Velocity is a key parameter determining the migration imaging resolution of ground penetrating radars (GPR).The method combining minimum image entropy and migration usually estimates the medium velocity by calculating the entropy curves using the overall migration profile as a fixed window.Therefore,such a method is not applicable to non-uniformly distributed media.Moreover,for this method,a too-high or too-low test velocity will make the convergence position of hyperbolic diffracted waves go beyond the fixed window,thus reducing the estimation accuracy.This study proposed a minimum entropy method based on a velocity-controlled moving window,in which the calculation window in the migration profile is accurately controlled by the test velocity.Then,this method was combined with inverse time migration to estimate the optimal migration velocity.By automatically adjusting the position of the calculation window using the trial velocity,this method keeps the convergence position of hyperbolic diffracted waves at the center of the calculation window.In this manner,stable and accurate entropy curves can be obtained.By comparing the calculation results with those of the minimum entropy method based on a fixed window,this study verified the correctness and effectiveness of the minimum entropy method based on a velocity-controlled moving window for a typical hyperbolic diffracted wave.As revealed by numerical experiments and the tests of measured data,compared with the minimum entropy method based on a fixed window,the minimum entropy method based on a velocity-controlled moving window can keep the convergence position of hyperbolic diffracted waves accurately at the center of the calculation window,yielding more stable entropy curves,lower computational complexity,higher estimation accuracy of the migration velocity,and better imaging performance of reverse time migration.
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