Obtaining Effective Q Factors at Different Offsets from CMP Records

Abstract The introduction of the effective Q parameter enables the acquisition of an easily accessible Q field for Q-compensated pre-stack time migration (QPSTM). By definition, this Q parameter is derived from the vertical travel characteristics of seismic waves, a constraint that limits its applicability exclusively to scenarios where the seismic wave incidence angle equals 0°. In practical applications, however, an averaging accumulation strategy is commonly adopted, which leads to the aggregation of Q factors across different offsets into a single average value. For a given reflection point, relying on this single effective Q factor to perform attenuation compensation during the imaging of seismic data with varying offsets can no longer satisfy the requirements of high-precision compensation. To address this limitation, this study proposes a method for determining effective Q factors at different offsets directly from common midpoint (CMP) gathers. An effective Q parameter applicable to non-zero incidence angles is first defined; unlike the traditional effective Q, which adopts a straight-ray path, this new definition utilizes a crooked ray path to calculate the travel time of seismic waves in layered media, thereby accommodating the actual propagation characteristics of seismic waves under non-normal incidence conditions. On the basis of the spectral ratio method, multiple equations involving unknown Q factors are subsequently constructed. This is achieved by comparing seismic data traces at different offsets that propagate through the same reflection point, a step that ensures the physical consistency of the data used for Q inversion. Finally, the least squares method is applied to solve the established equations, yielding the optimal effective Q factor for each individual offset. Both synthetic model tests and real seismic data applications demonstrate the effectiveness and reliability of the proposed method.