Towards Entire Wavefield Inversion in Highly Scattering Volcanic Environments using Fourier Neural Operators

Seismic imaging in volcanic environments is highly challenging due to significant scattering of seismic waves on multiple spatial scales. When these wavefields are recorded on the surface by seismic arrays, seismograms generally contain information-rich codas in addition to ballistic first arrivals. Later reflected and refracted arrivals are often completely masked by the scattered coda waves. Despite the potential information contained in the coda waves their incoherency usually forces imaging to rely solely on first arrival travel time tomography, which smooths out fine scale detail, such as important individual feeder dykes. Volcanic regions such as Iceland may provide the opportunity to directly use the scattered wavefield to produce improved velocity models from seismic data, using machine learning approaches. Machine learning-driven inversion also has the potential to offer marked speed-up over conventional seismic inversion once a neural network is trained to acceptable performance. Rapid velocity model estimation is of particular importance in volcanic settings, where magmatic intrusions during periods of increased volcanic activity can pose a significant risk to both society and industry. In this study we show how machine learning could play a role in real-time seismic imaging of the upper crust beyond the current resolution of seismic tomography. We also show how machine learning could play a role in producing higher resolution images of the upper volcanic crust. We train a Fourier Neural Operator-based neural network to invert for 2D P-wave velocity models from a single earthquake gather. We first create a foundational dataset of 30,000 2D velocity models with depthwise gradients representative of Icelandic crust, perturbed by up to 25% with anti-persistent Von Kármán series and 1000m correlation lengths. Secondly, we forward model the wavefield gather through each velocity model using SPECFEM2D, accounting for attenuation and broadband source properties. Thirdly we train a Fourier Neural Operator (FNO) to predict 2D P-wave velocity models from single earthquake gathers. From here we show that FNO performance generalises to unseen earthquake gathers not included during training or validation steps, recovering the broadscale 2D velocity structure. Finally, we repeat FNO training with 4,000 additional models and earthquake gathers with random walk-based, low-velocity dyke intrusions down to the order of 200m scale-widths. We show that the trained FNO model can successfully recover these fine-scale dykes using strongly scattered seismic data but that recovery fidelity is influenced by earthquake source location. We discuss how FNO-based seismic inversion can complement cognate methodologies such as emerging fibre-optic geodesy and seismicity approaches to monitor for dyke and sill intrusions in real-time.