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Relying on the semi-analytical model without considering rock failure and crack propagation, the simulated results indicate the time-varying velocities near the borehole is disturbed larger than far from the hole, i.e., the properties at two- or three-times hole radius are unchanged. The semi-analytical model offers an important approach for inferring pore pressure and the distribution of crack initiation zones based on the relationship between borehole velocities and in situ stresses surrounding the permeable borehole.