声爆问题一直是制约超声速客机发展的障碍之一，因此低声爆设计技术在超声速客机的设计中尤为重要。逆向增广Burgers方程可将中场声压信号反演至近场，能够为低声爆反设计工作提供优化目标。围绕逆向增广Burgers方程展开研究，运用算子分裂法和正则化伪抛物型方程法对逆向方程进行数值求解，并求取对应的反向等效面积。借助3个标准算例，对数值方法的收敛性、求解准确度、不同中场高度及不同周向角下反演技术的计算精度进行了研究。针对逆向增广Burgers方程的特点，探讨了在中场设置目标波形进行反设计方法的可行性，并对声压信号中高频分量的传播特性进行了研究。研究认为上述方法能够较为准确地完成中场至近场的声压信号反演计算，并且使用中场目标波形代替地面目标波形能减轻反演距离对反演计算过程的影响。

Sonic boom has always been one of the obstacles restricting the development of supersonic airliners. Hence， the low sonic boom design technology is particularly important in the design of supersonic airliners. The inverse augmented Burgers equation can invert the mid-field sound pressure signal to the near-field and provide optimization objectives for the low sonic boom inverse design. This study uses the operator splitting technique and the pseudoparabolic equation method to numerically solve the inverse Burgers equation and calculate the corresponding reversed equivalent-area. With the assistance of the three standard examples， we investigate the convergence of the numerical method， the accuracy of the solution， and the calculation accuracy of the inversion technique at different field heights and different rolling angles. Based on the characteristics of the inverse augmented Burgers equation， the feasibility of setting target waveforms in the mid-field for the inverse design method is discussed， and the propagation characteristics of high-frequency components in the sound pressure signal are studied. The research shows that the above method can accurately complete the inversion calculation of the sound pressure signal from the mid-field to near-field， and that using mid-field target waveforms instead of ground target waveforms can reduce the influence of the inversion distance on the inversion calculation process.