# 4-C seismic method

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

Throughout this textbook, we discussed processing, inversion, and interpretation of compressional or P-wave seismic data. Specifically, we had in mind a compressional seismic source and the reflected signal recorded by each receiver being a compressional seismic wave-field. Recall from analysis of amplitude variation with offset that for non-normal incidence at a layer boundary, an incident compressional plane wave is partitioned into not just reflected and transmitted compressional-wave components, but also reflected and transmitted shear-wave, or S-wave components. Hence, a fraction of the incident P-wave is converted into a reflected S-wave. The amplitudes of the individual components are described by the Zoeppritz equations (12). By way of prestack amplitude inversion of nonzero-offset P-wave data described in analysis of amplitude variation with offset, we are then able to make an estimate of the S-wave reflectivity as an AVO attribute (equations 37 and 49).

 $\cos \varphi _{1}A_{1}+{\frac {\alpha _{1}}{\beta _{1}}}\sin \psi _{1}B_{1}+{\frac {\alpha _{1}}{\alpha _{2}}}\cos \varphi _{2}A_{2}-{\frac {\alpha _{1}}{\beta _{2}}}\sin \psi _{2}B_{2}=\cos \varphi _{1},$ (12a)

 $-\sin \varphi _{1}A_{1}+{\frac {\alpha _{1}}{\beta _{1}}}\cos \psi _{1}B_{1}+{\frac {\alpha _{1}}{\alpha _{2}}}\sin \varphi _{2}A_{2}+{\frac {\alpha _{1}}{\beta _{2}}}\cos \psi _{2}B_{2}=\sin \varphi _{1},$ (12b)

 $-\cos 2\psi _{1}A_{1}-\sin 2\psi _{1}B_{1}+{\frac {\rho _{2}}{\rho _{1}}}\cos 2\psi _{2}A_{2}-{\frac {\rho _{2}}{\rho _{1}}}\sin 2\psi _{2}B_{2}=\cos 2\psi _{1},$ (12c)

 $\sin 2\varphi _{1}A_{1}-{\frac {\alpha _{1}^{2}}{\beta _{1}^{2}}}\cos 2\psi _{1}B_{1}+{\frac {\rho _{2}\beta _{2}^{2}\alpha _{1}^{2}}{\rho _{1}\beta _{1}^{2}\alpha _{2}^{2}}}\sin 2\varphi _{2}A_{2}+{\frac {\rho _{2}\alpha _{1}^{2}}{\rho _{1}\beta _{1}^{2}}}\cos 2\psi _{2}B_{2}=\sin 2\varphi _{1}.$ (12d)

 $R_{i}=a_{i}{\frac {\Delta \alpha }{\alpha }}+b_{i}{\frac {\Delta \beta }{\beta }},$ (37)

 $R_{i}=a_{i}R_{P}+b_{i}R_{S},$ (49)

In a conventional marine seismic survey, we cannot record P-to-S converted-wave energy even if we deploy sensors that can register the shear-wave energy. This is because the upcoming converted-wave energy is not transmitted through the water column to reach the recording cable since fluids cannot support shear strain. Thus, to capture the converted-wave energy, we need to record it at the water bottom using an ocean-bottom cable (OBC). And to record it, we need to use geophones that register velocity of the particle motion that is perpendicular to the direction of the wave propagation. Since the upcoming wave is primarily in the vertical direction, we need to use a geophone that records the particle motion in the horizontal direction. In fact, for a good reason that will be obvious later in the section, we need to deploy not one, but two horizontal geophones that are oriented perpendicular to one another. To complement the recording of the pressure wave by a hydrophone, again for a reason that will be obvious later in the section, we might also wish to record the vertical component of the particle motion using a vertical geophone. Hence, an OBC recording is done using three geophones and one hydrophone for each receiver unit along the cable, making it a four-component (4-C) seismic survey. The final product from the analysis of a 4-C survey data is a pair of P-wave and S-wave image sections (in the case of a 2-D survey) or volumes (in the case of a 3-D survey). Strictly the P-wave data are associated with P-to-P reflections and S-wave data are associated with P-to-S converted waves. Heretofore, we shall refer to these two wave types as PP and PS, respectively, so as to explicitly indicate that they both are generated by a P-wave source. (An S-wave source would have generated SS and SP data.)

Much of the P-to-S conversion takes place, not at the water bottom, but at reflectors that correspond to layer boundaries with significant contrast in elastic properties . This fortuitous phenomenon is caused by the very low speeds of shear waves in seabed sediments  .

