(解放軍軍械工程學(xué)院 七系，石家莊 050003)
摘 要: 針對(duì)鐵磁物質(zhì)反演方法中反演解的病態(tài)性問(wèn)題，提出基于光滑約束的磁梯度張量3D正則化反演方法。首先，利用積分靈敏度矩陣和粗糙度矩陣對(duì)經(jīng)典Tikhonov正則化理論框架下的反演模型進(jìn)行約束，避免由于反演參數(shù)多于采集點(diǎn)數(shù)而導(dǎo)致的不穩(wěn)定；然后，通過(guò)定義正則化修正系數(shù)確定合理的初始正則化因子，從而減少因正則化因子引入而在反演結(jié)果中介入的誤差；最后，利用物性參數(shù)上下限約束函數(shù)，將反演過(guò)程中的解轉(zhuǎn)換到合理的值域范圍內(nèi)，得到與原始模型更加吻合的反演結(jié)果。仿真及實(shí)驗(yàn)結(jié)果表明：該反演方法能夠準(zhǔn)確還原磁性異常體的輪廓形態(tài)，具有較好的橫向和縱向分辨率。
關(guān)鍵字: 光滑約束；磁梯度張量；積分靈敏度矩陣；粗糙度矩陣；正則化因子
（Seventh Department, Ordnance Engineering College, Shijiazhuang 050003, China）
Abstract:For the ill-posed problem of ferromagnetic materials inversion method, the method based on 3D magnetic gradient tensor regularization inversion method was proposed based on smooth constraint condition. First, the unstable defect caused by the number of inverse parameter far than observational points by using the integral sensitivity matrix and the roughness matrix in the classical Tikhonov regularization under the framework of the theory to constrain the model is avoided. Then, errors are reduced due to regularization factor introduced in the inversion results, by defining regularization correction factor to determine a reasonable initial regularization factor. Finally, by using the upper and lower constraint function of physical parameters, the solution to a reasonable value range in the inversion process is converted and the inversion results which are more consistent with the original model are obtained. Simulation and experimental results show that this inversion method can reflect the outline shade of the magnetic anomaly, and has good lateral and vertical resolution.
Key words: smooth constraint; magnetic gradient tensor; integral sensitivity matrix; roughness matrix; regularization factor
