Cold-Diffusion Driven Downward Continuation of Gravity Data
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arXiv
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| Format: | Preprint |
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2025
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| author | Jain, Adarsh Bharadwaj, Pawan Seelamantula, Chandra Sekhar |
| author_facet | Jain, Adarsh Bharadwaj, Pawan Seelamantula, Chandra Sekhar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cold-Diffusion Driven Downward Continuation of Gravity Data Jain, Adarsh Bharadwaj, Pawan Seelamantula, Chandra Sekhar Geophysics 86A22 (Primary) 68T07, 31A25, 86A20 (Secondary) 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. |
| title | Cold-Diffusion Driven Downward Continuation of Gravity Data |
| topic | Geophysics 86A22 (Primary) 68T07, 31A25, 86A20 (Secondary) |
| url | https://arxiv.org/abs/2510.21191 |