Polychromatic multiparameter FWI backed by symbolic abstractions

We describe a method of full waveform inversion (FWI) for simultaneously resolving velocity and anisotropy using multiple independent monochromatic frequency-space solutions to the wave equation. Operating with more than one monochromatic solution combines benefits of both frequency and time domain approaches without a substantial increase in computational complexity. By computing many frequency-space solutions during a single time-space propagation, we address scaling issues related to large sparse matrices for three spatial dimensions in the frequency domain. We use a domain-specific language (DSL) to symbolically represent the mathematics of seismic modeling and inversion and automatically generate high performance kernels that run on any modern CPU or GPU hardware. In this abstract, we first describe frequency domain FWI and compare time domain and monochromatic approaches. Then, we introduce our polychromatic approach and describe multiparameter inversion for velocity and anisotropy, including our self-adjoint pseudo-acoustic tilted transversely isotropic (TTI) propagators. We highlight the advantages of using a DSL to symbolically abstract the physics of modeling and inversion and decouple it from the computer science implementation. Finally, we summarize our experience from practical field application.