Poynting vector minimal reflection boundary conditions

A method for exploring for hydrocarbons, comprising:

• simulating a seismic waveform, using a computer, wherein computations are performed on a computational grid representing a subsurface region, said computational grid using perfectly matched layer (PML) boundary conditions;
• wherein, in the simulation, the PML boundary conditions are defined to reduce computational instabilities at a boundary by steps including,
• representing direction of energy propagation by a Poynting vector, and
• dissipating energy that represents noise or reflections at the boundary that do not correspond to reflections from geological objects, with a dissipation operator operating on the Poynting vector, in a direction of energy propagation instead of in a phase velocity direction;
• and
• using the simulated waveform in performing full waveform inversion or reverse time migration of seismic data;
• obtaining a physical property model from the inversion or a subsurface image from the migration;
• and
• using the physical property model or the subsurface image to explore for hydrocarbons.