Anisotropic parameter inversion based on pre-stack azimuth gather seismic data is one of the primary methods for fracture prediction, among which two algorithms, RüGER approximate equation and Fourier series expansion, are more widely used. Both the anisotropic gradient in the RüGER approximate equation and the second-order term in the Fourier series expansion can characterize the crack intensity. In the experiment, the applicability of applying this two equations was compared in the single-layer interface and the fracture layer of the actual drilled wells, respectively, and the fracture spatial prediction results were compared in the actual volcanic rock development zone. There are dimensional differences in the prediction of fracture strength between the two equations of single interface model. The range of fracture strength of RüGER approximation equation is larger than that of Fourier series expansion. Multiple results exist for the calculation of fracture orientation using the RüGER approximation equation, which may result in an orientation perpendicular to the fracture. However, when applied to the fractured layers observed in wells, both methods yielded broadly consistent results regarding fracture orientation and strength. In the application to the volcanic rock formation of the LFS area in the southern Songliao Basin, the Fourier series' second-order term slightly outperformed the RüGER equation in aligning with the fracture strength interpretations derived from electrical imaging logging. Additionally, the predicted fracture orientations from both methods matched those interpreted from imaging logging. It is concluded that the Fourier series equation for predicting fractures is more suitable for popularization and application in the field of volcanic rocks.