The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.
Application of Analytical Solution to Steady-State Temperature Field by Double-Row-Pipe Freezing and Verification with Field Measurement: A Case Study of Connected Aisle
