# Full waveform inversion guided by travel time tomography

arXiv: https://arxiv.org/abs/1607.00968 · HTML: https://mlsanity.com/paper/1607.00968/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2016.

## Built on by (most cited first, 3 of 3)

- [Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop](https://mlsanity.com/paper/2110.07584/) (2021)
- [Physics-guided Full Waveform Inversion using Encoder-Solver Convolutional Neural Networks](https://mlsanity.com/paper/2405.17696/) (2024)
- [Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel](https://mlsanity.com/paper/2605.14370/) (2026)

## Abstract (arXiv)

Full waveform inversion (FWI) is a process in which seismic numerical simulations are fit to observed data by changing the wave velocity model of the medium under investigation. The problem is non-linear, and therefore optimization techniques have been used to find a reasonable solution to the problem. The main problem in fitting the data is the lack of low spatial frequencies. This deficiency often leads to a local minimum and to non-plausible solutions. In this work we explore how to obtain low frequency information for FWI. Our approach involves augmenting FWI with travel time tomography, which has low-frequency features. By jointly inverting these two problems we enrich FWI with information that can replace low frequency data. In addition, we use high order regularization, in a preliminary inversion stage, to prevent high frequency features from polluting our model in the initial stages of the reconstruction. This regularization also promotes the non-dominant low-frequency modes that exist in the FWI sensitivity. By applying a joint FWI and travel time inversion we are able to obtain a smooth model than can later be used to recover a good approximation for the true model. A second contribution of this paper involves the acceleration of the main computational bottleneck in FWI--the solution of the Helmholtz equation. We show that the solution time can be reduced by solving the equation for multiple right hand sides using block multigrid preconditioned Krylov methods.