Full Waveform Inversion Using the Hypergradient Descent Method

Optimizing step length or learning rate is crucial for efficient gradient-based inversions, including seismic full waveform inversions and deep learning. Hypergradient descent methods, initially proposed for deep learning, update hyperparameters using gradient descent techniques. We applied the hypergradient descent method to update the step length in full waveform inversion. While this approach still requires selecting an appropriate learning rate for hypergradient descent, it eliminates the need to manually tune and schedule the step length in full waveform inversion. We implemented the hypergradient descent method with the Adam optimizer to invert seismic data and compared the results to those obtained using a line search method. Numerical examples demonstrated that the hypergradient descent method accelerated full waveform inversion and produced results comparable to those from the conventional line search method.