The transverse isotropy (TI) parameters ε and δ control amplitude variation with offset (AVO) response at most angles of incidence used in exploration, although the value of δ is not usually known and is difficult to measure. Published measurements on TI materials show that there is a useful empirical correlation between [Formula: see text] and δ. The relationship between δ and [Formula: see text] can be simplified by assuming a linear relationship between [Formula: see text] and [Formula: see text]. Anellipticity parameter η also shows a useful empirical correlation with [Formula: see text]. The correlations imply that knowledge of [Formula: see text] is sufficient to make an estimate of the anellipticity of the P‐ and S‐wavefronts in a rock, regardless of the lithology. In this way, the effect of TI on the AVO response of a particular interface may be estimated in the absence of any more accurate data. The empirical relationships indicate that rocks tend to become more anelliptic with increasing [Formula: see text]. Rocks with [Formula: see text] smaller than about 1.8 tend to have zero to small positive values of δ, while rocks with [Formula: see text] larger than around 2 tend to have zero to medium negative δ values. Most previous work has assumed a positive value of δ in shales, but this is not necessarily true. If in fact the δ of a shale is negative ([Formula: see text] is around 2 or higher), and overlies a sandstone, the positive change in δ across the interface could cause a false negative AVO gas indicator. If shale with [Formula: see text] less than 1.8, as measured in organic‐rich and overpressured shales, overlies a water‐filled sandstone, this could cause a false positive AVO gas indicator. However, if the effect of TI can be estimated, then the chances of success for AVO analysis in correctly predicting the presence of hydrocarbons can be increased.
A highly efficient and accurate tool for predicting the seismic response of reservoir fluid flow has been developed which integrates the finite‐difference injection method with a reservoir simulator and a petrophysical model. Finite‐difference methods allow for the full response to be synthesized as the wavefield interacts with a seismic model. This includes wave propagation in arbitrary heterogeneous anisotropic and anelastic media, scattering, and mode conversions. The finite‐difference injection method, in turn, can be used to efficiently synthesize the seismic response from models after local alterations to the model. Thus, it is ideally suited for time‐lapse seismic studies. The modeling methodology is demonstrated on a case study from the Gullfaks field in the North Sea. Six complete marine seismic surveys over the reservoir at different stages during waterflood oil production were synthesized. A total of 180 shot gathers were synthesized with computational savings of a factor of 54 after one single full simulation. The computational savings for the analogous 3-D study are 370 or greater after the initial simulation. The surface seismic response acquired along a towed streamer was processed through to stack and migrated. In a noise‐free environment the replacement of oil by water at a constant pressure caused visible changes in the synthetic seismic response that closely correspond to the impedance changes in the reservoir because of fluid flow. Downhole permanent sensor or vertical seismic profiling configurations were also considered; they provided a particularly suitable acquisition geometry for time‐lapse seismic monitoring. The recorded wavefields during and before production were greatly different (comparable to the magnitude of the wavefield itself). Moreover, multicomponent measurements may allow for elimination of changes attributable to environmental effects in the overburden and source characteristics. The study also indicates that monitoring the phase change of a reflector below a reservoir may provide a fluid flow indicator. The simulation technique thus provides an important tool for designing downhole surveys and deploying permanent sensors.
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