GeoBUS - A Probabilistic Workflow Combining ERT Inverse Modeling and Implicit Geological Modeling

The interface between different rock units is usually described as a sharp boundary in geological models. Such geological interfaces are often a main target of geological as well as geophysical investigations. In the inverse images derived from electrical resistivity tomography (ERT), geological interfaces are typically represented by a continuous, smooth change in the electrical resistivity. This smoothing of interfaces is often unwanted since it deviates significantly from typical geological features where the exact location of the interface can be precisely determined.

The proposed GeoBUS workflow (Geological modeling by Bayesian Updating of Scalar fields) aims to generate probabilistic geological models which include the information from probabilistic ERT inversion results using Bayesian updates. The GeoBUS workflow consists of three main steps. The method “Kalman ensemble generator” (KEG), a numerical implementation for computing Bayesian updates, plays an important role in this workflow.

In the first step of the GeoBUS workflow, the KEG is used for inversion of ERT data. The KEG generates probabilistic, yet smooth images of the subsurface in terms of electrical resistivity.

In the second step of the GeoBUS workflow, we perform implicit geological modeling of the subsurface creating an ensemble of scalar fields. For the geological modeling, we use point information, i.e. the location and orientation of present geological units, along with the uncertainty associated to both location and orientation. The resulting ensemble consists of scalar fields that are defined everywhere in space and build the basis of the geological model. Drawing contours into each scalar field for the scalar field values for which geological interfaces are confirmed, we create an ensemble of geological models.

For the third and final step of the GeoBUS workflow, we adopt the subsurface discretization used for the ERT inverse modeling and use the ensemble of geological models from step two to assign a probabilistic scalar field value to each cell of the discretized subsurface. This discrete version of the scalar field is used as the prior for a second KEG application. Based on literature values, we assign a probability density function for electrical resistivity values to each geological unit of the geological model to formulate a corresponding likelihood. Using the KEG, we derive a Bayesian update of the discretized scalar field combining the petrophysical likelihood and the information from the ERT inversion. This results in a posterior scalar field which again can be used to generate an ensemble of geological models that now includes the information from the geophysical measurements.

We demonstrate this novel workflow for simple and synthetic two-dimensional subsurface models, generating both synthetic geological and geophysical data. This way we aim to (1) create simple benchmark examples, and (2) give a first evaluation of the performance of the GeoBUS workflow.