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Abstract: Angle domain common imaging gathers (ADCIGs) serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise. Thus, they play a significant role in seismic data processing. Recently, the Poynting vector method, due to its lower computational requirements and higher resolution, has become a commonly used approach for obtaining ADCIGs. However, due to the viscoelastic properties of underground media, attenuation effects (phase dispersion and amplitude attenuation) have become a factor, which is important in seismic data processing. However, the primary applications of ADCIGs are currently confined to acoustic and elastic media. To assess the influence of attenuation and elastic effects on ADCIGs, we introduce an extraction method for ADCIGs based on fractional viscoelastic equations. This method enhances ADCIGs accuracy by simultaneously considering both the attenuation and elastic properties of underground media. Meanwhile, the S-wave quasi tensor is used to reduce the impact of P-wave energy on S-wave stress, thus further increasing the accuracy of PS-ADCIGs. In conclusion, our analysis examines the impact of the quality factor Q on ADCIGs and offers theoretical guidance for parameter inversion.