In a previous paper, we introduced a framework for carrying out petrophysically and geologically guided geophysical inversions. In that framework, petrophysical and geological information is modelled with a Gaussian Mixture Model (GMM). In the inversion, the GMM serves as a prior for the geophysical model. The formulation was confined to problems in which a single physical property model was sought, with a single geophysical dataset. In this paper, we extend that framework to jointly invert multiple geophysical datasets that depend on multiple physical properties. The petrophysical and geological information is used to couple geophysical surveys that, otherwise, rely on independent physics. This requires advancements in two areas. First, an extension from a univariate to a multivariate analysis of the petrophysical data, and their inclusion within the inverse problem, is necessary. Second, we address the practical issues of simultaneously inverting data from multiple surveys and finding a solution that acceptably reproduces each one, along with the petrophysical and geological information. To illustrate the efficacy of our approach and the advantages of carrying out multi-physics inversions, we invert synthetic gravity and magnetic data associated with a kimberlite deposit. The kimberlite pipe contains two distinct facies embedded in a host rock. Inverting the datasets individually leads to a binary geological model: background or kimberlite. A multi-physics inversion, with petrophysical information, differentiates between the two main kimberlite facies of the pipe. Through this example, we also highlight the capabilities of our framework to work with interpretive geologic assumptions when minimal quantitative information is available. In those cases, the dynamic updates of the Gaussian Mixture Model allow us to perform multi-physics inversions by learning a petrophysical model.

中文翻译：

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使用动态高斯混合模型进行岩石物理和地质引导的多物理场反演

在之前的一篇论文中，我们介绍了一个用于进行岩石物理和地质引导地球物理反演的框架。在该框架中，岩石物理和地质信息使用高斯混合模型 (GMM) 建模。在反演中，GMM 作为地球物理模型的先验。该公式仅限于寻求单一物理属性模型和单一地球物理数据集的问题。在本文中，我们扩展了该框架以联合反演依赖于多种物理属性的多个地球物理数据集。岩石物理和地质信息用于耦合地球物理调查，否则依赖于独立物理。这需要在两个领域取得进展。首先，将岩石物理数据的单变量分析扩展为多变量分析，并将它们包含在逆问题中是必要的。其次，我们解决了同时反演来自多个调查的数据的实际问题，并找到了一个可接受地再现每个数据以及岩石物理和地质信息的解决方案。为了说明我们的方法的有效性和进行多物理场反演的优势，我们对与金伯利岩矿床相关的合成重力和磁性数据进行了反演。金伯利岩管包含嵌入在主岩中的两个不同的相。单独反转数据集会产生二元地质模型：背景或金伯利岩。具有岩石物理信息的多物理反演可区分管道的两个主要金伯利岩相。通过这个例子，我们还强调了我们的框架在可用定量信息最少的情况下处理解释性地质假设的能力。在这些情况下，高斯混合模型的动态更新使我们能够通过学习岩石物理模型来执行多物理场反演。