The approximate constant Q and linearized reflection coefficients based on the generalized fractional wave equation.

The fractional parameter in a generalized fractional model is set to control the degree of absorption. However, it does not have an explicit physical meaning, even though it may be estimated from seismic data. Therefore, it is necessary to establish a common reference, which is physically significant for the fractional parameter in model applications. In this paper, a reference is presented according to the constant Q model. The proposed reference can be used to analyze the fractional parameter in different value interval ranges. When the fractional parameter is small, the related absorptive mechanism is equivalent to a constant Q model. When the fractional parameter is large, it reveals an attenuation mechanism corresponding to a frequency-dependent Q. This analysis makes the fractional parameter more practical in other applications. The study also investigates how to derive the generalized linearized reflection coefficient with the fractional parameter for amplitude variation with offset/frequency. The linearized formulas are used to directly analyze the effects of the parameter contrast. They can also be used to directly estimate the related parameters in detail. According to the study, a known fractional parameter could be analyzed in practice. The synthetic results confirmed that the theory could extend the application of the generalized fractional wave equation. [ABSTRACT FROM AUTHOR]