Cold-Diffusion Driven Downward Continuation of Gravity Data

TL;DR

This work reframes downward continuation of gravity data as a concurrent deconvolution problem solvable with a cold-diffusion network that leverages an exponential kernel tied to the upward-continuation operator. By training a single neural inverse across multiple continuation steps, the method achieves robust performance under correlated noise and performs on par with oracle Tikhonov reconstructions, while enabling data visualization at multiple depths. It outperforms traditional regularization and CNN-based DC approaches on synthetic and field data, and maintains high fidelity across a range of continuation heights with a single model. The approach offers practical benefits for gravity data interpretation, including efficiency, edge preservation, and potential applicability to magnetic data and UAV-based surveys.

Abstract

Gravity data can be better interpreted after enhancing high-frequency information via downward continuation. Downward continuation is an ill-posed deconvolution problem. It has been tackled using regularization techniques, which are sensitive to the choice of regularization parameters. More recently, convolutional neural networks such as the U-Net have been trained using synthetic data to potentially learn prior information and perform deconvolution without the need to adjust the regularization parameters. Our experiments reveal that the U-Net is highly sensitive to correlated noise, which is ubiquitously present in geophysical field data. In this paper, we develop a framework based on the $\textbf{cold-diffusion model}$ using the exponential kernel associated with downward continuation. The exponential form of the kernel allows us to train the U-Net to tackle multiple concurrent deconvolution problems with varying levels of blur. This allows our framework to be more robust and quantitatively outperform traditional U-Net-based approaches. The performances also closely matches that of $\textbf{oracle}$ Tikhonov reconstruction technique, which has access to the ground truth.

Figures (13)

• Figure 1: Schematic illustration of downward continuation.
• Figure 2: Upward continuation kernel in the Fourier domain for illustrative values of $\Delta z=100$, $\mathrm{d}x=50$.
• Figure 3: U-Net architecture used for cold-diffusion.
• Figure 4: Schematic representation of diffusion steps generated with the upward continuation kernel.
• Figure 5: Qualitative evaluation of different techniques for downward continuation. The images have been normalized to the range [$-1, 1$] for the purpose of visualization.