Theoretical models and laboratory measurements both suggest that the interaction of solids and fluids in a reservoir formation can lead to strong attenuation measured by a low quality factor Q. When the reservoir layer is relatively thin, the loss of energy from a propagating seismic wave may be negligible. However, the low Q in such a layer can still have a measurable influence on reflections as it makes the reflection coefficient complex. A numerical modeling method that can simulate such effects rapidly for complex, laterally heterogeneous media will help to quantify the effects on reflected waveforms. Born scattering theory is useful for such problems, though it does not seem to have been applied in previous studies to modeling including finite Q values represented by complex elastic moduli. Here therefore we introduce a new implementation of the Born algorithm that does allow this type of modeling. Validation against full waveform results shows that results are accurate, and the seismograms also show that phase changes indicate the presence of low Q even when the reflecting reservoir layer is thin. The instantaneous phase seismic attribute can help to identify these effects, providing a potentially useful hydrocarbon indicator.
Many direct hydrocarbon indicators have been proposed to make use of seismic data to better locate economic concentrations of oil or gas in the subsurface. For example, amplitude variation with offset (AVO) methods often provide useful results (Shuey, 1985; Castagna et al., 1993; Ross, 2000; Stovas et al., 2006). This method, and other approaches based on detecting velocity changes associated with hydrocarbons, typically assume purely elastic wave propagation. On the other hand, some recent investigations suggest that attenuation may also be an important process that affects seismic data (Goloshubin and Korneev, 2000; Goloshubin et al., 2002; Castagna et al., 2003). The propagation of waves through an highly attenuating layer will cause preferential loss of high frequencies, motivating the search for changes in frequency content that may provide additional hydrocarbon indicators. This is especially true since careful laboratory measurements suggest that the quality factor Q may approach values on the order of 10 in some cases (Batzle et al., 2005). In addition, theoretical models for the effective properties of seismic velocities also suggest that rocks with pore fluids can lead to attenuation. An interesting example is fractures with fluids (Pointer et al., 2000), as characterizing the distribution, orientation and concentration of fractures is an important task for reservoir characterization.
However, there is another interesting problem that may arise is practical settings, since many reservoirs are not very thick, perhaps 10 m or less. Under such conditions, the distance of propagation through the attenuating medium with a low Q value is only a small fraction of the seismic wavelength, which is on the order of 100 m. Therefore the loss of energy associated with the layer will be small and other measures of seismic waveforms must be considered to attempt to detect the low Q region.
