基于速度移动窗的最小熵法在GPR逆时偏移中的应用

Application of the minimum entropy method based on a velocity-controlled moving window to the reverse time migration of ground-penetrating radars

速度是决定探地雷达(GPR)偏移成像分辨率的关键参数,基于图像最小熵与偏移相结合的方法通常将整体偏移剖面作为固定窗计算熵值曲线来估计介质速度,不但难以适用于介质非均匀分布情况,而且试速度过大或过小均会使双曲线绕射波的收敛位置溢出固定窗,降低估计精度。为此,本文利用试速度精确控制偏移剖面中的计算窗,提出了一种基于速度移动窗的最小熵法,并与逆时偏移相结合,估计最佳偏移速度。该方法通过试速度自动调整计算窗位置,可使双曲线绕射波收敛位置始终位于计算窗中心,从而获得稳定、准确的熵值曲线。将一条典型双曲线绕射波的固定窗和速度移动窗最小熵法的计算结果作对比,验证了速度移动窗的最小熵法的正确性和有效性。数值试验和实测数据测试表明:与固定窗最小熵法相比,速度移动窗的最小熵法可将双曲线绕射波收敛位置精确固定于计算窗中心,熵值曲线更稳定,计算量更小,偏移速度估计精度更高,逆时偏移成像效果更好。

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 o-verall 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 com-bined 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 mini-mum 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 calcu-lation window,yielding more stable entropy curves,lower computational complexity,higher estimation accuracy of the migration velocity,and better imaging performance of reverse time migration.