Joint geophysical, petrophysical and geologic inversion using a dynamic Gaussian mixture model

We present a framework for petrophysically and geologically guided inversion to perform multi-physics joint inversions. Petrophysical and geological information is included in a multi-dimensional Gaussian mixture model that regularizes the inverse problem. The inverse problem we construct consists of a suite of three cyclic optimizations over the geophysical, petrophysical and geological information. The two additional problems over the petrophysical and geological data are used as a coupling term. They correspond to updating the geophysical reference model and regularization weights. This guides the inverse problem towards reproducing the desired petrophysical and geological characteristics. The objective function that we define for the inverse problem is comprised of multiple data misfit terms: one for each geophysical survey and one for the petrophysical properties and geological information. Each of these misfit terms has its target misfit value which we seek to fit in the inversion. We detail our reweighting strategies to handle multiple data misfits at once. Our framework is modular and extensible, and this allows us to combine multiple geophysical methods in a joint inversion and to distribute open-source code and reproducible examples. To illustrate the gains made by multi-physics inversions, we apply our framework to jointly invert, in 3D, synthetic potential fields data based on the DO-$27$ kimberlite pipe case study (Northwest Territories, Canada). The pipe contains two distinct kimberlite facies embedded in a host rock. We show that inverting the datasets individually, even with petrophysical information, leads to a binary geologic model consisting of background or kimberlite. A joint inversion, with petrophysical information, can differentiate the two main kimberlite facies of the pipe.