We investigate the data requirements for a reliable analysis of frequency-dependent Q caused by scattering in a finely layered geological structure. Numerical wave propagation experiments in stochastic models were performed. We set up autoregressive-moving average [ARMA(1,1)] models for the reflection coefficients with non-Gaussian distribution functions and used published parameter sets estimated for sedimentary sequences from real log data. For ARMA models, analytical expressions for the scattering attenuation a and the quality factor Q can be derived from the O'Doherty-Anstey formula.
The aim of this study is to investigate whether scattering attenuation as derived from the O'Doherty-Anstey formula is measurable with sufficient accuracy with a traditional vertical seismic profile (VSP) configuration in realistic sedimentary sequences, and if so, whether the data can be inverted to yield the statistics of the sediment sequence. The main result is that reliable estimation of scattering attenuation requires VSP data over a considerable depth interval, depending on the magnitude of the attenuation with errors in the estimates increasing inversely as the depth range increases.
Extensions of the O'Doherty-Anstey theory to nonnormal incidence have been given in the literature. We examine the angle dependence of the results using both elastic plane-wave modeling and acoustic point-source modeling. For the weak medium variations considered, elastic effects (e.g., mode conversions) and point-source effects are negligible at angles up to about 25 degrees.