A level set based method for 2D elastic waveform inversion with a stochastic gradient descent approach with a 3D and machine learning prospect

Source abstract

Full waveform inversion as a numerical tool for seismic image reconstruction has been developed for a long time. In seismic background, most of the research concentrates on forward model such as acoustic or Helmholtz equation to simulate the model reconstruction. However, considering that the seismic wave generated during data acquisition is elastic wave, such method for application would lead to a physical error; some researchers instead apply an elastic forward model for full waveform inversion, but it involves with multi-parameter estimation, and will therefore result in a so-called ‘cross-talk’ phenomenon, where parameters compensate each other during the iteration. In high-contrast cases such as salt dome reconstruction, this result is extremely obvious. Therefore we apply a level set representation so as to model the object and background parameter so as to avoid this result, and keeps that all the model parameters in the same topology. However, traditional line search technique elastic wave inversion is highly time-costly, especially with a large-scale source and sensor set. Therefore, we apply a stochastic gradient descent technique so as to reduce the gradient computation cost for a 2D model set; we also apply a cross-validation method in machine learning so as to detect overfitting with noisy data. This will be a good starting point for our future extension to 3D models in practical cases in seismic imaging.