Efficient One-Step Surface-Wave Tomography through Implicit Differentiation and Jacobian Factorization
Abstract
Surface-wave tomography provides important constraints on the crust and upper mantle, but directly inverting millions of measurements for three-dimensional structure remains computationally demanding. We develop an efficient Gauss--Newton framework for one-step surface-wave tomography that jointly inverts multiperiod interstation traveltimes for shear-wave velocity, accounting for both lateral wave propagation and depth sensitivity. Implicit differentiation of the converged discrete Eikonal equations provides individual traveltime sensitivity kernels, which are constructed efficiently by reusing the Eikonal dependency structure across receivers. A factorized Jacobian retains these kernels separately from shared model and dispersion mappings, reducing storage and repeated-product costs within each linearized solve. Synthetic experiments show that the framework recovers three-dimensional velocity anomalies with fewer model updates and lower model errors than the tested comparison workflows at similar data fits. Computational benchmarks demonstrate substantial savings in operator storage and the cost of linearized model updates compared with using explicitly assembled Jacobians. We apply the framework to 6.34 million Rayleigh-wave phase traveltimes across the contiguous United States. The recovered model captures major crustal and uppermost mantle velocity variations, including the broad contrast between the tectonically active western United States and the continental interior, consistent with previous surface-wave studies. These results demonstrate a practical Gauss--Newton approach to imaging the crust and upper mantle using large surface-wave data sets.
Related
- Efficient Uncertainty Quantification for Marine CSEM via Swi-DREI: A Physics-Driven Deep Reparameterization Ensemble Approach with Implicit Regularization
- A Physics-Constrained Implicit Profile Network for Continuous Reconstruction of Tropical Cyclone Near-Surface Wind Profiles
- An AI-assisted conditioning and geological interpretation workflow for usage in implicit geological modeling
- Source Identification and Apportionment of Heavy Metals in Tobacco Farmland Soils via Positive Matrix Factorization and Geochemical Indices
- Coarse-to-fine multi-resolution hash encoding for implicit full waveform inversion
BibTeX
@misc{jiang2026efficient,
title = {{Efficient One-Step Surface-Wave Tomography through Implicit Differentiation and Jacobian Factorization}},
author = {Yiran Jiang and Ping Tong and Jianwei Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32142},
eprint = {2609.32142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32142},
}
RIS
TY - UNPB
TI - Efficient One-Step Surface-Wave Tomography through Implicit Differentiation and Jacobian Factorization
AU - Yiran Jiang
AU - Ping Tong
AU - Jianwei Ma
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32142
UR - https://arxiv.org/abs/2609.32142
AB - Surface-wave tomography provides important constraints on the crust and upper mantle, but directly inverting millions of measurements for three-dimensional structure remains computationally demanding. We develop an efficient Gauss--Newton framework for one-step surface-wave tomography that jointly inverts multiperiod interstation traveltimes for shear-wave velocity, accounting for both lateral wave propagation and depth sensitivity. Implicit differentiation of the converged discrete Eikonal equations provides individual traveltime sensitivity kernels, which are constructed efficiently by reusing the Eikonal dependency structure across receivers. A factorized Jacobian retains these kernels separately from shared model and dispersion mappings, reducing storage and repeated-product costs within each linearized solve. Synthetic experiments show that the framework recovers three-dimensional velocity anomalies with fewer model updates and lower model errors than the tested comparison workflows at similar data fits. Computational benchmarks demonstrate substantial savings in operator storage and the cost of linearized model updates compared with using explicitly assembled Jacobians. We apply the framework to 6.34 million Rayleigh-wave phase traveltimes across the contiguous United States. The recovered model captures major crustal and uppermost mantle velocity variations, including the broad contrast between the tectonically active western United States and the continental interior, consistent with previous surface-wave studies. These results demonstrate a practical Gauss--Newton approach to imaging the crust and upper mantle using large surface-wave data sets.
ER -