  Frequency-domain wavefield solutions corresponding to the anisotropic
acoustic wave equations can be used to describe the anisotropic nature of the
earth. To solve a frequency-domain wave equation, we often need to invert the
impedance matrix. This results in a dramatic increase in computational cost as
the model size increases. It is even a bigger challenge for anisotropic media,
where the impedance matrix is far more complex. To address this issue, we use
the emerging paradigm of physics-informed neural networks (PINNs) to obtain
wavefield solutions for an acoustic wave equation for transversely isotropic
(TI) media with a vertical axis of symmetry (VTI). PINNs utilize the concept of
automatic differentiation to calculate its partial derivatives. Thus, we use
the wave equation as a loss function to train a neural network to provide
functional solutions to form of the acoustic VTI wave equation. Instead of
predicting the pressure wavefields directly, we solve for the scattered
pressure wavefields to avoid dealing with the point source singularity. We use
the spatial coordinates as input data to the network, which outputs the real
and imaginary parts of the scattered wavefields and auxiliary function. After
training a deep neural network (NN), we can evaluate the wavefield at any point
in space instantly using this trained NN. We demonstrate these features on a
simple anomaly model and a layered model. Additional tests on a modified 3D
Overthrust model and a model with irregular topography also show the
effectiveness of the proposed method.
