Analysis of absorption and dispersion effects in synthetic τ-p seismograms

Abstract

Analysis of absorption and dispersion effects may be done in intercept time‐ray parameter (τ-p) synthetic seismograms calculated using the slowness formulation of the reflectivity method. Seismograms initially computed in the frequency‐ray parameter (ω-p) domain to incorporate absorption and dispersion effects are then Fourier transformed to the (τ-p) domain. Absorption and dispersion are functions of p. Modeling both simple and more realistic stratigraphic sequences shows the interaction of only velocity and density for infinite Q and the complicated effects added when Q is finite. The observed null reflection at p = 0 for infinite Q is no longer null when Q is finite. For p ≠ 0, the inclusion of absorption and dispersion effects complicates the amplitude and phase of the seismic response. Reflectivity due to Q alone (i.e., at an interface with no impedance contrast), as a function of Q contrast and p, contains interesting variations of amplitude and phase. The responses of three geologically realistic models (a brine sand, a partially saturated gas sand, and an ocean‐sediment interface) demonstrate the cumulative nature of the attenuation effect and how the Q contributions become dominant when the acoustic impedance contrast is small. For large acoustic impedance contrasts, the attenuation effect occurs as an amplitude decay and phase rotation for some (especially high) frequencies. The modeling results suggest that absorption and dispersion effects should be taken into account in seismic inversion. Q estimations (in addition to velocity and density) are particularly desirable in exploration for hydrocarbons because of the sensitivity of Q to lithology and fluid content. Q contributes to the reflectivity information inherent in the seismic data.