To reduce uncertainties in reconstructed images, geologic information must be introduced in a numerically robust and stable way during the geophysical data inversion procedure. In the context of potential (gravity) data inversion, it is important to bound the physical properties by providing probabilistic information on the number of lithologies and ranges of values of possibly existing related rock properties (densities). For this purpose, we have introduced a generalization of bounding constraints for geophysical inversion based on the alternating direction method of multipliers. The flexibility of the proposed technique enables us to take into account petrophysical information as well as probabilistic geologic modeling, when it is available. The algorithm introduces a priori knowledge in terms of physically acceptable bounds of model parameters based on the nature of the modeled lithofacies in the region under study. Instead of introducing only one interval of geologically acceptable values for each parameter representing a set of rock properties, we define sets of disjoint intervals using the available geologic information. Different sets of intervals are tested, such as quasidiscrete (or narrow) intervals as well as wider intervals provided by geologic information obtained from probabilistic geologic modeling. Narrower intervals can be used as soft constraints encouraging quasidiscrete inversions. The algorithm is first applied to a synthetic 2D case for proof-of-concept validation and then to the 3D inversion of gravity data collected in the Yerrida Basin (Western Australia). Numerical convergence tests show the robustness and stability of the bound constraints that we apply, which is not always trivial for constrained inversions. This technique can be a more reliable uncertainty reduction method as well as an alternative to other petrophysically or geologically constrained inversions based on the more classic “clustering” or Gaussian-mixture approaches.

中文翻译：

---

使用乘法器的交替方向方法进行地质约束反演的不相交区间约束，适用于重力数据

为了减少重建图像中的不确定性，在地球物理数据反演过程中，必须以数字稳健的方式引入地质信息。在潜在（重力）数据反演的背景下，重要的是通过提供有关岩性数和可能存在的相关岩石特性（密度）值范围的概率信息来限制物理特性。为此，我们基于乘子的交替方向方法引入了地球物理反演的边界约束的概括。所提出技术的灵活性使我们能够考虑岩石物理信息以及概率地质建模（如果可用）。该算法根据研究区域中建模岩相的性质，根据模型参数的物理可接受范围引入了先验知识。代替为代表一组岩石属性的每个参数仅引入一个地质可接受值的区间，我们使用可用的地质信息定义不相交区间的集合。测试了不同的间隔集，例如准离散（或窄）间隔以及由概率地质建模获得的地质信息所提供的较宽间隔。较窄的间隔可以用作鼓励准离散反演的软约束。该算法首先应用于合成的2D情况以进行概念验证，然后再应用于Yerrida盆地（西澳大利亚州）收集的重力数据的3D反演。数值收敛测试显示了我们应用的约束约束的鲁棒性和稳定性，这对于约束反演并不总是微不足道的。该技术可以是更可靠的减少不确定性的方法，并且可以替代基于更经典的“聚类”或高斯混合方法的其他岩石物理或地质约束反演。