Shallow-to-deep velocity model building via diffusion models-Part I: Method and Proof of concept
Abstract
Seismic velocity model building (VMB) is fundamental for understanding subsurface structures. Traditional methods demand high-quality starting models and, also, remain limited in resolution in coverage and computationally intensive. Recent generative diffusion model-based approaches capture statistical priors to support traditional inversion methods, but these approaches do not account for the top to bottom progression of information (layer stripping) involved in surface recorded data, where deep velocity information depends on the shallow. To address this issue, we propose a depth-progressive diffusion framework that constructs velocity models incrementally from shallow to deep by propagating prior information. Our method trains on paired shallow-deep velocity patches with variable overlap and explicit depth encoding, integrating multiple geophysical constraints including well logs and seismic images (representing structural information). During inference, we synthesize overlapping depth slices using a progressive algorithm and merge them with Gaussian-weighted blending to eliminate boundary artifacts. This approach leverages both learned geological distributions and observed shallow priors while providing uncertainty quantification. Extensive numerical experiments on in-distribution tests and an out-of-distribution test demonstrate excellent VMB accuracy with a strong correlation between predicted uncertainty and actual errors. As a proof of concept, this part I employs idealized structural constraints derived from vertical reflectivity to validate the methodological framework. The companion paper (Part II) extends the approach to realistic structural constraints relying on migrated images with field data applications.
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BibTeX
@misc{cheng2026shallowtodeep,
title = {{Shallow-to-deep velocity model building via diffusion models-Part I: Method and Proof of concept}},
author = {Shijun Cheng and Randy Harsuko and Tariq Alkhalifah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26454},
eprint = {2609.26454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26454},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Shallow-to-deep velocity model building via diffusion models-Part I: Method and Proof of concept
AU - Shijun Cheng
AU - Randy Harsuko
AU - Tariq Alkhalifah
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26454
UR - https://arxiv.org/abs/2609.26454
AB - Seismic velocity model building (VMB) is fundamental for understanding subsurface structures. Traditional methods demand high-quality starting models and, also, remain limited in resolution in coverage and computationally intensive. Recent generative diffusion model-based approaches capture statistical priors to support traditional inversion methods, but these approaches do not account for the top to bottom progression of information (layer stripping) involved in surface recorded data, where deep velocity information depends on the shallow. To address this issue, we propose a depth-progressive diffusion framework that constructs velocity models incrementally from shallow to deep by propagating prior information. Our method trains on paired shallow-deep velocity patches with variable overlap and explicit depth encoding, integrating multiple geophysical constraints including well logs and seismic images (representing structural information). During inference, we synthesize overlapping depth slices using a progressive algorithm and merge them with Gaussian-weighted blending to eliminate boundary artifacts. This approach leverages both learned geological distributions and observed shallow priors while providing uncertainty quantification. Extensive numerical experiments on in-distribution tests and an out-of-distribution test demonstrate excellent VMB accuracy with a strong correlation between predicted uncertainty and actual errors. As a proof of concept, this part I employs idealized structural constraints derived from vertical reflectivity to validate the methodological framework. The companion paper (Part II) extends the approach to realistic structural constraints relying on migrated images with field data applications.
ER -