Monitoring of water volume in a porous reservoir using seismic data: Validation of a numerical model with a field experiment

This study validates a neural network-based numerical model that utilizes 3D discontinuous Galerkin seismic simulations to directly estimate water volume in porous reservoirs, demonstrating its effectiveness through field experiments in Laukaa, Finland, to advance sustainable groundwater management.

The Gist

The Big Picture: Finding Water Without Digging

Imagine you have a giant, invisible bathtub buried underground. You know it's full of sand, but you don't know how much water is actually inside it. Usually, to find out, you'd have to dig hundreds of holes (drill wells) to take samples. That's expensive, slow, and messy.

This paper describes a smarter way: using sound waves to "listen" to the water.

The researchers built a small, controlled "bathtub" (a sand pool) in Finland. They dropped heavy weights to create seismic "thuds" (like a drum beat) and listened to how the sound traveled through the sand. Their goal? To teach a computer (an Artificial Intelligence) to look at those sound recordings and instantly guess exactly how much water is in the pool, without ever digging a hole.

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The Analogy: The "Sandwich" and the "Echo"

Think of the ground as a giant sandwich:

1. The Bread (Top): Dry air and sand.
2. The Filling (Middle): Wet sand (saturated with water).
3. The Plate (Bottom): Solid rock or clay.

When you drop a heavy weight on the ground, it sends a shockwave through this sandwich.

• Sound travels differently through wet sand than dry sand. It's like the difference between shouting in a quiet library (dry) versus shouting while underwater (wet). The water makes the sound move faster and change its shape.

The researchers placed 57 "ears" (sensors) all over the ground to catch these echoes.

The Challenge: The "Black Box" Problem

In the past, scientists had to do a lot of complicated math to figure out the water level. They had to guess the porosity (how many holes are in the sand), the exact type of sand, and the water table height, one by one. It was like trying to solve a Rubik's cube blindfolded.

The New Approach:
Instead of doing the math step-by-step, the researchers decided to teach a computer to be a master guesser.

1. The Training Camp (Synthetic Data):
   Before they touched the real ground, they built a virtual version of the sand pool inside a supercomputer. They simulated thousands of different scenarios:

   • "What if the sand is wetter?"
   • "What if the water level is lower?"
   • "What if the sand grains are bigger?"

   They ran these simulations and fed the resulting sound patterns into a Neural Network (a type of AI). The AI learned the pattern: "Oh, when the sound looks like X, the water volume is Y."

2. The Real Test (Field Data):
   They went to the real sand pool in Finland, dropped the weights, and recorded the real sounds. They fed these real sounds into the AI they had trained.

   The Result: The AI looked at the real sound and said, "Based on what I learned in the training camp, there is exactly X amount of water here." And guess what? It was right!

The "Secret Sauce": SHAP Analysis

One of the coolest parts of this paper is how they figured out why the AI was right. They used a tool called SHAP (which sounds like a magic spell, but it's just a way to explain AI decisions).

Think of the 57 sensors as a choir of 57 singers. The AI is the conductor.

• The Question: "Which singers are actually doing the singing, and which ones are just standing there?"
• The SHAP Answer: The analysis showed that the singers (sensors) closest to the drum (the weight drop) were the most important. The ones far away didn't matter as much.

This is huge because it means in the future, we might not need 57 sensors. We could just use the 10 best ones (the ones closest to the source) and still get a great answer. It saves money and time!

Why Does This Matter?

• Water is Running Out: Groundwater levels are dropping fast all over the world. We need to know how much water is left to manage it wisely.
• No More Guessing: This method proves we can monitor water reserves accurately without destroying the landscape with drilling.
• The Future: While this experiment was in a small, perfect sand pool, the researchers believe this "AI + Seismic Sound" method could eventually be scaled up to monitor massive, complex underground aquifers that supply cities with drinking water.

In a Nutshell

The researchers taught a computer to "hear" the difference between wet and dry sand. By training it on millions of fake scenarios, they created a tool that can look at real-world sound waves and instantly tell us how much water is hidden underground. It's like giving geologists a pair of X-ray glasses that see water volume directly, saving us from having to dig up the whole planet to find out.

Technical Summary

1. Problem Statement

Global groundwater levels are declining rapidly, necessitating advanced, non-invasive techniques to monitor and manage aquifers. Traditional geophysical methods often require separate, complex determinations of reservoir parameters (e.g., water-table level and porosity) to estimate water volume. This study addresses the challenge of directly estimating the total water volume in a porous reservoir using seismic data, bypassing intermediate parameter inversion. The specific goal is to validate a numerical model and a neural network-based estimator against real-world field data from a controlled experimental site.