In this section, we shall briefly review acquisition and analysis techniques specific to 4-C seismic data. Before we proceed, however, we need to ask the question why we would want to go through the expense of conducting a 4-C OBC survey. Is there any exploration or development objective that we cannot achieve using conventional P-wave data, but we can with S-wave data? To answer this crucial question, first, we make reference to one of the AVO interpretation strategies discussed in analysis of amplitude variation with offset. Specifically, by AVO inversion of prestack amplitudes, we wish to estimate P-wave and S-wave reflectivities and do a crossplot analysis to infer fluid types and saturation in reservoir rocks. If, instead of indirectly extracting these AVO attributes from conventional P-wave data, we record both PP and PS data by a 4-C survey, we may be able to broaden our understanding of properties of reservoir fluids and rocks.

Known potential applications of converted-wave data are summarized below   .

1. Imaging beneath gas plumes,
2. Imaging beneath salt domes,
3. Imaging beneath basalts,
4. Delineating reservoir boundaries with a higher S-wave impedance contrast than P-wave impedance contrast,
5. Differentiating sand from shale,
6. Detection of fluid phase change from oil-bearing to water-bearing sands,
7. Detection of vertical fracture orientation,
8. Mapping hydrocarbon saturation, and
9. Mapping oil-water contact.

We now refer to a few examples illustrating the use of PS data. Figure 11.6-1a shows portions of a dipole sonic log measured at a well from a producing field. The S-wave velocity curve shows a marked contrast at the top- (A) and base- (B) reservoir unit. It, however, does not show a significant contrast at oil-water contact (OWC). The P-wave velocity curve shows a difference in the gradients within the postreservoir and reservoir units, but it does not show a marked contrast at the top-reservoir boundary as does the S-wave velocity curve (A). This is because of a lack of acoustic impedance contrast between the shales of the postreservoir unit and the oil sands of the reservoir unit. The oil-water contact, on the other hand, corresponds to a significant contrast on the P-wave velocity curve. While the position and geometry of the oil-water contact are important in terms of the production history of the field, this is not the only strategic information that is needed for the development. Specifically, for production, it is the top-reservoir boundary that needs to be delineated accurately so as to place the horizontal well trajectory close to the top and avoid missing a significant vertical oil column.

Compare the PP section derived from the conventional streamer 3-D survey and the PS section derived from the 4-C OBC survey, both of the same vintage, shown in Figures 11.6-1b and 11.6-1c. The PP section shows a strong event at 2 s that corresponds to the strong contrast on the P velocity curve associated with the oil-water contact (Figure 11.6-1a). Nevertheless, the top reservoir is nearly impossible to identify on this section. The PS section, on the other hand, shows two strong events with irregular geometry at about 3.6 s and 3.8 s. These events correspond to the strong contrasts on the S velocity curve associated with the top- and base-reservoir boundaries labeled A and B in Figure 11.6-1a, respectively.

It is important to note that the PS section is not a replacement for the PP section; instead, they are complementary. The PP section provides the information about the oil-water contact while the PS section provides the information about the top-reservoir boundary. Both are needed for optimum development of the field.

Another case for converted-wave data is shown in Figure 11.6-2. The PP section shows a zone of gas plume associated with the underlying leaky reservoir. The gas-saturated formations cause amplitude and traveltime distortions of the P-wave that passes through the anomalous zone. This can make the geometry of the underlying reservoir unit difficult to delineate. The gas plume actually represents a complex overburden that gives rise to strong lateral velocity variations. As such, the complexity of the overburden can be resolved by earth modeling in depth and the underlying reservoir zone can, in some cases, be imaged by prestack depth migration with an acceptable accuracy. The S-wave, on the other hand, is relatively unscathed by the presence of gas within the overburden; hence, the PS data provide a more accurate time image of the reservoir zone as compared to the time image derived from the PP data. Note also from both the sections in Figure 11.6-2 and the 3-D image volumes shown in Figure 11.6-3 that the reflectors within the overburden above the gas plume zone are stronger in the PP data compared to the PS data. This is because only a fraction of the incident P-wave energy is converted to S-wave energy at layer boundaries. Once again, the PP and PS data complement each other, and it certainly is not one or the other. While the PS section provides a better image of the reservoir structure, the PP section clearly indicates the presence of a gas plume above. This anomalous pressure zone has to be taken seriously during well planning.