<p>Hydraulic fracturing operations frequently induce seismic activity, posing unprecedented challenges to underground infrastructure integrity and regional safety. The induced seismicity waveform is more complex than the Ricker wavelet, restricting the application of the Continuous Fourier Transform (CFT) in the theoretical analysis of transient stress. In this study, the Discrete Fourier Transform (DFT) was introduced into the theoretical solution process of transient response, and a minimum-phase seismic wavelet was proposed to represent the induced seismicity load, exhibiting multiple oscillations, gradual attenuation and energy concentrated primarily in the initial phase. The dynamic stress concentration distribution of the lined tunnel under induced seismicity disturbances was analyzed by combining the DFT and wave function expansion method. The theoretical results were further validated through comparison with numerical results. The effects of the lined tunnel parameters and disturbance characteristics on transient response were evaluated in detail, and practical insights for seismic-resistant management were provided. The theoretical and numerical results revealed that the seismic-resistance mechanisms of flexible and rigid linings differed. Dynamic stress concentrations primarily occur at the rock interface for the flexible lined tunnel. The flexible lining absorbs the seismic energy, thereby reducing the peaks of dynamic stresses. For the rigid lined tunnel, dynamic stress concentrations mainly appeared at the tunnel interface. The high strength and stiffness of rigid linings enable them to directly withstand the high dynamic stresses. Selecting lining materials with shear modulus values similar to the rock and increasing the lining thickness can effectively reduce dynamic stress concentrations around both types of tunnels.</p>