MicroFlow: Domain-Specific Optical Flow for Ground Deformation Estimation in Seismic Events

TL;DR

MicroFlow addresses the problem of estimating dense ground displacement fields from pre- and post-seismic satellite imagery in the absence of dense ground truth and under temporal perturbations. It introduces a domain-specific optical-flow approach with a correlation-independent encoder-decoder backbone, iterative refinements with explicit warping, and a non-convex log Total Variation regularization to achieve sub-pixel accuracy while preserving fault discontinuities. Experiments on the semi-syntheticFaultDeform dataset and real Ridgecrest imagery show superior performance over patch-based methods and correlation-dependent DL models, including robust fault localization and smooth estimates away from faults. The method generalizes across multiple resolutions and sensors, offering a practical tool for seismic deformation analysis with improved photometric fidelity and resilience to temporal changes.

Abstract

Dense ground displacement measurements are crucial for geological studies but are impractical to collect directly. Traditionally, displacement fields are estimated using patch matching on optical satellite images from different acquisition times. While deep learning-based optical flow models are promising, their adoption in ground deformation analysis is hindered by challenges such as the absence of real ground truth, the need for sub-pixel precision, and temporal variations due to geological or anthropogenic changes. In particular, we identify that deep learning models relying on explicit correlation layers struggle at estimating small displacements in real-world conditions. Instead, we propose a model that employs iterative refinements with explicit warping layers and a correlation-independent backbone, enabling sub-pixel precision. Additionally, a non-convex variant of Total Variation regularization preserves fault-line sharpness while maintaining smoothness elsewhere. Our model significantly outperforms widely used geophysics methods on semi-synthetic benchmarks and generalizes well to challenging real-world scenarios captured by both medium- and high-resolution sensors. Project page: https://jbertrand89.github.io/microflow/.

Figures (16)

• Figure 1: Going from (a) high-resolution to (b)-(d) medium-resolution remote sensing optical images acquired before and after real seismic events and the relative North-South displacement estimations. Classical models (1-2) become overly sensitive to temporal change while state-of-the-art data-driven models (3-4) fail to achieve subpixel precision. In the small to very small displacement regime, encoder-decoder models need iterative refinements and a non convex a-posteriori regularization to effectively estimate dense ground displacement fields (5). It boosts the localization and sharpness of seismic faults both for (a) high resolution and (b) medium resolution sensors, and improves the robustness to external perturbations of the signal such as (c) geological activities and (d) human activities, among others.
• Figure 2: Overview of MicroFlow for estimation dense ground displacement fields. MicroFlow regresses dense displacement fields ($u_3$, $v_3$) by jointly encoding images $I_1$ and $I_2$ through a set of correlation independent encoder-decoder networks ($g_1$, $g_2$, $g_3$) with iterative refinements. It achieves sub-pixel precision and recovers missing faults (notably in the top right corner). An a-posteriori non-convex LTV regularization reveals the original displacement field, maintaining the sharpness of the fault while preserving smoothness away from the fault to correct noisy estimates caused by temporal change.
• Figure 3: Correlation dependent vs Correlation independent encoder-decoder networks. Standard architectures rely on correlation dependent encoder-decoder networks, which are not robust to very small displacement fields. Instead, we use a correlation independent network as the backbone of our iterative procedure.
• Figure 4: Correlation-dependent backbones lag behind in predicting small to very small displacement fields, unlike their correlation-independent counterparts both for high resolution (a) and medium resolution (b) images. This is illustrated for two iterative algorithms, one with explicit warping (IR) and one with recurrent units (RAFT).
• Figure 5: Displacement profiles comparing estimates from COSI-Corr, MicMac, GeoFlowNet, and our proposed method, across the three faults depicted in orange, magenta and cyan on the left sub-figure.