# Integration of the Biot–Gassmann Fluid Substitution Method and Machine Learning-Based Velocity–Stress Relationship for Estimating In Situ Stresses

## TL;DR

This paper combines Biot–Gassmann fluid substitution with machine learning to estimate in situ stresses using low-frequency acoustic velocity data from dry rocks.

## Contribution

The novel integration of Biot–Gassmann-derived velocities with ML/DL models improves in situ stress prediction using low-frequency data.

## Key findings

- ML/DL models trained on Biot–Gassmann-derived velocities achieved R² of 0.86–0.975 for stress prediction.
- SHAP analysis enhanced model reliability and scientific validation of stress estimation.
- Dry rock experiments with 75 stress configurations enabled accurate low-frequency velocity–stress modeling.

## Abstract

Recent advancements have shown that in situ stresses
can be reliably
estimated through an integrated machine/deep learning (ML/DL)-based
framework, which relies on models trained and validated using true
triaxial ultrasonic velocity (TUV) experimental data that involve
measurements of ultrasonic velocity in saturated rocks under varying
stress configurations. However, when the goal is to interpret lower
frequency measurements, it may be more appropriate to run experiments
on dry rocks and then obtain Biot–Gassmann-derived equivalent
saturated velocities (low-frequency approximation) and employ these
quantities for training ML/DL models to predict in situ stress. Whether
the dispersion effect of frequency on the velocity–stress relationship
substantially impacts in situ stress prediction is an important and
unresolved question. This work presents an enhancement of ML/DL-based
workflow by training and implementing ML/DL models using equivalent
saturated acoustic velocities (low-frequency) obtained by applying
Biot–Gassmann fluid substitution on the ultrasonic velocities
of dry cores. The models were trained on TUV data sets derived from
three subsurface cores extracted from the geothermal well 16B(78)-32
at the Utah FORGE site. Each core was subjected to 75 unique stress
configurations for velocity measurement in the dry state. The ML/DL
trained on the TUV data set with equivalent saturated velocities demonstrated
promising performance to predict in situ stress in subsurface geological
rocks using velocity–stress relationships with R
2 of 0.86, 0.971, and 0.975 and root mean squared error
(RMSE) of 2.59, 1.92, and 1.80 for validation/testing phases of vertical,
minimum horizontal, and maximum horizontal stress models, respectively.
Additionally, interpretation and explanation by Shapley additive explanations
(SHAP) analysis further improved scientific validation and model reliability
for estimating in situ stresses.