基于球坐标的地幔密度成像理论及方法研究

With the accumulation of global geophysical data, the main task of solid-geophysics steers to making known the geological processes of continental lithosphere and their regularity. Global high-resolution and high-precision gravity data are an important basic data for solid-Earth Sciences. It provides access to construct crustal and mantle density perturbations models regionally and globally. Therefore, studying mantle density imaging technology is necessary to the development of solid geophysics. Due to the curvature of the Earth's surface, the current inversion techniques in the Cartesian coordinate system are difficult to reveal the mantle density distribution correctly. It is needed to develop an inversion scheme on a sphere method. This proposal aims to develop 3-D gravity inversion theory and technique in spherical coordinates. Through studying objective functions, model spatial structure choosing and its weighting, structural constraining and prior information implementing by using series of model tests, we would set up an inversion method scheme to imaging the mantle density in spherical coordinates, and apply it to interpret regional and global properties of the mantle and the regularity of mass movement inside the Earth.

随着全球地球物理场数据的大量积累，固体地球物理学的主要任务转变为揭示大陆岩石圈地质作用过程和规律性。全球覆盖的高分辨率、高精度重力数据是固体地球科学研究重要的基础数据，它为获取区域及全球壳幔高分辨密度扰动模型创造了条件。因此，研究地幔密度成像方法技术是固体地球物理发展的必然。由于地球表面是曲面，目前的直角坐标系中的反演技术难以正确地展现地幔密度分布特征，需要研究球面上的反演方法。本项目旨在开展球坐标系三维重力反演理论的基础上，通过试验确定模型目标函数、空间结构加权、结构约束和先验信息应用方法，依此建立基于球坐标的地幔密度成像反演方法体系，并运用于研究区域及全球地幔属性和物质运动的规律性。

本项目研究目标是发展三维重力反演理论、建立基于球坐标下地幔密度成像反演方法体系，拟解决的关键问题是如何提高纵向分辨率问题。围绕研究目标，通过引用细剖分来精化Tesseroid正演，并将了顾及体积因素的深度加权技术引入球坐标下重力和重力梯度反演算法，采用根据异常波长可变的深度加权技术，有效低提高了反演的纵向分辨率。该方法已在菲律宾板块及邻区、西南印度洋洋中脊地区、地中海地区和天山地区应用，以研究地幔密度结构与岩石圈构造及其演化的关系。同时，发展了基于球面三角剖分（Spherical Triangular Tessellation, STT）的球坐标的建模和重力场正演方法，该方法不仅可以克服不同纬度上Tesseroid表面积和体积不等导致的影响，而且可方便地构建多分辨率网络结构模型以及高精度地拟合复杂变化界面，这种建模方法具有计算引力及其梯度的解析公式，由此开发出了基于球面三角棱柱体球坐标下重力反演方法