基于曲波变换的大地电磁二维稀疏正则化反演

为了提高二维大地电磁反演对异常体边界的刻画能力,我们引入曲波变换建立一种新的稀疏正则化反演方法.与传统的在空间域中对模型电阻率参数求解的方式不同,我们借助曲波变换将二维电阻率模型转换为曲波系数,并采用L1范数约束以保证系数的稀疏性.曲波变换是一种多尺度分析方法,其系数分为粗尺度系数和精细尺度系数,粗尺度的系数代表电阻率模型的整体概貌,而精细尺度中较大系数代表目标体的边缘细节.此外,曲波变换的窗函数满足各向异性尺度关系,并具有多方向性,因此曲波变换可以近似最佳地提取目标体的边缘特征信息,这为我们在反演中恢复边界提供有利条件.通过对大地电磁的理论模型合成数据和实测数据反演,验证了基于曲波变换稀疏正则化反演对异常体边界的刻画能力优于常规的L2范数和L1范数反演方法.

2D magnetotelluric sparse regularization inversion based on curvelet transform

In order to improve the ability to describe the boundary of anomalous body of 2D magnetotelluric (MT) inversions, we introduce the curvelet transform to construct a sparse regularization inversion algorithm. This is different from the conventional methods that apply constraints on the model in the space domain. We convert the 2D resistivity model to curvelet coefficients via a curvelet transform and the L1-norm measure is applied to keep the sparsity of the coefficients. Curvelet transform is a multi-scale analysis, its coefficients contain both coarse- and fine-scale information of the model. The coefficients of the coarse scale represent the overview of the resistivity model, while the large coefficients of the rest scales represent the detailed edges of the targets. Furthermore, the window function of the curvelet transform satisfies the anisotropic scale relationship and has the characteristic of arbitrary directionality. Thus, the curvelet transform can extract the boundary features of the target objects in an approximately optimally way, which provides favorable conditions to recover the boundary in the inversion. We test our inversion methods both on synthetic and field MT data and illustrate the sparse regularization inversion based on curvelet transform is superior to the conventional L2- and L1-norm inversions for describing the boundary of the anomalous body.