We have developed an inversion method for recovery of the geometry of an arbitrary number of geologic units using a regularized least-squares framework. The method addresses cases in which each geologic unit can be modeled using a constant physical property. Each geologic unit or group assigned the same physical property value is modeled using the signed distance to its interface with other units. We invert for this quantity and recover the location of interfaces between units using the level-set method. We formulate and solve the inverse problem in a least-squares sense by inverting for such signed distances. The sensitivity matrix to perturbations of the interfaces is obtained using the chain rule, and model mapping from the signed distance is used to recover the physical properties. Exploiting the flexibility of the framework that we develop allows any number of rock units to be considered. In addition, it allows the design and use of regularization incorporating prior information to encourage specific features in the inverted model. We apply this general inversion approach to gravity data favoring minimum adjustments of the interfaces between rock units to fit the data. The method is first tested using noisy synthetic data generated for a model compoed of six distinct units, and several scenarios are investigated. It is then applied to field data from the Yerrida Basin (Australia) where we investigate the geometry of a prospective greenstone belt. The synthetic example demonstrates the proof of concept of the proposed methodology, whereas the field application provides insights into, and potential reinterpretation of, the tectonic setting of the area.

中文翻译：

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在正则化最小二乘框架中将水平集反演推广到任意数量的地质单元

我们开发了一种使用正则化最小二乘框架恢复任意数量地质单元几何形状的反演方法。该方法解决了可以使用恒定物理属性对每个地质单元进行建模的情况。每个分配了相同物理属性值的地质单元或组都使用到其与其他单元界面的有符号距离进行建模。我们反演这个数量并使用水平集方法恢复单元之间的界面位置。我们通过对这样的有符号距离求反，在最小二乘意义上制定和解决反问题。使用链式法则获得界面扰动的灵敏度矩阵，并使用符号距离的模型映射来恢复物理特性。利用我们开发的框架的灵活性，可以考虑任意数量的岩石单元。此外，它还允许设计和使用包含先验信息的正则化，以鼓励反演模型中的特定特征。我们将这种通用反演方法应用于重力数据，有利于对岩石单元之间的界面进行最小调整以适应数据。该方法首先使用为由六个不同单元组成的模型生成的嘈杂合成数据进行测试，并研究了几种情况。然后将其应用于来自耶里达盆地（澳大利亚）的现场数据，在那里我们研究了预期绿岩带的几何形状。综合示例展示了所提议方法的概念证明，而现场应用则提供了对以下内容的洞察和潜在的重新解释：