Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks

SUMMARY Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equation can be used describe nature of Earth. To solve a frequency-domain equation, we often need invert impedance matrix. This results in dramatic increase computational cost as model size increases. It is even bigger challenge for media, where matrix far more complex. In addition, conventional finite-difference method produces numerical dispersion artefacts solving equations media. address these issues, use emerging paradigm physics-informed neural networks (PINNs) obtain an transversely isotropic (TI) media with vertical axis symmetry (VTI). PINNs utilize concept automatic differentiation calculate their partial derivatives, which are free artefacts. Thus, loss function train network provide functional VTI form equation. Instead predicting pressure wavefields directly, scattered avoid dealing point-source singularity. We spatial coordinates input data network, outputs real and imaginary parts auxiliary function. After training deep evaluate at any point space almost instantly using this trained without calculating inverse. demonstrate features on simple 2-D anomaly layered model. Additional tests modified 3-D Overthrust irregular topography further validate effectiveness proposed method.