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AcousticVRZ

sweep.equations.AcousticVRZ 

AcousticVRZ(spatial_order=4, device='cpu', backend='torch', dim=2)

Bases: sweep.equations.base.SecondOrderEquation

Second-order 2-D acoustic wave equation in variable-density VRZ form.

Pressure-only scalar acoustics with explicit density coupling through an impedance-like auxiliary parameter z. The Laplacian carries an extra term ∇b · ∇p (with b = vp / z, κ = z · vp), so the propagator is a single second-order PDE in h1 that correctly refracts at sharp impedance contrasts without needing a staggered velocity field. Absorbing boundaries via split-step CPML (cpmlr).

Reference: 10.3997/2214-4609.202010332.

Models (constructor input order)

  • vp (m/s): Acoustic velocity model.
  • z: Auxiliary parameter used by the VRZ formulation.

Wavefields

  • h1 (aliases: pressure, p): Primary VRZ acoustic pressure-like wavefield; default source and receiver.
  • h2 (aliases: pressure_prev): Previous-step VRZ acoustic pressure-like wavefield (internal).
  • psix: CPML memory variable for the x-derivative term (internal).
  • psiz: CPML memory variable for the z-derivative term (internal).
  • zetax: CPML auxiliary wavefield for the x-direction update (internal).
  • zetaz: CPML auxiliary wavefield for the z-direction update (internal).

Defaults

  • source_type: ['h1']
  • receiver_type: ['h1']
  • pml_type: 'cpmlr'

Build the 2-D VRZ acoustic equation operator.

Parameters:

  • spatial_order –

    FD accuracy order of the spatial Laplacian and the auxiliary first-derivative kernels used by the ∇b · ∇p term — 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, …). Performance note (impl='c' on CUDA): the compiled kernels ship template specialisations only for spatial_order ∈ {2, 4, 6, 8}. Above 8 the dispatcher drops to a generic runtime path (order = -1 in src/sweep/csrc/cuda/equations/acoustic_vrz2d/forward.cu) which uses more registers and runs noticeably slower. The PyTorch eager path is unaffected. Defaults to 4.

  • device –

    Device for the operator's static gradient kernels. Use 'cuda' / a torch.device for GPU runs so the propagator can follow without a host↔device copy. Defaults to 'cpu'.

  • backend –

    Array / programming backend, 'torch' or 'jax'. When you later want impl='c', leave this on 'torch' — the compiled CUDA kernels go through the Torch binding. Defaults to 'torch'.

  • dim –

    Stored dimensionality. Always 2 for this class; use :class:AcousticVRZ3D for 3-D. Defaults to 2.