Reformulation of Parker-Oldenburg's method for Earth's spherical approximation
Reformulation of Parker-Oldenburg's method for Earth's spherical approximation
复制标题
地球球面近似的 Parker-Oldenburg 方法的重新表述
DOI：
10.1093/gji/ggaa200
复制
发表时间：
2020
影响因子：
2.8
通讯作者：
Tenzer Robert
中科院分区：
文献类型：
--
作者：
Chen Wenjin;Tenzer Robert
帕克-奥尔登堡方法可能是根据重力数据估计密度界面深度的最常用技术。为了解释所报告的大密度变化，例如在莫霍界面、海洋海水密度和海洋沉积物之间、或沉积物和下伏基岩之间的密度变化，一些作者将此方法扩展到可变密度模型。考虑到重力数据和界面几何形状之间的函数关系是针对地球平面近似推导出来的，帕克-奥尔登堡方法适用于局部研究。然而，由于忽视地球的球形性，这种方法在（大规模）区域、大陆或全球研究中的应用实际上受到错误的限制。因此，帕克-奥尔登堡的方法也针对地球的球形近似进行了重新表述，但仅假设密度均匀。在（大规模）区域或全球研究的背景下，考虑界面处密度异质性的重要性变得更加重要。为了解决这个问题，我们推广了用于异质密度界面深度的 Parker-Oldenburg 方法（为球坐标系定义）。此外，我们扩展了重力梯度数据的定义，重力梯度数据在地球科学应用中的使用大大增加，特别是在发射重力场和稳态海洋环流探测器（GOCE）重力梯度测量卫星任务之后。为了完整起见，我们还提供了潜力的表达式。该研究对帕克-奥尔登堡方法在平面和球形情况下的方法进行了最完整的回顾，该方法定义了势能、重力和重力梯度，同时在界面处结合了均匀或异质密度模型。为了提高以地球重力场和界面几何形状的球谐函数描述的重力正演建模和反演的数值效率，我们使用快速傅里叶变换技术进行球谐函数分析和合成。 （新导出的）功能模型经过数值测试。我们在（大规模）区域研究区域的结果证实，考虑全球一体化和地球球形可以改善重力正演建模和反演的结果。
Parker–Oldenburg's method is perhaps the most commonly used technique to estimate the depth of density interface from gravity data. To account for large density variations reported, for instance, at the Moho interface, between the ocean seawater density and marine sediments, or between sediments and the underlying bedrock, some authors extended this method for variable density models. Parker–Oldenburg's method is suitable for local studies, given that a functional relationship between gravity data and interface geometry is derived for Earth's planar approximation. The application of this method in (large-scale) regional, continental or global studies is, however, practically restricted by errors due to disregarding Earth's sphericity. Parker–Oldenburg's method was, therefore, reformulated also for Earth's spherical approximation, but assuming only a uniform density. The importance of taking into consideration density heterogeneities at the interface becomes even more relevant in the context of (large-scale) regional or global studies. To address this issue, we generalize Parker–Oldenburg's method (defined for a spherical coordinate system) for the depth of heterogeneous density interface. Furthermore, we extend our definitions for gravity gradient data of which use in geoscience applications increased considerably, especially after launching the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity-gradiometry satellite mission. For completeness, we also provide expressions for potential. The study provides the most complete review of Parker–Oldenburg's method in planar and spherical cases defined for potential, gravity and gravity gradient, while incorporating either uniform or heterogeneous density model at the interface. To improve a numerical efficiency of gravimetric forward modelling and inversion, described in terms of spherical harmonics of Earth's gravity field and interface geometry, we use the fast Fourier transform technique for spherical harmonic analysis and synthesis. The (newly derived) functional models are tested numerically. Our results over a (large-scale) regional study area confirm that the consideration of a global integration and Earth's sphericty improves results of a gravimetric forward modelling and inversion.