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Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator f maps the subsurface velocity structures to seismic signals. The existing computational methods for solving full-waveform inversion are not only computationally expensive, but also yields low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying convolutional neural network (CNN) to directly derive the inversion operator so that the velocity structure can be obtained without knowing the forward operator f. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. Furthermore, we employ the conditional random field (CRF) on top of the CNN to generate structural predictions by modeling the interactions between different locations on the velocity model.

The full paper can be found on arxiv:

InversionNet: An Efficient and Accurate Data-driven Full Waveform Inversion

What is Full Waveform Inversion?

Seismic waves are mechanical perturbations that travel in the medium at a speed governed by the acoustic/elastic impedance of the medium in which they are traveling. Full waveform inversion (FWI) is non-linear data-fitting procedure that aims at obtaining detailed estimates of subsurface properties from seismic data, which can be the result of either passive or active seismic experiments.

Why is it hard to solve FWI?

The major challenges of solving FWI mostly come from three folds: ill-posedness, cycle skipping, and high computational cost. Similar to other geophysical exploration methods, FWI suffers from the limited data coverage, which results in extremely under-constrained inverse problems. Due to the fact that FWI is highly non-linear and sensitive to the initial guess, a naive approach to the FWI problem typically converges to a local minima. When the starting model is far away from the global minimum (common in field applications), a deterministic algorithm is unable to move the events in seismic data to the correct cycle. The miss match to correct wavefield phase is also called cycle skipping. Having low-frequency components in inversion is critical to alleviate this cycle skipping issue. High computational cost is another challenging for solving FWI problems. Most of the existing approaches to solve FWI rely on iterative nonlinear optimization techniques. At each iteration, it is cubic cost to obtain the gradient, provided with a 2-D subsurface model.