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In hypervelocity impacts of projectiles into thin flat targets, shock initiation and interaction dominate the responses of projectiles and targets, and especially dominate the features of the debris cloud. To estimate the geometric features of the wave front during the first complete propagation in the spherical-projectile, the Geometric Propagation Model (GPM) is built in this paper to describe the geometry of the shock wave front, which proposes an ellipse contour as a function of time and equivalent speed. The GPM identifies the geometric features of the wave front as a function of time and impact velocity successfully. Combined with the GPM and SPH simulation, the shock pressure distribution and attenuation in the spherical-projectile have been obtained. Meanwhile, the attenuation of shock pressure and speed are presented as a function of impact velocity, respectively, and a method for obtaining the equivalent speed of the shock wave is proposed by the GPM. The GPM may be applicable to hypervelocity events involving any monolithic materials as long as the equivalent speed could be supplied from numerical simulation. The GPM proposed in this paper and the corresponding shock wave analysis provide a new insight into the processes of the quantitative analysis of the initiation of the debris cloud. Keywords: Hypervelocity impact, Shock wave, Numerical simulation, Debris cloud formation