# Direct multi-modal inversion of geophysical logs using deep learning

arXiv: https://arxiv.org/abs/2201.01871 · HTML: https://mlsanity.com/paper/2201.01871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [A Decision Support System for Multi-target Geosteering](https://mlsanity.com/paper/1903.03933/) (2019)
- [Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements](https://mlsanity.com/paper/2005.08868/) (2020)

## Built on by (most cited first, 2 of 2)

- [High-Precision Geosteering via Reinforcement Learning and Particle Filters](https://mlsanity.com/paper/2402.06377/) (2024)
- [Automated machine learning for borehole resistivity measurements](https://mlsanity.com/paper/2207.09849/) (2022)

## Abstract (arXiv)

Geosteering of wells requires fast interpretation of geophysical logs, which is a non-unique inverse problem. Current work presents a proof-of-concept approach to multi-modal probabilistic inversion of logs using a single evaluation of an artificial deep neural network (DNN). A mixture density DNN (MDN) is trained using the "multiple-trajectory-prediction" (MTP) loss functions, which avoids mode collapse typical for traditional MDNs, and allows multi-modal prediction ahead of data. The proposed approach is verified on the real-time stratigraphic inversion of gamma-ray logs. The multi-modal predictor outputs several likely inverse solutions/predictions, providing more accurate and realistic solutions than a deterministic regression using a DNN. For these likely stratigraphic curves, the model simultaneously predicts their probabilities, which are implicitly learned from the training geological data. The stratigraphy predictions and their probabilities obtained in milliseconds from the MDN can enable better real-time decisions under geological uncertainties.