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Acoustic1st

sweep.equations.Acoustic1st 

Acoustic1st(spatial_order=4, device='cpu', backend='jax', **kwargs)

Bases: sweep.equations.base.FirstOrderEquation

First-order 2-D acoustic wave equation in pressure-velocity form.

Variable-density scalar acoustics on a staggered grid: a pressure field p and particle velocities (vx, vz) evolve together. The default boundary type is 'cpmls' (staggered-grid recursive CPML), which couples four memory variables (phix, phiz, psix, psiz); 'spml' is also supported and switches to a split-pressure formulation with two pressure components (px, pz) instead of p.

Reference: 10.1190/GEO2011-0345.1.

Models (constructor input order)

  • vp (m/s): Acoustic P-wave velocity model.
  • rho (kg/m^3): Density model.

Wavefields (cpmls mode — the default)

  • p (aliases: pressure): Acoustic pressure field; default source and receiver.
  • vx (aliases: velocity_x): Particle velocity in the x direction.
  • vz (aliases: velocity_z): Particle velocity in the z direction.
  • phix: CPML memory variable for the x-derivative term (internal).
  • phiz: CPML memory variable for the z-derivative term (internal).
  • psix: CPML auxiliary field in the x direction (internal).
  • psiz: CPML auxiliary field in the z direction (internal).

Wavefields (spml mode)

  • px: Split-field pressure component in the x direction (internal).
  • pz: Split-field pressure component in the z direction (internal).
  • vx (aliases: velocity_x): Particle velocity in the x direction.
  • vz (aliases: velocity_z): Particle velocity in the z direction.

Defaults

  • source_type: ['p']
  • receiver_type: ['p']
  • pml_type: 'cpmls'

Build the first-order acoustic equation operator.

Parameters:

  • spatial_order –

    FD accuracy order of the staggered first-derivative operator — e.g. spatial_order=4 is fourth-order accurate. Internally the half-stencil width is M = spatial_order // 2 (used for loop bounds and PML padding). Must be an even integer (2, 4, 6, 8, 10, …). Higher orders reduce grid dispersion at the cost of more compute per step and a wider PML halo. This equation has no compiled impl='c' path; use impl='eager' (the default). The PyTorch / JAX eager path accepts any even order. Defaults to 4.

  • device –

    Device for the operator's static gradient kernels. Use 'cuda' / a torch.device for GPU runs. Defaults to 'cpu'.

  • backend –

    Array / programming backend, 'torch' or 'jax'. Defaults to 'jax' for this class (the original research implementation); pass backend='torch' to stay on PyTorch.

  • **kwargs –

    forwarded to :class:FirstOrderEquation for forward-compatibility (currently unused).

interior_substeps 

interior_substeps()

The lossless-interior leapfrog as an ordered list of reversible sub-steps (single source of truth — used for BOTH forward and reverse).

Each sub-step updates ONE field group using the OTHER (a pure shear), so evaluating it at -dt exactly inverts it; composing the list in reverse order at -dt therefore inverts the whole step exactly — no separate, sign-flipped reverse body to maintain. The forward step is compose(substeps, +dt) in order (+ CPML, handled by func).