2. Methodology

A. Experimental Setup (Field Data)

• Location: A man-made sand pool at the Natural Resources Institute Finland (Luke) in Laukaa.
• Geometry: A rectangular porous medium (approx. 29.5m x 14.2m) with a controlled water-table level, surrounded by impermeable clay.
• Acquisition:
  • Source: A drop-weight source (metallic rod dropped from 5, 10, or 15 cm heights) acting as a vertical force.
  • Receivers: 57 three-component (3C) 5 Hz geophones arranged in a 3D grid on the surface.
  • Ground Truth: Water-table levels were monitored via gauge wells to calculate true water volumes for validation.
  • Conditions: Measurements were taken at seven distinct water-table levels (ranging from -31.3 cm to -88.7 cm).

B. Numerical Modeling (Synthetic Data Generation)

To train the neural network, a massive synthetic dataset was generated using a high-fidelity physics-based solver:

• Governing Physics: The model uses Biot's poroviscoelastic theory coupled with viscoelastic wave equations to simulate wave propagation in porous (water/air-saturated) and elastic media.
• Attenuation: Modeled using a Generalized Maxwell Body (GMB) rheology to account for frequency-dependent attenuation and viscodynamic drag.
• Solver: A 3D Discontinuous Galerkin (DG) method implemented in C/C++ with MPI and GPU acceleration (NVIDIA V100).
• Parameterization:
  • Physical parameters (porosity, permeability, moduli, tortuosity) were randomized from uniform distributions based on site-specific geological data.
  • Source Uncertainty: The source location was randomized within a 10 cm window to simulate field repositioning errors.
  • Wavelets: Training data used the first derivative of a Gaussian; testing used a Ricker wavelet to ensure generalization.
• Data Preprocessing:
  • Time-domain data (0.35s windows) were transformed to the frequency domain.
  • Deconvolution: A reference receiver was used to normalize the source wavelet effects, creating a source-independent input.
  • Noise Modeling: Additive white noise and amplitude-dependent noise were injected to mimic field conditions.

C. Neural Network Architecture

• Input: Frequency-domain data (Real and Imaginary parts of horizontal and vertical velocity components) from 56 receivers across 21 frequency bins (31.4–88.6 Hz), resulting in an input vector of size 4,704.
• Architecture: A fully connected Deep Neural Network (DNN) with five hidden layers (neurons: 2570, 3920, 3360, 2730, 3400).
• Training:
  • Dataset: 15,000 training samples and 3,000 validation samples.
  • Optimization: Adam optimizer with Random Search for hyperparameter tuning (learning rate, activation functions, regularization).
  • Loss Function: Mean Squared Error (MSE) with L2 regularization.
  • Strategy: Early stopping to prevent overfitting; "Inverse Crime" avoidance by using different mesh resolutions and basis orders for training vs. testing.

D. Interpretability Analysis

• SHAP (Shapley Additive Explanations): Applied to determine the contribution of each receiver to the final water volume prediction. This was used to analyze which sensors are most critical and to test if a reduced sensor array could maintain accuracy.

3. Key Contributions

1. Direct Volume Estimation: Demonstrated a framework to estimate total water volume directly from seismic responses, eliminating the need for intermediate inversion of porosity or water-table height.
2. Field Validation: Successfully validated a synthetic-data-trained neural network against controlled field experiments, a rare achievement in geophysical inverse problems.
3. Robustness to Source Variability: The model successfully generalized to different source signatures (Gaussian vs. Ricker) and source location uncertainties.
4. Sensor Optimization via SHAP: Provided a data-driven method to identify optimal receiver placement, showing that receivers closest to the source contribute most significantly to the estimation.

4. Results

• Accuracy: The neural network achieved high accuracy in estimating water volume for the full receiver array. The estimated volumes closely matched the ground truth derived from the known geometry and water-table levels.
• Outlier Analysis: One field data sample showed significant bias. Analysis revealed this was due to high variability in repeated measurements (high RMSE) at that specific water-table level, likely caused by unmodeled noise or source-receiver offset issues.
• Receiver Configuration Impact:
  • Full Array: Provided the lowest error metrics (RMSE ~2.98 m³ for field data).
  • SHAP-Based Selection (Top 10 Receivers): Maintained performance close to the full array, proving that a sparse array near the source is effective.
  • Random Selection: Significantly degraded accuracy (RMSE ~7.22 m³ for field data), highlighting the critical importance of receiver placement.
• Generalization: The model trained on synthetic data successfully predicted volumes for real field data, demonstrating the potential for transferring synthetic-trained models to real-world scenarios.

5. Significance and Conclusion

This study presents a promising framework for sustainable groundwater management by offering a cost-effective, high-resolution method to monitor aquifer volumes without extensive drilling.

• Practical Application: The ability to use synthetic data to train models that generalize to field conditions reduces the cost and time associated with data acquisition and labeling.
• Sensor Design: The SHAP analysis provides actionable insights for designing seismic monitoring arrays, suggesting that strategic placement of fewer sensors can yield results comparable to dense arrays.
• Future Outlook: While the current study focuses on a simplified, controlled environment, the methodology establishes a foundation for applying deep learning to more complex, heterogeneous natural aquifers. The work underscores the value of combining high-fidelity numerical modeling, deep learning, and explainable AI (XAI) in geophysics.