Analysis of amplitude variation with offset
In the mathematical foundation of elastic wave propagation, we review the theory of seismic wave propagation in an elastic continuum. The earth’s upper crust that is of interest in seismic prospecting, however, is made up of rock layers with different elastic moduli. When seismic waves travel down in the earth and encounter layer boundaries with velocity and density contrast, the energy of the incident wave is partitioned at each boundary. Specifically, part of the incident energy associated with a compressional source is mode-converted to a shear wave; then, both the compressional- and shear-wave energy are partly reflected from and partly transmitted through each of these layer boundaries.
The fraction of the incident energy that is reflected depends upon the angle of incidence. Analysis of reflection amplitudes as a function of incidence angle can sometimes be used to detect lateral changes in elastic properties of reservoir rocks, such as change in Poisson’s ratio. This may then suggest a change in the ratio of P-wave velocity to S-wave velocity, which in turn may imply a change in fluid saturation within the reservoir rocks.
By way of CMP recording geometry, reflection amplitudes are not measured as a function of angle; instead, they are measured as a function of source-receiver offset. Nevertheless, a range of incidence angles is spanned by a range of offsets. Amplitude-versus-offset analysis, therefore, provides the information on amplitude-versus-angle.
Figure 11.2-1 shows a moveout-corrected CMP gather with a strong reflection at 1.25 s. Note the amplitude variations with offset — in this case, amplitudes increasing with offset. By picking the peak amplitudes and plotting them against offset, an amplitude variation with offset (AVO) curve is derived for a target horizon at each CMP location. Then, an AVO pattern may emerge, which can then be used to infer reservoir parameters.
The pattern with which amplitudes vary with offset depends on the combination of reservoir rock and fluid properties. Detection of a pattern is dictated primarily by the signal-to-noise ratio and the range of incidence angle that is spanned by the offset range of the CMP gather for a target horizon. The shallower the reflector, the wider the range of incidence angle; hence, AVO indicators are best determined for shallow targets.
The following discussion on reflection and refraction of seismic waves is based on flat layer boundaries. Reflection amplitudes also depend upon the dip of the reflecting boundary and its curvature. We can remove the dip and curvature effects by performing prestack time migration. The resulting CMP gathers are associated with reflectors in their migrated positions and reflection amplitudes can then be associated with a locally flat earth model.
- Introduction to reservoir geophysics
- Seismic resolution
- Acoustic impedance estimation
- Vertical seismic profiling
- 4-D seismic method
- 4-C seismic method
- Seismic anisotropy
- Mathematical foundation of elastic wave propagation