[Paper Review] A Deep Learning Approach to the Inversion of Borehole Resistivity Measurements

Mostafa Shahriari, David Pardo+4 more|arXiv (Cornell University)|Oct 5, 2018

Geophysical and Geoelectrical MethodsEarth and Planetary Sciences32 references3 citations

TL;DR

This paper proposes a deep neural network (DNN)-based approach to accelerate real-time inversion of borehole resistivity measurements for well geosteering. By training a DNN offline to approximate the inverse problem of mapping LWD measurements to subsurface resistivity layers, the method enables sub-second inversion per wellbore position, delivering physically plausible models with uncertainty quantification, though accuracy requires further refinement for field deployment.

ABSTRACT

We use borehole resistivity measurements to map the electrical properties of the subsurface and to increase the productivity of a reservoir. When used for geosteering purposes, it becomes essential to invert them in real time. In this work, we explore the possibility of using Deep Neural Network (DNN) to perform a rapid inversion of borehole resistivity measurements. Herein, we build a DNN that approximates the following inverse problem: given a set of borehole resistivity measurements, the DNN is designed to deliver a physically meaningful and data-consistent piecewise one-dimensional layered model of the surrounding subsurface. Once the DNN is built, we can perform the actual inversion of the field measurements in real time. We illustrate the performance of DNN of logging-while-drilling measurements acquired on high-angle wells via synthetic data.

Motivation & Objective

• To develop a fast, real-time inversion method for logging-while-drilling (LWD) resistivity measurements to support well geosteering.
• To overcome the computational burden of traditional inverse solvers by approximating the inverse mapping using deep neural networks (DNNs).
• To provide physically reliable and data-consistent one-dimensional layered resistivity models from borehole measurements.
• To enable uncertainty quantification in inversion results through DNN-based prediction confidence.
• To explore the feasibility of using DNNs as initial approximations for subsequent refinement with more accurate but slower inversion methods.

Proposed method

• A deep neural network (DNN) is trained offline to approximate the inverse mapping $\boldsymbol{\cal I}$, which maps borehole resistivity measurements $\bf M$ and well trajectory $\bf T$ to subsurface resistivity parameters $\bf p$.
• The DNN is trained on synthetic data generated using rapid forward solvers for 1.5D layered models, simulating electromagnetic wave propagation governed by Maxwell’s equations.
• The network architecture is designed to enforce physical consistency and data compatibility, with loss functions incorporating regularization to avoid non-physical solutions.
• During online inference, the trained DNN processes new measurement sets in seconds, producing resistivity profiles and uncertainty maps for each logging position.
• The method treats the inverse problem as a function approximation task, bypassing iterative optimization and enabling real-time deployment.
• The approach leverages the fact that DNNs can be evaluated rapidly once trained, making them suitable for time-critical applications like geosteering.

Experimental results

Research questions

• RQ1 Can a deep neural network be effectively trained to approximate the inverse problem of borehole resistivity measurement inversion with sufficient accuracy for real-time geosteering?
• RQ2 How well can a DNN generalize to new synthetic LWD measurement sets not seen during training, particularly in high-angle well geometries?
• RQ3 Can the DNN provide not only resistivity estimates but also reliable uncertainty quantification for each predicted layer?
• RQ4 What are the limitations of DNN-based inversion in terms of accuracy, data requirements, and scalability to 2D and 3D subsurface models?
• RQ5 How does the DNN performance compare to conventional iterative inversion methods in terms of speed and reliability?

Key findings

• The DNN achieves inversion in a few seconds per wellbore with over a thousand logging positions, significantly faster than conventional iterative methods.
• Despite some inaccuracies in predicted resistivity layers, the DNN results are physically plausible and can serve as fast initial approximations for further refinement.
• The method successfully generates uncertainty maps alongside predictions, enhancing reliability for decision-making in geosteering.
• The DNN demonstrates robustness in synthetic examples involving high-angle wells and complex resistivity layering, though accuracy requires improvement.
• Training the DNN is computationally intensive (up to three weeks on GPU), but this is done offline, enabling real-time online inference.
• The approach shows promise for real-time applications but is currently limited by data requirements and generalization to higher-dimensional models.