Velocity Model Building and Editing with Guided Denoising Diffusion Implicit Models

Abstract

Velocity-model building is a fundamental component of seismic imaging, yet it remains a challenging inverse problem due to limited data coverage, nonlinearity, and the need to integrate heterogeneous information such as well logs. We introduce a unified framework for velocity-model editing and full velocity-model building that combines learned diffusion priors with structurally preconditioned inverse formulations. A diffusion model trained on high-resolution synthetic velocity examples provides a data-driven prior that is exploited through Denoising Diffusion Implicit Model (DDIM) inversion and guided sampling. For localized editing, the diffusion prior is coupled with a structurally preconditioned Tikhonov well-matching inversion, enabling controlled modification of selected regions while preserving global consistency. For full velocity-model building, we formulate a well-matching inverse problem augmented with imaging-based regularization and solve it using conventional least-squares, the proposed DDIM-guided method, and Diffusion Posterior Sampling (DPS). Synthetic experiments demonstrate that diffusion-based approaches recover sharper and more realistic velocity structures than classical inversion. Field-data applications on the Viking Graben dataset confirm robustness under realistic acquisition conditions. An ablation study highlights the critical role of structural slope guidance in inversion performance. Overall, the proposed framework bridges inverse problems and generative modeling, offering a flexible approach for practical seismic imaging workflows.

Figures (12)

• Figure 1: Overview of the DDIM-based inversion and guided editing workflow. Top row: DDIM inversion of the initial velocity model, mapping the background model $\mathbf{v}_0$ into its latent representation $\mathbf{v}_T$. Bottom row: Guided masked DDIM sampling, where editing is restricted to the target region (dashed orange box) through a latent-space mask and steered by data-driven constraints, while preserving the background structure outside the masked area.
• Figure 2: (a) Background velocity model $\mathbf{v}_0$. (b) Corresponding latent representation $\mathbf{v}_T$ obtained through DDIM inversion. (c) Reconstructed velocity model $\hat{\mathbf{v}}_0$ recovered by deterministic DDIM sampling.
• Figure 3: Synthetic test setup and velocity-profile comparison. (a) Initial velocity model $\mathbf{v}_0$, where the black dashed line marks the well position. (b) Masked latent representation $\mathbf{v}_T$ obtained through DDIM inversion. (c) Reverse Time Migration (RTM) image used to derive structural guidance. (d) Local slope field $\boldsymbol{\gamma}$ estimated from the RTM image. (e) Well-log positioned at $x = 5733\mathrm{m}$.
• Figure 4: Results comparison for the VME synthetic test. (a) Ground-truth velocity model. (b) Conventional Tikhonov-regularized least-squares inversion. (c) Velocity-model editing result obtained with the proposed diffusion-guided approach. (d) Editing result obtained using the Diffusion Posterior Sampling (DPS) framework. The two white dashed lines indicate the locations at which velocity profiles are extracted; the black dashed line marks the well position. In panels (e) and (f), the black dashed curve denotes the ground-truth velocity profile, the blue curve corresponds to the Tikhonov least-squares result, the green curve to the DPS result, and the red curve to the proposed method.
• Figure 5: Velocity-model building (VMB) comparison for the synthetic test. (a) Original (ground-truth) velocity model. (b) Velocity model obtained from Tikhonov-regularized least-squares inversion. (c) Velocity-model building result obtained with the proposed diffusion-based method. (d) Velocity-model building result obtained using Diffusion Posterior Sampling (DPS). The two white dashed lines indicate the locations at which velocity profiles are extracted, while the black dashed line marks the well position. (e) Velocity profile extracted at $x = 4911.7,\mathrm{m}$. (f) Velocity profile extracted at $x = 6671.5,\mathrm{m}$.