基于L_p范数正则化的V字型密度界面重力反演

Gravity inversion for V-shaped density interface based on L_p-norm regularization

V字型密度界面是一类常见的密度界面,如海沟、半地堑以及俯冲带之下的莫霍面,利用重力数据刻画此类密度界面形态对于区域构造研究、油气勘探以及物理海洋学等都具有重要意义.本文首先建立了Lp-范数形式的模型约束函数,并利用正则化原理将其与重力数据误差函数和已知深度约束函数结合形成V字型密度界面反演的目标函数,推导了目标函数的梯度表达式,并以非线性共轭梯度法为核心给出了反演流程.二维简单模型试算结果表明p=5时该方法能准确地刻画V字型密度界面起伏特征,且亦能准确地应用于二维复杂密度界面和三维界面的反演.最后将反演方法应用于挑战者深渊及邻区的实际资料处理之中,利用研究区海底地形数据和沉积层厚度数据对自由空间重力异常逐层剥离而得到莫霍面引起的重力异常,用本文方法对此重力异常进行反演,结果呈现了板块俯冲作用引起的V字型莫霍面起伏特征.

The V-shaped density interface is commonly seen such as the ocean trench,half-graben,and the Moho beneath a subduction zone.Delineating the relief of these V-shaped density interfaces is of significance in regional tectonic research,physical oceanography and oil and gas exploration.Among inversion methods of the density interface,the regularization approach,which applies prior information,can guarantee the inversion result to fit the known depth of the interface to be estimated.It can also control the shape of the interface via the model constraint function in the regularization item,making the inversion result agree with the real geologic feature.We have designed a model constraint function in the form of L p-norm and then integrated it with the gravity data misfit function and the known depth constraint function to establish an objective function for V-shaped density interface inversion.Subsequently,we have derived the gradient of the objective function and built the inversion process taking the nonlinear conjugate gradient algorithm as the core.The effect of our proposed inversion method is related to the value of p.The test results conducted with a two-dimensional simple model show that the method can be used to accurately estimate the V-shaped density interface relief when p=5,and the correctness of the proposed method is further confirmed by a two-dimensional V-shaped density interface with complex shape.The test results of a three-dimensional V-shaped density interface show that our proposed method is also appropriate for three-dimensional inversion.At the end of this article,the inversion method is tested with real gravity data of the Challenger Deep and adjacent regions.The gravity anomalies caused by the Moho were calculated by removing extra gravity effects layer by layer from the free-air gravity anomalies under the constraint of the submarine topography and sedimentary thickness data in this area.Inversion of these gravity anomalies using our proposed method shows that the method is able to delineate the relief of a V-shaped Moho under a subduction zone.The estimated depth of the Moho beneath the Challenger Deep ranges 18 km to 20 km,while the depth at the edge of the western Pacific Ocean is 8 km to 12 km,which,to some extent,suggests crustal complexity in the study area.Furthermore,a large inclination of the Pacific subduction slab is inferred from the locations of the maximum of the submarine topography and Moho depth in this area,indicating a relatively slow convergence between the Pacific and Philippine plates.