectrum (a) of the stack in Figure 11.2-30, (b) of the stack in Figure 11.2-31, and (c) of the stack in Figure 11.2-32. Each panel comprises the amplitude spectrum as a function of time (top) and the spectrum averaged over time (bottom).
Figure 11.2-34 Autocorrelogram (a) of the stack in Figure 11.2-30, (b) of the stack in Figure 11.2-31, and (c) of the stack in Figure 11.2-32.